├── .gitignore ├── .travis.yml ├── LICENSE ├── README.md ├── geomle ├── __init__.py ├── data.py ├── geomle.py ├── mle.py └── utils.py ├── paper ├── FinalNtb.ipynb ├── PlotNtb.ipynb ├── img │ ├── DMcurve.png │ ├── Explain.png │ ├── Noise.png │ ├── Nsteps.png │ ├── Sphere.png │ └── intro.png └── result │ ├── exp_new.npy │ ├── result_dm.csv │ ├── result_dm_new.csv │ ├── result_dm_nonuniform.csv │ ├── result_noise_mpe.csv │ ├── result_noise_mpe_new.csv │ ├── result_noise_std.csv │ ├── result_noise_std_new.csv │ ├── result_num.csv │ ├── result_sphere.csv │ ├── result_time_dim.csv │ └── result_time_num.csv ├── requirements.txt ├── setup.py └── tests └── test_geomle.py /.gitignore: -------------------------------------------------------------------------------- 1 | *.pyc 2 | *.ipynb_checkpoints 3 | .DS_Store 4 | 5 | *.nt.bz2 6 | *.tar.gz 7 | *.tgz 8 | -------------------------------------------------------------------------------- /.travis.yml: -------------------------------------------------------------------------------- 1 | language: python 2 | python: 3 | - "3.6" 4 | sudo: false 5 | cache: 6 | pip: true 7 | before_install: 8 | - pip3 install -U pip 9 | install: 10 | - pip3 install -r requirements.txt 11 | - python3 setup.py install 12 | script: 13 | - python -m pytest 14 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2019 Mokrov Nikita, Marina Gomtsyan, Maxim Panov and Yury Yanovich 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # GeoMLE 2 | 3 | [![Build Status](https://travis-ci.com/premolab/GeoMLE.svg?branch=master)](https://travis-ci.com/premolab/GeoMLE) 4 | 5 | This repo contains code for our paper [Geometry-Aware Maximum Likelihood Estimation of Intrinsic Dimension](https://arxiv.org/abs/1904.06151) 6 | 7 | ## Abstract 8 | 9 | The existing approaches to intrinsic dimension estimation usually are not reliable when the data are nonlinearly embedded in the high dimensional space. In this work, we show that the explicit accounting to geometric properties of unknown support leads to the polynomial correction to the standard maximum likelihood estimate of intrinsic dimension for flat manifolds. The proposed algorithm (GeoMLE) realizes the correction by regression of standard MLEs based on distances to nearest neighbors for different sizes of neighborhoods. Moreover, the proposed approach also efficiently handles the case of nonuniform sampling of the manifold. We perform numerous experiments on different synthetic and real-world datasets. The results show that our algorithm achieves state-of-the-art performance, while also being computationally efficient and robust to noise in the data. 10 | 11 | ## Quick Start with library GeoMLE 12 | 13 | ### Data generation 14 | ```python 15 | from geomle import DataGenerator 16 | DG = DataGenerator() 17 | data = DG.gen_data('Sphere', 1000, 2, 1) 18 | ``` 19 | #### Algorithm Levina-Bickel (MLE) 20 | ```python 21 | from geomle import mle 22 | mle(data) 23 | ``` 24 | #### Algorithm GeoMLE 25 | ```python 26 | from geomle import geomle 27 | geomle(data) 28 | ``` 29 | 30 | ## Experiments 31 | 32 | All experiments you can find in [notebook](paper/FinalNtb.ipynb): 33 | 34 | - [x] Decribing algorithms 35 | - [x] Test with nonuniform distibution 36 | - [x] Dependence on manifold dimension 37 | - [x] Dependence on number of points 38 | - [x] Comparing algorithms with Dolan-More curves 39 | - [x] Dependence on noise 40 | - [ ] Dependence on neigbors (k1 and k2) 41 | 42 | 43 | ## Algorithms 44 | 45 | In this paper we compare our approch with many famous algorithms: 46 | * MLE 47 | * ESS 48 | * MIND 49 | * DANCo 50 | * Local PCA 51 | 52 | We use this [implementation](https://cran.r-project.org/web/packages/intrinsicDimension/index.html) in R. 53 | 54 | ## BibTex 55 | 56 | ``` 57 | @article{GeoMLE2019, 58 | title={Geometry-Aware Maximum Likelihood Estimation of Intrinsic Dimension}, 59 | author={Marina Gomtsyan and Nikita Mokrov and Maxim Panov and Yury Yanovich}, 60 | journal={arXiv preprint arXiv:1904.06151}, 61 | year={2019}, 62 | url = {https://arxiv.org/abs/1904.06151}, 63 | } 64 | ``` 65 | 66 | 67 | -------------------------------------------------------------------------------- /geomle/__init__.py: -------------------------------------------------------------------------------- 1 | from .data import DataGenerator 2 | from .mle import bootstrap_intrinsic_dim_scale_interval as mle 3 | from .geomle import geomle 4 | 5 | 6 | __all__ = ('DataGenerator', 7 | 'geomle', 8 | 'mle') -------------------------------------------------------------------------------- /geomle/data.py: -------------------------------------------------------------------------------- 1 | __all__ = ('DataGenerator') 2 | 3 | import pandas as pd 4 | import numpy as np 5 | from .utils import bound_nonuniform_sampler, uniform_sampler 6 | 7 | class DataGenerator(): 8 | 9 | def __init__(self, 10 | random_state: int = None, 11 | type_noise: str = 'norm'): 12 | 13 | self.set_rng(random_state) 14 | self.set_gen_noise(type_noise) 15 | self.dict_gen = { 16 | #syntetic data 17 | 'Helix1d': gen_helix1_data, 18 | 'Helix2d': gen_helix2_data, 19 | 'Helicoid': gen_helicoid_data, 20 | 'Spiral': gen_spiral_data, 21 | 'Roll': gen_roll_data, 22 | 'Scurve': gen_scurve_data, 23 | 'Star': gen_star_data, 24 | 'Moebius': gen_moebius_data, 25 | 26 | 'Sphere': gen_sphere_data, 27 | 'Norm': gen_norm_data, 28 | 'Uniform': gen_uniform_data, 29 | 'Cubic': gen_cubic_data, 30 | 31 | 'Affine_3to5': gen_affine3_5_data, 32 | 'Affine': gen_affine_data, 33 | 34 | 'Nonlinear_4to6': gen_nonlinear4_6_data, 35 | 'Nonlinear': gen_nonlinear_data, 36 | 'Paraboloid': gen_porabaloid_data, 37 | 38 | # #real data 39 | # 'Digits': get_digits, 40 | # 'Isomap': get_Isomap, 41 | # 'Hands': get_Hands, 42 | # 'ISOLET': get_ISOLET, 43 | # 'MNISTd': get_MNISTd 44 | } 45 | 46 | 47 | def set_rng(self, random_state:int=None): 48 | if random_state is not None: 49 | np.random.seed(random_state) 50 | 51 | def set_gen_noise(self, type_noise:str): 52 | if not hasattr(self, 'rng'): 53 | self.set_rng() 54 | if type_noise == 'norm': 55 | self.gen_noise = np.random.randn 56 | if type_noise == 'uniform': 57 | self.gen_noise = lambda n, dim: np.random.rand(n, dim) - 0.5 58 | 59 | def gen_data(self, name:str, n:int, dim:int, d:int, type_sample:str='uniform', noise:float=0.0): 60 | # Parameters: 61 | # -------------------- 62 | # name: string 63 | # Type of generetic data 64 | # n: int 65 | # The number of sample points 66 | # dim: int 67 | # The dimension of point 68 | # d: int 69 | # The hyperplane dimension 70 | # noise: float, optional(default=0.0) 71 | # The value of noise in data 72 | 73 | # Returns: 74 | # data: pd.Dataframe of shape (n, dim) 75 | # The points 76 | assert name in self.dict_gen.keys(),\ 77 | 'Name of data is unknown' 78 | if (type_sample == 'uniform'): 79 | if name == 'Sphere': 80 | sampler = np.random.randn 81 | else: 82 | sampler = np.random.rand 83 | elif (type_sample == 'nonuniform'): 84 | if name == 'Sphere': 85 | sampler = uniform_sampler 86 | else: 87 | sampler = bound_nonuniform_sampler 88 | else: 89 | assert False, 'Check type_sample' 90 | 91 | data = self.dict_gen[name](n=n, dim=dim, d=d, sampler=sampler) 92 | noise = self.gen_noise(n, dim) * noise 93 | 94 | return data + noise 95 | 96 | 97 | ############################################################################# 98 | # SYNTETIC DATA # 99 | ############################################################################# 100 | from sklearn import datasets as ds 101 | 102 | def gen_spiral_data(n, dim, d, sampler): 103 | assert d < dim 104 | assert d == 1 105 | assert dim >= 3 106 | t = 10 * np.pi * sampler(n) 107 | data = pd.DataFrame(np.vstack([100 * np.cos(t), 100 * np.sin(t), 108 | t, np.zeros((dim - 3, n))])).T 109 | assert data.shape == (n, dim) 110 | return data 111 | 112 | def gen_helix1_data(n, dim, d, sampler): 113 | assert d < dim 114 | assert d == 1 115 | assert dim >= 3 116 | t = 2 * np.pi / n + sampler(n) * 2 * np.pi 117 | data = pd.DataFrame(np.vstack([(2 + np.cos(8*t))*np.cos(t), 118 | (2 + np.cos(8*t))*np.sin(t), 119 | np.sin(8*t), np.zeros((dim - 3, n))])).T 120 | assert data.shape == (n, dim) 121 | return data 122 | 123 | def gen_helix2_data(n, dim, d, sampler): 124 | assert d < dim 125 | assert d == 2 126 | assert dim >= 3 127 | r = 10 * np.pi * sampler(n) 128 | p = 10 * np.pi * sampler(n) 129 | data = pd.DataFrame(np.vstack([r*np.cos(p), r*np.sin(p), 130 | 0.5*p, np.zeros((dim - 3, n))])).T 131 | assert data.shape == (n, dim) 132 | return data 133 | 134 | def gen_helicoid_data(n, dim, d, sampler): 135 | assert d <= dim 136 | assert d == 2 137 | assert dim >= 3 138 | u = 2 * np.pi / n + sampler(n) * 2 * np.pi 139 | v = 5 * np.pi * sampler(n) 140 | data = pd.DataFrame(np.vstack([np.cos(v), 141 | np.sin(v) * np.cos(v), 142 | u, 143 | np.zeros((dim - 3, n))])).T 144 | assert data.shape == (n, dim) 145 | return data 146 | 147 | def gen_roll_data(n, dim, d, sampler): 148 | assert d < dim 149 | assert dim >= 3 150 | assert d == 2 151 | t = 1.5 * np.pi * (1 + 2 * sampler(n)) 152 | p = 21 * sampler(n) 153 | 154 | data = pd.DataFrame(np.vstack([t * np.cos(t), 155 | p, 156 | t * np.sin(t), 157 | np.zeros((dim - d - 1, n))])).T 158 | assert data.shape == (n, dim) 159 | return data 160 | 161 | def gen_scurve_data(n, dim, d, sampler): 162 | assert d < dim 163 | assert dim >= 3 164 | assert d == 2 165 | t = 3 * np.pi * (sampler(n) - 0.5) 166 | p = 2.0 * sampler(n) 167 | 168 | data = pd.DataFrame(np.vstack([np.sin(t), 169 | p, 170 | np.sign(t) * (np.cos(t) - 1), 171 | np.zeros((dim - d - 1, n))])).T 172 | assert data.shape == (n, dim) 173 | return data 174 | 175 | 176 | def gen_sphere_data(n, dim, d, sampler): 177 | assert d < dim 178 | # V = np.random.randn(n, d + 1) 179 | V = sampler(n, d+1) 180 | data = pd.DataFrame(np.hstack([V/np.sqrt((V**2).sum(axis=1))[:,None], 181 | np.zeros((n, dim - d - 1))])) 182 | assert data.shape == (n, dim) 183 | return data 184 | 185 | def gen_norm_data(n, dim, d, sampler): 186 | assert d <= dim 187 | norm_xyz = np.random.multivariate_normal(np.zeros(d), np.identity(d), n) 188 | data = pd.DataFrame(np.hstack([norm_xyz, np.zeros((n, dim - d))])) 189 | assert data.shape == (n, dim) 190 | return data 191 | 192 | def gen_uniform_data(n, dim, d, sampler): 193 | assert d <= dim 194 | uniform_xyz = np.random.uniform(size=(n, d)) 195 | data = pd.DataFrame(np.hstack([uniform_xyz, np.zeros((n, dim - d))])) 196 | assert data.shape == (n, dim) 197 | return data 198 | 199 | def gen_cubic_data(n, dim, d, sampler): 200 | assert d < dim 201 | cubic_data = np.array([[]]*(d + 1)) 202 | for i in range(d + 1): 203 | n_once = int(n / (2 * (d + 1)) + 1) 204 | #1st side 205 | data_once = sampler(d + 1, n_once) 206 | data_once[i] = 0 207 | cubic_data = np.hstack([cubic_data, data_once]) 208 | #2nd side 209 | data_once = sampler(d + 1, n_once) 210 | data_once[i] = 1 211 | cubic_data = np.hstack([cubic_data, data_once]) 212 | cubic_data = cubic_data.T[:n] 213 | data = pd.DataFrame(np.hstack([cubic_data, np.zeros((n, dim - d - 1))])) 214 | assert data.shape == (n, dim) 215 | return data 216 | 217 | def gen_moebius_data(n, dim, d, sampler): 218 | assert dim == 3 219 | assert d == 2 220 | 221 | phi = sampler(n) * 2 * np.pi 222 | rad = sampler(n) * 2 - 1 223 | data = pd.DataFrame(np.vstack([(1+0.5*rad*np.cos(5.0*phi))*np.cos(phi), 224 | (1+0.5*rad*np.cos(5.0*phi))*np.sin(phi), 225 | 0.5*rad*np.sin(5.0*phi)])).T 226 | 227 | assert data.shape == (n, dim) 228 | return data 229 | 230 | def gen_affine_data(n, dim, d, sampler): 231 | assert dim >= d 232 | 233 | p = sampler(d, n) * 5 - 2.5 234 | v = np.eye(dim, d) 235 | # v = np.random.randint(0, 10, (dim, d)) 236 | data = pd.DataFrame(v.dot(p).T) 237 | 238 | assert data.shape == (n, dim) 239 | return data 240 | 241 | def gen_affine3_5_data(n, dim, d, sampler): 242 | assert dim == 5 243 | assert d == 3 244 | 245 | p = 4 * sampler(d, n) 246 | A = np.array([[ 1.2, -0.5, 0], 247 | [ 0.5, 0.9, 0], 248 | [-0.5, -0.2, 1], 249 | [ 0.4, -0.9, -0.1], 250 | [ 1.1, -0.3, 0]]) 251 | b = np.array([[3, -1, 0, 0, 8]]).T 252 | data = A.dot(p) + b 253 | data = pd.DataFrame(data.T) 254 | 255 | assert data.shape == (n, dim) 256 | return data 257 | 258 | def gen_nonlinear4_6_data(n, dim, d, sampler): 259 | assert dim == 6 260 | assert d == 4 261 | 262 | p0, p1, p2, p3 = sampler(d, n) 263 | data = pd.DataFrame(np.vstack([p1**2 * np.cos(2*np.pi*p0), 264 | p2**2 * np.sin(2*np.pi*p0), 265 | p1 + p2 + (p1-p3)**2, 266 | p1 - 2*p2 + (p0-p3)**2, 267 | -p1 - 2*p2 + (p2-p3)**2, 268 | p0**2 - p1**2 + p2**2 - p3**2])).T 269 | 270 | assert data.shape == (n, dim) 271 | return data 272 | 273 | def gen_nonlinear_data(n, dim, d, sampler): 274 | assert dim >= d 275 | m = int(dim / (2 * d)) 276 | assert dim == 2 * m * d 277 | 278 | p = sampler(d, n) 279 | F = np.zeros((2*d, n)) 280 | F[0::2, :] = np.cos(2*np.pi*p) 281 | F[1::2, :] = np.sin(2*np.pi*p) 282 | R = np.zeros((2*d, n)) 283 | R[0::2, :] = np.vstack([p[1:], p[0]]) 284 | R[1::2, :] = np.vstack([p[1:], p[0]]) 285 | D = (R * F).T 286 | data = pd.DataFrame(np.hstack([D] * m)) 287 | 288 | assert data.shape == (n, dim) 289 | return data 290 | 291 | def gen_porabaloid_data(n, dim, d, sampler): 292 | assert dim == 3 * (d + 1) 293 | 294 | E = np.random.exponential(1, (d+1, n)) 295 | X = ((1 + E[1:]/E[0])**-1).T 296 | X = np.hstack([X, (X ** 2).sum(axis=1)[:,np.newaxis]]) 297 | data = pd.DataFrame(np.hstack([X, np.sin(X), X**2])) 298 | 299 | assert data.shape == (n, dim) 300 | return data 301 | 302 | def gen_star_data(n, dim, d, sampler): 303 | assert dim >= d 304 | assert d == 1 305 | assert dim >= 2 306 | 307 | t = np.pi - sampler(n) * 2 * np.pi 308 | omega = 5 309 | X = np.concatenate((((1 + 0.3*np.cos(omega*t))*np.cos(t)).reshape(-1, 1), 310 | ((1 + 0.3*np.cos(omega*t))*np.sin(t)).reshape(-1, 1), 311 | np.zeros((n, dim - 2))), axis=1) 312 | 313 | data = pd.DataFrame(X) 314 | assert data.shape == (n, dim) 315 | return data 316 | 317 | ############################################################################# 318 | # REAL DATA # 319 | ############################################################################# 320 | # from scipy.io import loadmat 321 | # import zipfile 322 | # from PIL import Image 323 | # import io 324 | # from os.path import dirname, join 325 | 326 | # def get_digits(n=1797, dim=64, d=10): 327 | # assert (n, dim, d) == (1797, 64, 10) 328 | 329 | # data = ds.load_digits() 330 | # data = pd.DataFrame(data['data']) 331 | 332 | # assert data.shape == (n, dim) 333 | # return data 334 | 335 | 336 | # def get_Isomap(n=698, dim=4096, d=3): 337 | # assert (n, dim, d) == (698, 4096, 3) 338 | 339 | # module_path = dirname(__file__) 340 | # path = join(module_path, 'data', 'isomap', 'face_data.mat') 341 | # mat = loadmat(path) 342 | # data = pd.DataFrame(mat['images']).T 343 | 344 | # assert data.shape == (n, dim) 345 | # return data 346 | 347 | # def get_Hands(n=481, dim=245760, d=3): 348 | # assert (n, dim, d) == (481, 245760, 3) 349 | 350 | # module_path = dirname(__file__) 351 | # path = join(module_path, 'data', 'hands', 'hands.zip') 352 | # archive = zipfile.ZipFile(path, 'r') 353 | # data = [] 354 | # for file in archive.filelist: 355 | # data_tmp = archive.read(file) 356 | # img = Image.open(io.BytesIO(data_tmp)) 357 | # data.append(np.array(img).reshape(-1)) 358 | # data = pd.DataFrame(np.array(data)) 359 | 360 | # assert data.shape == (n, dim) 361 | # return data 362 | 363 | # def loadMNIST(prefix, folder ): 364 | # intType = np.dtype('int32' ).newbyteorder( '>' ) 365 | # nMetaDataBytes = 4 * intType.itemsize 366 | 367 | # data = np.fromfile(folder + "/" + prefix + '-images.idx3-ubyte', 368 | # dtype = 'ubyte' ) 369 | # magicBytes, nImages,\ 370 | # width, height = np.frombuffer(data[:nMetaDataBytes].tobytes(), intType) 371 | # data = data[nMetaDataBytes:].astype(dtype = 'float32') 372 | # data = data.reshape([nImages, width, height]) 373 | 374 | # labels = np.fromfile( folder + '/' + prefix + '-labels.idx1-ubyte', 375 | # dtype = 'ubyte' )[2 * intType.itemsize:] 376 | # return data, labels 377 | 378 | # def get_MNISTd(n=70000, dim=784, d = 0): 379 | # assert dim == 784 380 | # assert (n, d) == (6903, 0) or (n, d) == (7877, 1) or \ 381 | # (n, d) == (6990, 2) or (n, d) == (7141, 3) or \ 382 | # (n, d) == (6824, 4) or (n, d) == (6313, 5) or \ 383 | # (n, d) == (6876, 6) or (n, d) == (7293, 7) or \ 384 | # (n, d) == (6825, 8) or (n, d) == (6958, 9) or \ 385 | # (n, d) == (70000, 10) 386 | # assert (d >= 0) and (d <= 10) 387 | 388 | # module_path = dirname(__file__) 389 | # path = join(module_path, 'data', 'mnist') 390 | # trainingImages, trainingLabels = loadMNIST('train', path) 391 | # testImages, testLabels = loadMNIST('t10k', path) 392 | # data = np.vstack([trainingImages, testImages]).reshape(70000, -1) 393 | # data = pd.DataFrame(data) 394 | # label = np.concatenate([trainingLabels, testLabels]) 395 | # if d != 10: 396 | # mask = label == d 397 | # data = data.loc[mask] 398 | 399 | # assert data.shape[1] == dim 400 | # return data 401 | 402 | # def get_ISOLET(n=7797, dim=617, d=19): 403 | # assert (n, dim) == (7797, 617) 404 | # assert (d >= 16) and (d <= 22) 405 | 406 | # module_path = dirname(__file__) 407 | # path = join(module_path, 'data', 'isolet', 'isolet_csv') 408 | # df = pd.read_csv(path) 409 | # data = df[[col for col in df.columns if 'f' in col]] 410 | 411 | # assert data.shape == (n, dim) 412 | # return data -------------------------------------------------------------------------------- /geomle/geomle.py: -------------------------------------------------------------------------------- 1 | __all__ = ('geomle') 2 | 3 | import pandas as pd 4 | import numpy as np 5 | from sklearn.neighbors import NearestNeighbors 6 | from sklearn.linear_model import LinearRegression, Ridge 7 | from functools import partial 8 | 9 | def tolist(x): 10 | if type(x) in {int, float}: 11 | return [x] 12 | if type(x) in {list, tuple}: 13 | return list(x) 14 | if type(x) == np.ndarray: 15 | return x.tolist() 16 | 17 | def drop_zero_values(dist): 18 | mask = dist[:,0] == 0 19 | dist[mask] = np.hstack([dist[mask][:, 1:], dist[mask][:,0:1]]) 20 | dist = dist[:, :-1] 21 | assert np.all(dist > 0) 22 | return dist 23 | 24 | def mle_center(X, X_center, k=5, dist=None): 25 | """ 26 | Returns Levina-Bickel dimensionality estimation 27 | 28 | Input parameters: 29 | X - data points 30 | X_center - data centers 31 | k - number of nearest neighbours (Default = 5) 32 | dist - matrix of distances to the k nearest neighbors of each point (Optional) 33 | 34 | Returns: 35 | dimensionality estimation for the k 36 | """ 37 | if len(X_center.shape) != 2: 38 | X_center = X_center.values.reshape(1, -1) 39 | if dist is None: 40 | neighb = NearestNeighbors(n_neighbors=k+1, n_jobs=1, 41 | algorithm='ball_tree').fit(X) 42 | dist, ind = neighb.kneighbors(X_center) 43 | dist = drop_zero_values(dist) 44 | dist = dist[:, 0:k] 45 | assert dist.shape == (X_center.shape[0], k) 46 | assert np.all(dist > 0) 47 | d = np.log(dist[:, k - 1: k] / dist[:, 0:k - 1]) 48 | d = d.sum(axis=1) / (k - 2) 49 | d = 1. / d 50 | intdim_sample = d 51 | Rs = dist[:, -1] 52 | return intdim_sample, Rs 53 | 54 | def fit_poly_reg(x, y, w=None, degree=(1, 2), alpha=5e-3): 55 | """ 56 | Fit regression and return f(0) 57 | 58 | Input parameters: 59 | x - features (1d-array) 60 | y - targets (1d-array) 61 | w - weights for each points (Optional) 62 | degree - degrees of polinoms (Default tuple(1, 2)) 63 | alpha - parameter of regularization (Default 5e-3) 64 | 65 | Returns: 66 | zero coefficiend of regression 67 | """ 68 | X = np.array([x ** i for i in tolist(degree)]).T 69 | lm = Ridge(alpha=alpha) 70 | lm.fit(X, y, w) 71 | return lm.intercept_ 72 | 73 | def _func(df, degree, alpha): 74 | gr_df = df.groupby('k') 75 | R = gr_df['R'].mean().values 76 | d = gr_df['dim'].mean().values 77 | std = gr_df['dim'].std().values 78 | if np.isnan(std).any(): std = np.ones_like(std) 79 | return fit_poly_reg(R, d, std**-1, degree=degree, alpha=alpha) 80 | 81 | def geomle(X, k1=10, k2=40, nb_iter1=10, nb_iter2=20, degree=(1, 2), 82 | alpha=5e-3, ver='GeoMLE', random_state=None, debug=False): 83 | """ 84 | Returns range of Levina-Bickel dimensionality estimation for k = k1..k2 (k1 < k2) averaged over bootstrap samples 85 | 86 | Input parameters: 87 | X - data 88 | k1 - minimal number of nearest neighbours (Default = 10) 89 | k2 - maximal number of nearest neighbours (Default = 40) 90 | nb_iter1 - number of bootstrap iterations (Default = 10) 91 | nb_iter1 - number of bootstrap iterations for each regresion (Default = 20) 92 | degree - (Default = (1, 2)) 93 | alpha - (Default = 5e-3) 94 | random_state - random state (Optional) 95 | 96 | Returns: 97 | array of shape (nb_iter1,) of regression dimensionality estimation for k = k1..k2 averaged over bootstrap samples 98 | """ 99 | if random_state is None: 100 | rng = np.random 101 | else: 102 | rng = np.random.RandomState(random_state) 103 | nb_examples = X.shape[0] 104 | dim_space = X.shape[1] 105 | 106 | result = [] 107 | data_reg = [] 108 | for i in range(nb_iter1): 109 | dim_all, R_all, k_all, idx_all = [], [], [], [] 110 | for j in range(nb_iter2): 111 | idx = np.unique(rng.randint(0, nb_examples - 1, size=nb_examples)) 112 | X_bootstrap = X.iloc[idx] 113 | neighb = NearestNeighbors(n_neighbors=k2+1, n_jobs=1, 114 | algorithm='ball_tree').fit(X_bootstrap) 115 | dist, ind = neighb.kneighbors(X) 116 | dist = drop_zero_values(dist) 117 | dist = dist[:, 0:k2] 118 | assert np.all(dist > 0) 119 | 120 | for k in range(k1, k2+1): 121 | dim, R = mle_center(X_bootstrap, X, k, dist) 122 | dim_all += dim.tolist() 123 | R_all += R.tolist() 124 | idx_all += list(range(nb_examples)) 125 | k_all += [k] * dim.shape[0] 126 | 127 | data={'dim': dim_all, 128 | 'R': R_all, 129 | 'idx': idx_all, 130 | 'k': k_all} 131 | 132 | df = pd.DataFrame(data) 133 | if ver == 'GeoMLE': 134 | func = partial(_func, degree=degree, alpha=alpha) 135 | reg = df.groupby('idx').apply(func).values.mean() 136 | data_reg.append(df) 137 | elif ver == 'fastGeoMLE': 138 | df_gr = df.groupby(['idx', 'k']).mean()[['R', 'dim']] 139 | R = df_gr.groupby('k').R.mean() 140 | d = df_gr.groupby('k').dim.mean() 141 | std = df_gr.groupby('k').dim.std() 142 | reg = fit_poly_reg(R, d, std**-1, degree=degree, alpha=alpha) 143 | data_reg.append((R, d, std)) 144 | else: 145 | assert False, 'Unknown mode {}'.format(ver) 146 | reg = 0 if reg < 0 else reg 147 | reg = dim_space if reg > dim_space else reg 148 | result.append(reg) 149 | if debug: 150 | return np.array(result), data_reg 151 | else: 152 | return np.array(result) -------------------------------------------------------------------------------- /geomle/mle.py: -------------------------------------------------------------------------------- 1 | __all__ = ('bootstrap_intrinsic_dim_scale_interval') 2 | 3 | import pandas as pd 4 | import numpy as np 5 | from sklearn.neighbors import NearestNeighbors 6 | 7 | 8 | def intrinsic_dim_sample_wise(X, k=5, dist = None): 9 | """ 10 | Returns Levina-Bickel dimensionality estimation 11 | 12 | Input parameters: 13 | X - data 14 | k - number of nearest neighbours (Default = 5) 15 | dist - matrix of distances to the k nearest neighbors of each point (Optional) 16 | 17 | Returns: 18 | dimensionality estimation for the k 19 | """ 20 | if dist is None: 21 | neighb = NearestNeighbors(n_neighbors=k+1, n_jobs=1, algorithm='ball_tree').fit(X) 22 | dist, ind = neighb.kneighbors(X) 23 | dist = dist[:, 1:(k+1)] 24 | assert dist.shape == (X.shape[0], k) 25 | assert np.all(dist > 0) 26 | d = np.log(dist[:, k - 1: k] / dist[:, 0:k - 1]) 27 | d = d.sum(axis=1) / (k - 2) 28 | d = 1. / d 29 | intdim_sample = d 30 | return intdim_sample 31 | 32 | 33 | def intrinsic_dim_scale_interval(X, k1=10, k2=20, dist = None): 34 | """ 35 | Returns range of Levina-Bickel dimensionality estimation for k = k1..k2, k1 < k2 36 | 37 | Input parameters: 38 | X - data 39 | k1 - minimal number of nearest neighbours (Default = 10) 40 | k2 - maximal number of nearest neighbours (Default = 20) 41 | dist - matrix of distances to the k nearest neighbors of each point (Optional) 42 | 43 | Returns: 44 | list of Levina-Bickel dimensionality estimation for k = k1..k2 45 | """ 46 | intdim_k = [] 47 | if dist is None: 48 | neighb = NearestNeighbors(n_neighbors=k2+1, n_jobs=1, algorithm='ball_tree').fit(X) 49 | dist, ind = neighb.kneighbors(X) 50 | 51 | for k in range(k1, k2 + 1): 52 | m = intrinsic_dim_sample_wise(X, k,dist).mean() 53 | intdim_k.append(m) 54 | return intdim_k 55 | 56 | 57 | def bootstrap_intrinsic_dim_scale_interval(X, nb_iter=100, random_state=None, 58 | k1 = 10, k2 = 20, average = False): 59 | """ 60 | Returns range of Levina-Bickel dimensionality estimation for k = k1..k2 (k1 < k2) averaged over bootstrap samples 61 | 62 | Input parameters: 63 | X - data 64 | nb_iter - number of bootstrap iterations (Default = 100) 65 | random_state - random state (Optional) 66 | k1 - minimal number of nearest neighbours (Default = 10) 67 | k2 - maximal number of nearest neighbours (Default = 20) 68 | average - if False returns array of shape (nb_iter, k2-k1+1) of the estimations for each bootstrap samples (Default = True) 69 | 70 | Returns: 71 | array of shape (k2-k1+1,) of Levina-Bickel dimensionality estimation for k = k1..k2 averaged over bootstrap samples 72 | """ 73 | if random_state is None: 74 | rng = np.random 75 | else: 76 | rng = np.random.RandomState(random_state) 77 | 78 | nb_examples = X.shape[0] 79 | results = [] 80 | 81 | neighb = NearestNeighbors(n_neighbors=k2+1, n_jobs=1, algorithm='ball_tree').fit(X) 82 | dist, ind = neighb.kneighbors(X) 83 | 84 | Rs = [] 85 | for i in range(k1, k2 + 1): 86 | Rs.append(np.max(dist[:,:i])) 87 | 88 | for i in range(nb_iter): 89 | idx = np.unique(rng.randint(0, nb_examples - 1, size=nb_examples)) 90 | results.append(intrinsic_dim_scale_interval(X.iloc[idx], k1, k2, dist[idx,:])) 91 | results = np.array(results) 92 | 93 | if average: 94 | return results.mean(axis = 0),Rs 95 | else: 96 | return results,Rs -------------------------------------------------------------------------------- /geomle/utils.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | def bound_nonuniform_sampler(*args): 4 | x = np.random.randn(*args)*0.1 + 0.5 5 | x[x < 0] = -x[x < 0] 6 | x[x > 1] = x[x > 1] - 1 7 | x[x < 0] = -x[x < 0] 8 | return x 9 | 10 | def uniform_sampler(*args): 11 | x = np.random.rand(*args) 12 | x = (x - 0.5) * 3 13 | return x -------------------------------------------------------------------------------- /paper/img/DMcurve.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/stat-ml/GeoMLE/89a33a4eba3f38151f2f2d159b5410b8b2a84291/paper/img/DMcurve.png -------------------------------------------------------------------------------- /paper/img/Explain.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/stat-ml/GeoMLE/89a33a4eba3f38151f2f2d159b5410b8b2a84291/paper/img/Explain.png -------------------------------------------------------------------------------- /paper/img/Noise.png: -------------------------------------------------------------------------------- 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-------------------------------------------------------------------------------- /paper/result/exp_new.npy: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/stat-ml/GeoMLE/89a33a4eba3f38151f2f2d159b5410b8b2a84291/paper/result/exp_new.npy -------------------------------------------------------------------------------- /paper/result/result_dm.csv: -------------------------------------------------------------------------------- 1 | Dataset,MLE,GeoMLE,MIND,DANCo,ESS,PCA,CD,Hein,Num,Dim,RealDim 2 | 0,Sphere,3.013639805902005,3.0872891995322336,3.0,3.0,4.037315745156063,4.0,2.92505145072937,3.0,1000.0,5.0,3.0 3 | 1,Sphere,4.798884305725155,4.950614080213732,5.0,6.0,5.97784948980338,6.0,5.630488395690918,5.0,1000.0,10.0,5.0 4 | 2,Sphere,8.610642930844762,9.324459598106682,9.0,11.0,10.795737170293588,11.0,8.308697700500488,9.0,1000.0,15.0,10.0 5 | 3,Sphere,20.198529320612387,34.04020682813073,21.0,30.0,30.9234855747506,31.0,21.299259185791016,22.0,1000.0,35.0,30.0 6 | 4,Sphere,28.658537448915027,50.623368654255856,30.0,51.0,50.43720435605278,51.0,31.880531311035156,34.0,1000.0,55.0,50.0 7 | 5,Sphere,34.841300573845956,68.18273894194905,36.0,69.0,72.01602783824057,71.0,35.189571380615234,39.0,1000.0,75.0,70.0 8 | 6,Affine_3to5,2.7980654799318505,3.181926632616655,3.0,3.0,2.54301895902168,3.0,2.7138655185699463,3.0,1000.0,5.0,3.0 9 | 7,Affine,4.463963134708803,5.0,5.0,5.0,4.921666731139256,5.0,4.666239261627197,5.0,1000.0,5.0,5.0 10 | 8,Affine,8.12700678491592,10.0,8.0,9.0,9.911889004953855,10.0,8.113433837890625,8.0,1000.0,10.0,10.0 11 | 9,Affine,14.27138227414389,20.0,15.0,18.0,20.281979711148974,20.0,15.054671287536621,15.0,1000.0,20.0,20.0 12 | 10,Nonlinear_4to6,3.7944115427267047,4.198989757968069,4.0,5.0,3.3082804891773683,5.0,3.6734211444854736,4.0,1000.0,6.0,4.0 13 | 11,Nonlinear,4.05386262788275,3.4636997412110526,4.0,6.0,8.018278649251817,8.0,3.6288111209869385,4.0,1000.0,8.0,4.0 14 | 12,Nonlinear,6.711436032805054,7.0720318791672785,6.0,8.0,12.547815431288079,12.0,5.789442539215088,6.0,1000.0,36.0,6.0 15 | 13,Nonlinear,9.145189704827413,10.340591114902095,9.0,11.0,16.365773423922104,16.0,8.070981979370117,8.0,1000.0,64.0,8.0 16 | 14,Nonlinear,13.506403922568298,18.412690762226042,14.0,17.0,23.83408139036901,24.0,12.17765998840332,12.0,1000.0,72.0,12.0 17 | 15,Spiral,1.7715508497008194,1.5552449010474183,1.0,1.0,2.042579379624682,2.0,0.9274370670318604,1.0,1000.0,3.0,1.0 18 | 16,Spiral,1.710779222805897,1.3421220381637444,1.0,1.0,2.1027987634870104,2.0,0.8964508771896362,1.0,1000.0,13.0,1.0 19 | 17,Helix1d,0.9941473553069083,1.3861400946104314,1.0,1.0,2.648766670656972,3.0,0.9954587817192078,1.0,1000.0,3.0,1.0 20 | 18,Helix1d,0.9947665488431785,1.5665896495951106,1.0,1.0,2.630289709804285,3.0,1.051041841506958,1.0,1000.0,13.0,1.0 21 | 19,Helix2d,2.7558746187914567,3.0,3.0,3.0,2.559657452718259,3.0,2.162299633026123,2.0,1000.0,3.0,2.0 22 | 20,Helix2d,2.7431503234030905,2.902706909846829,3.0,3.0,2.572372697910991,3.0,2.1140449047088623,2.0,1000.0,13.0,2.0 23 | 21,Helicoid,2.1000711011649607,2.2891355411467567,2.0,2.0,1.8329164995028058,2.0,2.0599253177642822,2.0,1000.0,3.0,2.0 24 | 22,Helicoid,2.1012513058213114,2.2812965954166087,2.0,2.0,1.8267713384852804,2.0,1.9408973455429077,2.0,1000.0,13.0,2.0 25 | 23,Roll,1.932368123497151,2.3983728600365866,2.0,2.0,3.0015373918717216,3.0,1.8924803733825684,2.0,1000.0,3.0,2.0 26 | 24,Roll,1.9576929984942129,1.860676082614512,2.0,2.0,2.9753754261359546,3.0,2.072950839996338,2.0,1000.0,13.0,2.0 27 | 25,Scurve,1.9486051182140114,2.031757764938854,2.0,2.0,2.2820493068803254,3.0,1.765306830406189,2.0,1000.0,3.0,2.0 28 | 26,Scurve,1.9530362327405721,2.018642545966527,2.0,2.0,2.2363161247931327,3.0,2.0474600791931152,2.0,1000.0,13.0,2.0 29 | 27,Moebius,2.0116404712640925,1.3789687877737737,2.0,2.0,2.331367192622567,3.0,1.9713983535766602,2.0,1000.0,3.0,2.0 30 | 28,Uniform,4.425113757656701,4.653739856799858,5.0,5.0,4.985426197712547,5.0,4.716457843780518,5.0,1000.0,10.0,5.0 31 | 29,Uniform,7.8394196259954745,8.812669319786622,8.0,9.0,9.916299657041092,10.0,8.331207275390625,8.0,1000.0,15.0,10.0 32 | 30,Uniform,19.285677252534878,29.22445263439756,20.0,31.0,28.734820226894435,30.0,19.157045364379883,21.0,1000.0,35.0,30.0 33 | 31,Uniform,27.30504655192372,53.10559639637909,29.0,53.0,50.031131796318824,50.0,29.575124740600586,30.0,1000.0,55.0,50.0 34 | 32,Uniform,33.841061418647875,72.23348071242219,36.0,74.0,70.26436167307828,70.0,35.24174118041992,38.0,1000.0,75.0,70.0 35 | 33,Norm,15.390935913397332,20.0,16.0,20.0,19.909859193811112,20.0,13.71936321258545,15.0,1000.0,20.0,20.0 36 | 34,Norm,14.966046830353744,22.012000809576588,16.0,22.0,20.653945893138115,20.0,13.839305877685547,14.0,1000.0,50.0,20.0 37 | 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43,Cubic,19.908016186600587,29.42485236518437,21.0,31.0,30.478905768728588,31.0,21.230995178222656,22.0,1000.0,35.0,30.0 46 | 44,Cubic,34.54935942827334,72.83071000951182,37.0,77.0,70.84770612150623,71.0,34.558326721191406,40.0,1000.0,90.0,70.0 47 | 45,Sphere,2.9522648864561223,3.096606930683456,3.0,3.0,3.9981427144538135,4.0,2.9894187450408936,3.0,1000.0,5.0,3.0 48 | 46,Sphere,4.8746760496089,5.013797393154184,5.0,6.0,6.09481743913683,6.0,5.068347930908203,5.0,1000.0,10.0,5.0 49 | 47,Sphere,8.899076232413183,10.129521098613708,9.0,11.0,11.359643279655751,11.0,9.869621276855469,9.0,1000.0,15.0,10.0 50 | 48,Sphere,20.54810261028947,33.409405021310384,21.0,31.0,32.0031958951427,31.0,21.566781997680664,23.0,1000.0,35.0,30.0 51 | 49,Sphere,28.807122302377515,52.30801648584353,30.0,51.0,49.39792097230206,51.0,30.56488037109375,34.0,1000.0,55.0,50.0 52 | 50,Sphere,36.31329431379599,74.28162211586721,39.0,71.0,70.41395598653642,71.0,40.311744689941406,43.0,1000.0,75.0,70.0 53 | 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59,Nonlinear,13.088595883344789,17.07905659874509,13.0,17.0,23.433130009031316,24.0,12.219205856323242,12.0,1000.0,72.0,12.0 62 | 60,Spiral,1.7481298380273977,1.4778982984024633,1.0,1.0,2.1384607066367223,2.0,0.9554272890090942,1.0,1000.0,3.0,1.0 63 | 61,Spiral,1.7854906450912977,1.5750736396290563,1.0,1.0,2.1442310760055037,2.0,1.0266008377075195,1.0,1000.0,13.0,1.0 64 | 62,Helix1d,1.0010159105499221,1.3300195746299046,1.0,1.0,2.6414769713935415,3.0,1.026666283607483,1.0,1000.0,3.0,1.0 65 | 63,Helix1d,1.007332735620202,1.196929505608282,1.0,1.0,2.621709546628683,3.0,1.011697769165039,1.0,1000.0,13.0,1.0 66 | 64,Helix2d,2.7025169716193713,2.7771255437097175,3.0,3.0,2.530847000314963,3.0,1.9085829257965088,2.0,1000.0,3.0,2.0 67 | 65,Helix2d,2.7318512100083407,2.780501341843377,3.0,3.0,2.5320671470933562,3.0,2.0532877445220947,2.0,1000.0,13.0,2.0 68 | 66,Helicoid,2.078421188603639,2.216541047479983,2.0,2.0,1.8340177819140386,2.0,1.8319284915924072,2.0,1000.0,3.0,2.0 69 | 67,Helicoid,2.0467767275745192,2.2426624331436478,2.0,2.0,1.8599055761381202,2.0,1.8875043392181396,2.0,1000.0,13.0,2.0 70 | 68,Roll,1.973159129140423,1.7412284801956273,2.0,2.0,2.938748802951675,3.0,2.065098762512207,2.0,1000.0,3.0,2.0 71 | 69,Roll,1.9414079183509996,2.5150223429396554,2.0,2.0,2.9718560480630924,3.0,2.016658067703247,2.0,1000.0,13.0,2.0 72 | 70,Scurve,1.9459099507464548,2.106402850233869,2.0,2.0,2.218990205094702,3.0,2.030182123184204,2.0,1000.0,3.0,2.0 73 | 71,Scurve,1.9524456007360185,2.056570822778798,2.0,2.0,2.213367593885595,3.0,1.991113305091858,2.0,1000.0,13.0,2.0 74 | 72,Moebius,1.9875930638064931,1.3098487449256353,2.0,2.0,2.3583594073429386,3.0,2.0103158950805664,2.0,1000.0,3.0,2.0 75 | 73,Uniform,4.527826679171679,4.789411056304844,5.0,5.0,4.980779841339419,5.0,4.158812999725342,5.0,1000.0,10.0,5.0 76 | 74,Uniform,8.195791821644347,9.309931230277911,8.0,10.0,9.93955848993167,10.0,8.041481971740723,8.0,1000.0,15.0,10.0 77 | 75,Uniform,18.954180388520953,29.997356693869637,20.0,30.0,30.667173078203422,30.0,19.872455596923828,20.0,1000.0,35.0,30.0 78 | 76,Uniform,26.762657301629325,51.148677462288376,28.0,49.0,49.3619173369503,50.0,27.05409812927246,28.0,1000.0,55.0,50.0 79 | 77,Uniform,33.495498763457846,74.59764364936582,36.0,71.0,72.09050780823257,70.0,34.00596618652344,38.0,1000.0,75.0,70.0 80 | 78,Norm,14.667364180280094,20.0,15.0,20.0,19.77541478058328,20.0,13.223991394042969,14.0,1000.0,20.0,20.0 81 | 79,Norm,14.863041833500422,21.417456135209047,15.0,21.0,19.801652025845165,20.0,13.6536226272583,15.0,1000.0,50.0,20.0 82 | 80,Norm,26.796612663015487,50.0,29.0,46.0,49.84256479457465,50.0,23.857173919677734,26.0,1000.0,50.0,50.0 83 | 81,Norm,26.684644339803935,52.75160812175674,28.0,53.0,49.883694094944445,50.0,23.993066787719727,26.0,1000.0,70.0,50.0 84 | 82,Paraboloid,2.8338838349670903,3.0219355229732257,3.0,3.0,1.7848358313182793,1.0,2.232085943222046,2.0,1000.0,12.0,3.0 85 | 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91,Sphere,4.831250627564783,5.044631784191744,5.0,6.0,5.880641075326415,6.0,5.186689853668213,5.0,1000.0,10.0,5.0 94 | 92,Sphere,8.823380490090706,9.801441672025437,9.0,11.0,10.767756286830473,11.0,8.951297760009766,9.0,1000.0,15.0,10.0 95 | 93,Sphere,19.983928188570946,32.801270530143796,20.0,30.0,31.03625015263665,31.0,22.377958297729492,22.0,1000.0,35.0,30.0 96 | 94,Sphere,28.638620231344706,53.24766756554437,30.0,50.0,50.519634192202695,51.0,33.64901351928711,36.0,1000.0,55.0,50.0 97 | 95,Sphere,35.971669436924735,72.55531554492875,37.0,69.0,69.86583675884032,71.0,39.42461395263672,38.0,1000.0,75.0,70.0 98 | 96,Affine_3to5,2.7794450696516493,3.1836689950752524,3.0,3.0,2.5562341266956246,3.0,2.8445961475372314,3.0,1000.0,5.0,3.0 99 | 97,Affine,4.485743786092258,5.0,5.0,5.0,5.057164071137071,5.0,4.73973274230957,5.0,1000.0,5.0,5.0 100 | 98,Affine,8.075309589503775,10.0,8.0,10.0,10.025591032036528,10.0,8.9437894821167,9.0,1000.0,10.0,10.0 101 | 99,Affine,13.902430492797897,19.636499926719946,14.0,20.0,19.96542352313522,20.0,14.53799819946289,15.0,1000.0,20.0,20.0 102 | 100,Nonlinear_4to6,3.9042197593056334,4.086616486042657,4.0,5.0,3.2665540139956115,5.0,3.8747711181640625,4.0,1000.0,6.0,4.0 103 | 101,Nonlinear,4.061146853041331,3.259185149044849,4.0,5.0,7.857673766597053,8.0,3.527425765991211,4.0,1000.0,8.0,4.0 104 | 102,Nonlinear,6.781356722347542,6.848824724814482,6.0,8.0,12.138469954123508,12.0,5.6894426345825195,6.0,1000.0,36.0,6.0 105 | 103,Nonlinear,9.18175454523263,10.703640602222968,9.0,10.0,16.087014023518115,16.0,7.704755783081055,8.0,1000.0,64.0,8.0 106 | 104,Nonlinear,13.633954485109793,18.193521586252356,14.0,19.0,23.012957181424028,24.0,11.956697463989258,12.0,1000.0,72.0,12.0 107 | 105,Spiral,1.7403040881512473,1.4296000513257385,1.0,1.0,2.122608717215115,2.0,0.9301571846008301,1.0,1000.0,3.0,1.0 108 | 106,Spiral,1.8270019123595815,1.6247227365750894,1.0,1.0,2.113141319397089,2.0,1.0121439695358276,1.0,1000.0,13.0,1.0 109 | 107,Helix1d,1.0000849408017138,1.5771212429063066,1.0,1.0,2.583455965200609,3.0,0.9972369074821472,1.0,1000.0,3.0,1.0 110 | 108,Helix1d,0.9931593088315616,1.766534348596059,1.0,1.0,2.634214272965846,3.0,0.9357542395591736,1.0,1000.0,13.0,1.0 111 | 109,Helix2d,2.7651135783505967,2.711082919576856,3.0,3.0,2.517340923243667,3.0,2.0988850593566895,2.0,1000.0,3.0,2.0 112 | 110,Helix2d,2.7031312988657925,2.9759263998324808,3.0,3.0,2.533808477714328,3.0,1.9928441047668457,2.0,1000.0,13.0,2.0 113 | 111,Helicoid,2.085912952166753,2.312057753415371,2.0,2.0,1.8488505387778065,2.0,2.1499624252319336,2.0,1000.0,3.0,2.0 114 | 112,Helicoid,2.0760401707809906,2.202442883974813,2.0,2.0,1.8338139365900603,2.0,2.093752145767212,2.0,1000.0,13.0,2.0 115 | 113,Roll,1.9551072244028143,2.476449517112481,2.0,2.0,2.9376540267120075,3.0,1.9272212982177734,2.0,1000.0,3.0,2.0 116 | 114,Roll,1.9604346040041416,2.5127423742479422,2.0,2.0,2.9440017420186644,3.0,2.1722218990325928,2.0,1000.0,13.0,2.0 117 | 115,Scurve,1.9479237527203446,2.0514704148332394,2.0,2.0,2.1139011094591593,3.0,1.9736346006393433,2.0,1000.0,3.0,2.0 118 | 116,Scurve,1.9706257856394618,2.110554840912419,2.0,2.0,2.250629662550225,3.0,2.1339118480682373,2.0,1000.0,13.0,2.0 119 | 117,Moebius,2.0040797742776357,1.3123168262043456,2.0,2.0,2.285723536645892,3.0,2.140563488006592,2.0,1000.0,3.0,2.0 120 | 118,Uniform,4.461541105596604,4.715238662528844,5.0,5.0,4.916198667975847,5.0,4.867668151855469,5.0,1000.0,10.0,5.0 121 | 119,Uniform,8.065552106792035,9.117672149156187,8.0,10.0,9.822237495153612,10.0,8.407047271728516,9.0,1000.0,15.0,10.0 122 | 120,Uniform,18.840291616204713,29.485725297542302,19.0,28.0,30.61882615307249,30.0,19.98401641845703,20.0,1000.0,35.0,30.0 123 | 121,Uniform,27.180633514920434,52.25189371564215,29.0,52.0,49.85364851707956,50.0,27.9208984375,28.0,1000.0,55.0,50.0 124 | 122,Uniform,33.79753563251835,70.780509931031,35.0,71.0,68.67705252560631,70.0,34.55263900756836,36.0,1000.0,75.0,70.0 125 | 123,Norm,15.131727732944986,20.0,16.0,20.0,20.436027600528536,20.0,13.703354835510254,15.0,1000.0,20.0,20.0 126 | 124,Norm,14.788168889997909,22.342612182575728,16.0,22.0,20.162150175435734,20.0,14.090476036071777,15.0,1000.0,50.0,20.0 127 | 125,Norm,27.019148056443157,50.0,29.0,50.0,50.23692614830088,50.0,25.166061401367188,28.0,1000.0,50.0,50.0 128 | 126,Norm,27.282577192599252,54.3603954622098,28.0,52.0,48.88976823707594,50.0,24.09482765197754,26.0,1000.0,70.0,50.0 129 | 127,Paraboloid,2.8713030165180955,2.9830892472803607,3.0,3.0,1.780537237612429,1.0,2.026898145675659,2.0,1000.0,12.0,3.0 130 | 128,Paraboloid,4.729397543245664,5.92798845719613,5.0,7.0,1.4848857233654398,1.0,2.6248891353607178,3.0,1000.0,21.0,6.0 131 | 129,Paraboloid,5.881872741555061,9.368934588634769,6.0,8.0,1.2896694506079518,1.0,2.4973058700561523,3.0,1000.0,30.0,9.0 132 | 130,Paraboloid,6.590464899017544,11.828309921094922,7.0,9.0,1.2266068750297314,1.0,3.181636095046997,3.0,1000.0,39.0,12.0 133 | 131,Paraboloid,7.0766365135992055,14.890147966853913,7.0,8.0,1.1722006011360202,1.0,3.173250913619995,3.0,1000.0,48.0,15.0 134 | 132,Cubic,3.0203920698857334,3.084733875445654,3.0,3.0,4.0211005962790605,4.0,3.1822566986083984,3.0,1000.0,5.0,3.0 135 | 133,Cubic,19.174527542532264,30.136857429415542,20.0,29.0,31.001032132683214,31.0,20.34286880493164,21.0,1000.0,35.0,30.0 136 | 134,Cubic,33.937469564653796,71.89348008705865,35.0,70.0,73.46592573304801,71.0,32.33803176879883,35.0,1000.0,90.0,70.0 137 | 135,Sphere,2.9939989192559344,3.0067562055754204,3.0,3.0,4.004686683804575,4.0,2.9640066623687744,3.0,1000.0,5.0,3.0 138 | 136,Sphere,4.88787946848122,5.2027267928783205,5.0,6.0,6.108608869340807,6.0,4.6460280418396,5.0,1000.0,10.0,5.0 139 | 137,Sphere,8.922746225442665,10.020898603273501,9.0,11.0,10.738554078875923,11.0,8.73572063446045,9.0,1000.0,15.0,10.0 140 | 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170,Norm,27.5187093220473,50.0,29.0,48.0,49.354866159077986,50.0,24.26542854309082,26.0,1000.0,50.0,50.0 173 | 171,Norm,26.98287076472362,52.84766906452211,28.0,52.0,49.66183768610603,50.0,24.179195404052734,25.0,1000.0,70.0,50.0 174 | 172,Paraboloid,2.8565683406155653,3.1295172624148297,3.0,3.0,1.7913686573833778,1.0,2.2696664333343506,2.0,1000.0,12.0,3.0 175 | 173,Paraboloid,4.665089087104527,5.963093180780689,5.0,6.0,1.4793786554373378,1.0,2.6136739253997803,3.0,1000.0,21.0,6.0 176 | 174,Paraboloid,5.967877325035629,9.458665556860767,6.0,8.0,1.3099210703809412,1.0,3.138228416442871,3.0,1000.0,30.0,9.0 177 | 175,Paraboloid,6.662299924527101,12.50443734025969,7.0,8.0,1.2213818343212217,1.0,2.719686508178711,3.0,1000.0,39.0,12.0 178 | 176,Paraboloid,7.06589741649321,13.65473408431361,8.0,9.0,1.1606076659025286,1.0,3.2959084510803223,3.0,1000.0,48.0,15.0 179 | 177,Cubic,3.1347908361584627,3.118839868804586,3.0,3.0,3.942145409464585,4.0,3.334087371826172,3.0,1000.0,5.0,3.0 180 | 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194,Nonlinear,13.122351448457046,16.333515027037897,13.0,17.0,24.43137463732847,24.0,11.919271469116211,12.0,1000.0,72.0,12.0 197 | 195,Spiral,1.744129885501338,1.5542532089121797,1.0,1.0,2.1118166974797132,2.0,0.9376007318496704,1.0,1000.0,3.0,1.0 198 | 196,Spiral,1.7595468559647307,1.624355408670457,1.0,1.0,2.0584502625527,2.0,1.1191916465759277,1.0,1000.0,13.0,1.0 199 | 197,Helix1d,0.9930034485447228,1.3129897707185136,1.0,1.0,2.68200392659653,3.0,1.004554271697998,1.0,1000.0,3.0,1.0 200 | 198,Helix1d,1.0016596964855602,1.237690424661106,1.0,1.0,2.6001030862242605,3.0,1.0907936096191406,1.0,1000.0,13.0,1.0 201 | 199,Helix2d,2.696179448431814,2.4330168893893234,2.0,3.0,2.536180247302381,3.0,1.878188133239746,2.0,1000.0,3.0,2.0 202 | 200,Helix2d,2.7339672733730866,2.4244652003701663,3.0,3.0,2.4675075522280188,3.0,2.0445215702056885,2.0,1000.0,13.0,2.0 203 | 201,Helicoid,2.0894162973142776,2.2729097682183235,2.0,2.0,1.8487394975854843,2.0,2.0449211597442627,2.0,1000.0,3.0,2.0 204 | 202,Helicoid,2.0942420338848717,2.2701213763665193,2.0,2.0,1.8255509814316446,2.0,2.142183303833008,2.0,1000.0,13.0,2.0 205 | 203,Roll,1.9607232672603003,2.350232124649378,2.0,2.0,2.9620545239972564,3.0,1.8641055822372437,2.0,1000.0,3.0,2.0 206 | 204,Roll,1.9454669467169288,2.5312813383423527,2.0,2.0,2.9854648337770753,3.0,1.920366644859314,2.0,1000.0,13.0,2.0 207 | 205,Scurve,1.9343742598857296,2.0763443402839084,2.0,2.0,2.212960681930958,3.0,2.0299699306488037,2.0,1000.0,3.0,2.0 208 | 206,Scurve,1.9605353162143804,2.0700107647062276,2.0,2.0,2.192374632801496,3.0,1.8682019710540771,2.0,1000.0,13.0,2.0 209 | 207,Moebius,1.9778366966557828,1.21516020398927,2.0,2.0,2.3018390262960953,3.0,1.8048535585403442,2.0,1000.0,3.0,2.0 210 | 208,Uniform,4.41271975806279,4.656835767178864,4.0,5.0,4.960826187537338,5.0,4.594228744506836,5.0,1000.0,10.0,5.0 211 | 209,Uniform,7.974672970244514,8.731779045405201,8.0,10.0,9.859921630484651,10.0,8.425335884094238,9.0,1000.0,15.0,10.0 212 | 210,Uniform,19.06012067411183,29.48538442681861,20.0,29.0,29.78239499290045,30.0,19.314472198486328,20.0,1000.0,35.0,30.0 213 | 211,Uniform,27.37729206946853,50.63722098447389,29.0,49.0,50.838430297291985,50.0,28.15492820739746,31.0,1000.0,55.0,50.0 214 | 212,Uniform,33.997658039729195,71.70316923020687,36.0,69.0,68.65829697760734,70.0,35.57736587524414,36.0,1000.0,75.0,70.0 215 | 213,Norm,14.946930735149405,20.0,16.0,20.0,20.59784906174024,20.0,13.703303337097168,14.0,1000.0,20.0,20.0 216 | 214,Norm,15.22203573016282,22.154129381313346,16.0,23.0,20.93912463286402,20.0,13.933735847473145,15.0,1000.0,50.0,20.0 217 | 215,Norm,27.02215563574613,50.0,28.0,46.0,50.48193043763393,50.0,23.943504333496094,26.0,1000.0,50.0,50.0 218 | 216,Norm,27.579772005778167,56.325068208449665,29.0,54.0,49.41391997756134,50.0,24.725845336914062,27.0,1000.0,70.0,50.0 219 | 217,Paraboloid,2.7944860313888156,2.9202394963126546,3.0,3.0,1.8008745991787027,1.0,2.230445146560669,2.0,1000.0,12.0,3.0 220 | 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234,Affine,14.310569473995267,20.0,15.0,20.0,20.16242552076069,20.0,14.865837097167969,15.0,1000.0,20.0,20.0 237 | 235,Nonlinear_4to6,3.896629912516265,4.100457617949965,4.0,5.0,3.0836760392788283,5.0,3.8130781650543213,4.0,1000.0,6.0,4.0 238 | 236,Nonlinear,4.01131937657609,3.423130304906118,4.0,6.0,8.046632355758394,8.0,3.7260451316833496,4.0,1000.0,8.0,4.0 239 | 237,Nonlinear,6.640261317787266,6.511958611497258,6.0,8.0,11.688698230242672,12.0,5.5630598068237305,6.0,1000.0,36.0,6.0 240 | 238,Nonlinear,9.101059750519948,10.448048666089715,9.0,11.0,16.024091673034057,16.0,7.809560775756836,8.0,1000.0,64.0,8.0 241 | 239,Nonlinear,13.67567850753133,18.40534095830553,14.0,17.0,23.427330198521172,24.0,12.088587760925293,12.0,1000.0,72.0,12.0 242 | 240,Spiral,1.7407185968311438,1.5351100761474468,1.0,1.0,2.0765284655618297,2.0,1.064180612564087,1.0,1000.0,3.0,1.0 243 | 241,Spiral,1.741300767582885,1.4846180884686373,1.0,1.0,2.0493921924136713,2.0,0.9305784702301025,1.0,1000.0,13.0,1.0 244 | 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282,Nonlinear,6.738806342013285,6.754183341737493,6.0,8.0,12.258612507500914,12.0,5.765381336212158,6.0,1000.0,36.0,6.0 285 | 283,Nonlinear,9.23727564548983,10.228431850443839,9.0,11.0,15.7132288184678,16.0,7.923585414886475,8.0,1000.0,64.0,8.0 286 | 284,Nonlinear,13.608559327871136,17.559547713584372,14.0,19.0,23.8698307924116,24.0,12.62466049194336,13.0,1000.0,72.0,12.0 287 | 285,Spiral,1.763143285540436,1.524773384202886,1.0,1.0,2.1198244438831453,2.0,0.9522878527641296,1.0,1000.0,3.0,1.0 288 | 286,Spiral,1.7846724365493698,1.6472685662029656,1.0,1.0,2.0896091047709753,2.0,1.0047279596328735,1.0,1000.0,13.0,1.0 289 | 287,Helix1d,1.0090032597562868,1.1088570687434556,1.0,1.0,2.586698835397989,3.0,0.964385986328125,1.0,1000.0,3.0,1.0 290 | 288,Helix1d,0.9912250506593442,1.3058764577393027,1.0,1.0,2.5635936793386653,3.0,1.009834885597229,1.0,1000.0,13.0,1.0 291 | 289,Helix2d,2.7436151626610914,2.7912311869682624,3.0,3.0,2.5733545716856936,3.0,1.9602605104446411,2.0,1000.0,3.0,2.0 292 | 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298,Uniform,4.451564756671178,4.751170624269275,5.0,5.0,4.8470362396828826,5.0,4.982565879821777,5.0,1000.0,10.0,5.0 301 | 299,Uniform,8.160005315600445,9.260479610016713,9.0,10.0,9.863453956317036,10.0,8.367286682128906,9.0,1000.0,15.0,10.0 302 | 300,Uniform,19.219294460692385,29.470262702635512,20.0,29.0,30.052660627073035,30.0,19.599260330200195,21.0,1000.0,35.0,30.0 303 | 301,Uniform,26.781566497408168,50.47709512747802,28.0,50.0,48.68773751408499,50.0,26.040651321411133,28.0,1000.0,55.0,50.0 304 | 302,Uniform,33.98060131973838,73.01319683488788,36.0,73.0,70.44982794358611,70.0,35.205265045166016,38.0,1000.0,75.0,70.0 305 | 303,Norm,15.03623361287664,20.0,15.0,20.0,19.86039927047829,20.0,13.735798835754395,14.0,1000.0,20.0,20.0 306 | 304,Norm,15.003431725230005,22.129932510578794,16.0,21.0,20.080210179836687,20.0,13.900763511657715,15.0,1000.0,50.0,20.0 307 | 305,Norm,27.13515980343321,50.0,29.0,46.0,48.637192239165024,50.0,22.956037521362305,25.0,1000.0,50.0,50.0 308 | 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345,Uniform,19.028225488589708,29.924057521594346,20.0,31.0,30.4657310497791,30.0,20.05685806274414,20.0,1000.0,35.0,30.0 348 | 346,Uniform,27.503659272468152,50.625783356323886,29.0,47.0,48.184317965640794,50.0,27.521942138671875,30.0,1000.0,55.0,50.0 349 | 347,Uniform,34.252716126778225,74.07935526676243,36.0,67.0,70.04292062570248,70.0,34.46240997314453,37.0,1000.0,75.0,70.0 350 | 348,Norm,15.159081779557223,20.0,16.0,20.0,20.0329552403605,20.0,13.804464340209961,15.0,1000.0,20.0,20.0 351 | 349,Norm,14.783974587877173,20.978008943857297,15.0,21.0,20.876521326964397,20.0,13.889734268188477,15.0,1000.0,50.0,20.0 352 | 350,Norm,26.694696937235495,50.0,28.0,48.0,50.43007148068511,50.0,24.054258346557617,26.0,1000.0,50.0,50.0 353 | 351,Norm,27.42873569289861,53.47010638252647,29.0,49.0,50.29279059099176,50.0,24.20049285888672,26.0,1000.0,70.0,50.0 354 | 352,Paraboloid,2.859641756414142,2.9875806146344774,3.0,3.0,1.7777913395263156,1.0,2.203115701675415,2.0,1000.0,12.0,3.0 355 | 353,Paraboloid,4.758970214340571,5.802943493923829,5.0,6.0,1.4710866921490207,1.0,2.5267560482025146,3.0,1000.0,21.0,6.0 356 | 354,Paraboloid,5.916689976529968,8.83522778426362,6.0,8.0,1.3278542284655166,1.0,2.5256121158599854,2.0,1000.0,30.0,9.0 357 | 355,Paraboloid,6.5096744523244485,10.951468172857261,7.0,8.0,1.2175278968670693,1.0,3.1277379989624023,3.0,1000.0,39.0,12.0 358 | 356,Paraboloid,6.963863804833085,14.282761435034644,7.0,9.0,1.1658699487122326,1.0,3.25545334815979,3.0,1000.0,48.0,15.0 359 | 357,Cubic,3.0476397863615388,3.1569981714973427,3.0,3.0,4.089928253214166,4.0,2.9227914810180664,3.0,1000.0,5.0,3.0 360 | 358,Cubic,19.48335360176353,29.53483349105419,20.0,30.0,30.826856809981788,31.0,20.112957000732422,21.0,1000.0,35.0,30.0 361 | 359,Cubic,34.18686234678189,74.22366608034613,36.0,74.0,71.85344235722467,71.0,34.96773910522461,39.0,1000.0,90.0,70.0 362 | 360,Sphere,2.960019290793002,3.1105284866911846,3.0,3.0,4.01684140101535,4.0,2.8911428451538086,3.0,1000.0,5.0,3.0 363 | 361,Sphere,4.796370360884271,5.0297913494870095,5.0,6.0,5.8361779332494494,6.0,4.9308576583862305,5.0,1000.0,10.0,5.0 364 | 362,Sphere,8.753853288263734,9.918736013981382,9.0,12.0,10.839940002676986,11.0,8.90211009979248,9.0,1000.0,15.0,10.0 365 | 363,Sphere,20.5490340591085,31.6195280164458,21.0,31.0,31.283838683646902,31.0,23.403682708740234,23.0,1000.0,35.0,30.0 366 | 364,Sphere,29.06580130516416,54.53547455160916,30.0,50.0,51.76017070155615,51.0,31.41923713684082,33.0,1000.0,55.0,50.0 367 | 365,Sphere,36.343109682916946,75.0,38.0,70.0,73.03992175788194,71.0,38.690704345703125,41.0,1000.0,75.0,70.0 368 | 366,Affine_3to5,2.8324221667619773,3.1718162634511806,3.0,3.0,2.5957702424551967,3.0,2.9698867797851562,3.0,1000.0,5.0,3.0 369 | 367,Affine,4.362153534032998,5.0,4.0,5.0,4.958365769137722,5.0,4.620956897735596,4.0,1000.0,5.0,5.0 370 | 368,Affine,8.17906164988975,10.0,8.0,10.0,9.81909120088796,10.0,8.497963905334473,8.0,1000.0,10.0,10.0 371 | 369,Affine,14.22251419835054,20.0,15.0,20.0,20.082230748482214,20.0,15.445515632629395,16.0,1000.0,20.0,20.0 372 | 370,Nonlinear_4to6,3.8300969695215135,4.1074134595959855,4.0,5.0,3.1845008890749837,5.0,3.612987518310547,4.0,1000.0,6.0,4.0 373 | 371,Nonlinear,4.08401700217571,3.421051123646496,4.0,6.0,8.168330252063676,8.0,3.73567533493042,4.0,1000.0,8.0,4.0 374 | 372,Nonlinear,6.603763264013966,6.564435751477549,6.0,8.0,11.91725476298286,12.0,5.533533573150635,5.0,1000.0,36.0,6.0 375 | 373,Nonlinear,9.416870676208708,10.715106311542067,9.0,10.0,15.90641413660213,16.0,8.062159538269043,7.0,1000.0,64.0,8.0 376 | 374,Nonlinear,13.50447088350871,17.078799562402047,13.0,17.0,24.948926579607644,24.0,12.017448425292969,11.0,1000.0,72.0,12.0 377 | 375,Spiral,1.752899726586747,1.548081954063358,1.0,1.0,2.0807406267571458,2.0,1.0218344926834106,1.0,1000.0,3.0,1.0 378 | 376,Spiral,1.7506235390007776,1.475085211810569,1.0,1.0,2.0708364712447525,2.0,1.0735325813293457,1.0,1000.0,13.0,1.0 379 | 377,Helix1d,1.0143730217111047,1.2384570798984842,1.0,1.0,2.6495064990766646,3.0,1.1121528148651123,1.0,1000.0,3.0,1.0 380 | 378,Helix1d,1.0043243084510312,1.1810249742382073,1.0,1.0,2.6043580064395186,3.0,0.9604995846748352,1.0,1000.0,13.0,1.0 381 | 379,Helix2d,2.7088522057731876,2.8533147788789353,3.0,3.0,2.549418363495617,3.0,2.0696170330047607,2.0,1000.0,3.0,2.0 382 | 380,Helix2d,2.7014268348133417,2.5001051495314828,2.0,3.0,2.5438647502147163,3.0,1.8622416257858276,2.0,1000.0,13.0,2.0 383 | 381,Helicoid,2.0846055746924055,2.380021540334578,2.0,2.0,1.8377120244558074,2.0,2.069695234298706,2.0,1000.0,3.0,2.0 384 | 382,Helicoid,2.035037399290107,2.3114828944237282,2.0,2.0,1.8319601654563327,2.0,1.909002661705017,2.0,1000.0,13.0,2.0 385 | 383,Roll,1.9371770121542111,3.0,2.0,2.0,2.9551250152170385,3.0,1.887024164199829,2.0,1000.0,3.0,2.0 386 | 384,Roll,1.9557252498729372,2.299444303024956,2.0,2.0,3.011846791999727,3.0,2.0361318588256836,2.0,1000.0,13.0,2.0 387 | 385,Scurve,1.9387129472267643,1.9925111560201865,2.0,2.0,2.207988997049817,3.0,1.90701425075531,2.0,1000.0,3.0,2.0 388 | 386,Scurve,1.9418201781922906,2.0568921515858136,2.0,2.0,2.230348191239863,3.0,2.0680348873138428,2.0,1000.0,13.0,2.0 389 | 387,Moebius,1.9867092838732896,1.2579896603488983,2.0,2.0,2.3428867306824026,3.0,2.2453198432922363,2.0,1000.0,3.0,2.0 390 | 388,Uniform,4.495618364346722,4.770454034707689,5.0,5.0,5.006808988669047,5.0,4.788795471191406,5.0,1000.0,10.0,5.0 391 | 389,Uniform,8.12556448444041,9.241950205001068,8.0,10.0,9.958655205554832,10.0,8.376396179199219,8.0,1000.0,15.0,10.0 392 | 390,Uniform,18.921191287950727,29.413575499416773,20.0,29.0,29.15374175899493,30.0,19.331737518310547,20.0,1000.0,35.0,30.0 393 | 391,Uniform,27.35625142664721,49.47282624287605,29.0,53.0,49.23668906363451,50.0,29.72776985168457,31.0,1000.0,55.0,50.0 394 | 392,Uniform,33.53146842621595,70.66611001489535,36.0,71.0,71.99822734215958,70.0,34.33204650878906,36.0,1000.0,75.0,70.0 395 | 393,Norm,14.958213588500515,20.0,16.0,20.0,20.405920479588396,20.0,13.312904357910156,15.0,1000.0,20.0,20.0 396 | 394,Norm,15.134589454435705,22.705098883227148,16.0,22.0,20.417019741377384,20.0,13.523594856262207,14.0,1000.0,50.0,20.0 397 | 395,Norm,27.290165060869178,50.0,29.0,46.0,48.45713161110539,50.0,23.73616600036621,25.0,1000.0,50.0,50.0 398 | 396,Norm,26.959108912399596,50.94166386514414,29.0,52.0,50.11622068478959,50.0,24.077136993408203,26.0,1000.0,70.0,50.0 399 | 397,Paraboloid,2.8209899811650376,3.058996189994821,3.0,3.0,1.759484634370774,1.0,2.108990430831909,2.0,1000.0,12.0,3.0 400 | 398,Paraboloid,4.679932397774519,6.08335125586849,5.0,6.0,1.461905590449596,1.0,2.7409422397613525,3.0,1000.0,21.0,6.0 401 | 399,Paraboloid,5.8360124708474705,9.016257985808183,6.0,8.0,1.3054967107278326,1.0,3.0080277919769287,3.0,1000.0,30.0,9.0 402 | 400,Paraboloid,6.696503364825862,12.944481759459045,7.0,8.0,1.2194472071836249,1.0,2.9666895866394043,3.0,1000.0,39.0,12.0 403 | 401,Paraboloid,6.922352710982069,14.197366931093315,7.0,9.0,1.1633786351594002,1.0,3.573054790496826,3.0,1000.0,48.0,15.0 404 | 402,Cubic,3.0705247391307413,3.147960479797628,3.0,3.0,3.9227536295828864,4.0,2.9965641498565674,3.0,1000.0,5.0,3.0 405 | 403,Cubic,19.243835919370188,29.261997556018503,20.0,30.0,30.789479125904013,31.0,19.99090003967285,21.0,1000.0,35.0,30.0 406 | 404,Cubic,34.902056474637384,72.02652985780078,37.0,75.0,71.14449479775952,71.0,36.18771743774414,38.0,1000.0,90.0,70.0 407 | 405,Sphere,2.9783996858117776,3.0508285417080567,3.0,3.0,3.9668065967463817,4.0,3.1358702182769775,3.0,1000.0,5.0,3.0 408 | 406,Sphere,4.824769130793059,5.197050447550431,5.0,6.0,6.15220758082465,6.0,5.075606346130371,5.0,1000.0,10.0,5.0 409 | 407,Sphere,8.86756212958105,10.080522329141008,9.0,11.0,11.027357135419052,11.0,8.918981552124023,10.0,1000.0,15.0,10.0 410 | 408,Sphere,20.090124162239864,31.439472833574065,21.0,31.0,30.75657365911637,31.0,22.92632484436035,22.0,1000.0,35.0,30.0 411 | 409,Sphere,28.613359308718266,55.0,30.0,49.0,51.30944625204253,51.0,32.008487701416016,34.0,1000.0,55.0,50.0 412 | 410,Sphere,36.62515552810218,75.0,38.0,71.0,73.33563118573073,71.0,40.201236724853516,40.0,1000.0,75.0,70.0 413 | 411,Affine_3to5,2.836600509862634,3.324676552859526,3.0,3.0,2.592864295305511,3.0,2.9301199913024902,3.0,1000.0,5.0,3.0 414 | 412,Affine,4.462501748530342,5.0,5.0,5.0,5.019925222123573,5.0,4.5413103103637695,5.0,1000.0,5.0,5.0 415 | 413,Affine,8.285916559451822,10.0,8.0,9.0,10.201321623583198,10.0,8.468425750732422,8.0,1000.0,10.0,10.0 416 | 414,Affine,13.81777747564487,20.0,14.0,19.0,20.160339479761557,20.0,15.418538093566895,15.0,1000.0,20.0,20.0 417 | 415,Nonlinear_4to6,3.8512413873674936,4.1567614054862085,4.0,5.0,3.015247970158781,5.0,3.767810821533203,4.0,1000.0,6.0,4.0 418 | 416,Nonlinear,4.112822510124341,3.386147041353518,4.0,5.0,7.717468265269623,8.0,3.842580556869507,4.0,1000.0,8.0,4.0 419 | 417,Nonlinear,6.825219716402047,7.148629901948501,6.0,9.0,11.81798475517478,12.0,5.826848030090332,6.0,1000.0,36.0,6.0 420 | 418,Nonlinear,9.159945027660859,10.63319519960527,9.0,10.0,16.37895661831584,16.0,8.105765342712402,8.0,1000.0,64.0,8.0 421 | 419,Nonlinear,13.562874234453233,17.16106096858686,14.0,18.0,23.68000392416994,24.0,12.300105094909668,12.0,1000.0,72.0,12.0 422 | 420,Spiral,1.789340926387284,1.656650421330748,1.0,1.0,2.065628655154221,2.0,0.9219439625740051,1.0,1000.0,3.0,1.0 423 | 421,Spiral,1.7663304851756971,1.5261004033872276,1.0,1.0,2.0992730989629416,2.0,1.039484977722168,1.0,1000.0,13.0,1.0 424 | 422,Helix1d,1.0072811463800604,1.2349687428508576,1.0,1.0,2.654172342795546,3.0,1.0664379596710205,1.0,1000.0,3.0,1.0 425 | 423,Helix1d,1.0044264261157327,1.4910072485553123,1.0,1.0,2.6092696076180357,3.0,0.9135423302650452,1.0,1000.0,13.0,1.0 426 | 424,Helix2d,2.745205202482536,2.9851634596718273,3.0,3.0,2.5505814141239163,3.0,1.9555836915969849,2.0,1000.0,3.0,2.0 427 | 425,Helix2d,2.8256014106160543,2.9259121967177504,3.0,3.0,2.5757268125767454,3.0,1.9718495607376099,2.0,1000.0,13.0,2.0 428 | 426,Helicoid,2.084928787801918,2.258686941808005,2.0,2.0,1.8382414918605465,2.0,2.059587001800537,2.0,1000.0,3.0,2.0 429 | 427,Helicoid,2.0891741786858202,2.323685634337502,2.0,2.0,1.8147942298965072,2.0,2.0116944313049316,2.0,1000.0,13.0,2.0 430 | 428,Roll,1.9346781529751795,1.7201736944755104,2.0,2.0,2.9406731892848175,3.0,2.066171169281006,2.0,1000.0,3.0,2.0 431 | 429,Roll,1.9517623519035645,2.448919593277775,2.0,2.0,2.9538252512002074,3.0,2.0072405338287354,2.0,1000.0,13.0,2.0 432 | 430,Scurve,1.9552796751161992,2.0148991640034586,2.0,2.0,2.1814980626182714,3.0,1.9645421504974365,2.0,1000.0,3.0,2.0 433 | 431,Scurve,1.9344844494017788,2.0893327639382044,2.0,2.0,2.2627284581886524,3.0,2.121084213256836,2.0,1000.0,13.0,2.0 434 | 432,Moebius,1.9717168068122501,1.2078098863890436,2.0,2.0,2.3019155481055753,3.0,1.8406659364700317,2.0,1000.0,3.0,2.0 435 | 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100,Nonlinear_4to6,3.7319328969630856,4.210900742306474,4.0,4.0,3.0924322891847416,5.0,3.562645435333252,4.0,1000.0,6.0,4.0 103 | 101,Nonlinear,4.304252228763589,3.3983286396838337,4.0,5.0,7.929946384784486,8.0,3.7728700637817383,4.0,1000.0,8.0,4.0 104 | 102,Nonlinear,6.884346735362727,6.730318666169076,7.0,7.0,11.846515167145137,12.0,5.663153648376465,6.0,1000.0,36.0,6.0 105 | 103,Nonlinear,9.183375445662545,10.414229470302624,9.0,11.0,15.61896186779241,16.0,7.495347023010254,8.0,1000.0,64.0,8.0 106 | 104,Nonlinear,12.994022877026104,17.454286633549152,13.0,18.0,24.170616160965167,24.0,11.948537826538086,12.0,1000.0,72.0,12.0 107 | 105,Spiral,1.7399576647923922,1.6147690525756604,2.0,2.0,2.0751654378892077,2.0,0.8885128498077393,1.0,1000.0,3.0,1.0 108 | 106,Spiral,1.7477834559486305,1.6993409523513545,2.0,2.0,2.1571799416337125,2.0,1.0798178911209106,1.0,1000.0,13.0,1.0 109 | 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123,Norm,13.880234756782952,20.0,15.0,20.0,19.74509463573792,20.0,13.277400016784668,15.0,1000.0,20.0,20.0 126 | 124,Norm,13.804224685957406,21.27280961567427,15.0,21.0,20.19890938950476,20.0,14.186927795410156,14.0,1000.0,50.0,20.0 127 | 125,Norm,24.33132628776245,50.0,27.0,47.0,51.01417102213402,50.0,24.39381217956543,26.0,1000.0,50.0,50.0 128 | 126,Norm,24.351645253891487,51.855574578122,27.0,46.0,50.01634559324772,50.0,24.585905075073242,26.0,1000.0,70.0,50.0 129 | 127,Paraboloid,2.7333923635539623,3.0309841689788164,3.0,3.0,1.8017837715761333,2.0,1.906341791152954,2.0,1000.0,12.0,3.0 130 | 128,Paraboloid,4.217300943517667,5.953504114853216,5.0,5.0,1.4658387098789405,1.0,2.5725934505462646,2.0,1000.0,21.0,6.0 131 | 129,Paraboloid,4.829885098975862,9.051146529165656,5.0,6.0,1.3055460696201306,1.0,3.424220085144043,3.0,1000.0,30.0,9.0 132 | 130,Paraboloid,4.838588019594154,12.354342758636905,6.0,7.0,1.21432127482181,1.0,2.9440324306488037,3.0,1000.0,39.0,12.0 133 | 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147,Nonlinear,6.996015478539146,6.949823044796736,7.0,8.0,12.304958695981854,12.0,5.795685291290283,6.0,1000.0,36.0,6.0 150 | 148,Nonlinear,9.339752180019635,11.134340722200857,9.0,11.0,16.022105454129377,16.0,7.964322090148926,8.0,1000.0,64.0,8.0 151 | 149,Nonlinear,12.988763614577005,17.49365486358198,13.0,17.0,24.81693072870595,24.0,12.080082893371582,12.0,1000.0,72.0,12.0 152 | 150,Spiral,1.7180106518032092,1.4251145062164217,2.0,2.0,2.0838633424726662,2.0,0.9554095268249512,1.0,1000.0,3.0,1.0 153 | 151,Spiral,1.743111739926805,1.5771272448855176,2.0,2.0,2.050027591531927,2.0,1.095772624015808,1.0,1000.0,13.0,1.0 154 | 152,Helix1d,1.0807523791148592,1.2301294062405221,1.0,1.0,2.6141228925000144,3.0,1.0271183252334595,1.0,1000.0,3.0,1.0 155 | 153,Helix1d,1.0890196973380313,1.305292260186886,1.0,1.0,2.6317259584710913,3.0,1.0145316123962402,1.0,1000.0,13.0,1.0 156 | 154,Helix2d,2.7738722289518463,2.809373703769933,3.0,3.0,2.567998628678959,3.0,2.067741870880127,2.0,1000.0,3.0,2.0 157 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163,Uniform,4.283991564974198,4.752365125068594,5.0,5.0,5.062612641364076,5.0,5.1546430587768555,5.0,1000.0,10.0,5.0 166 | 164,Uniform,7.660161272236621,8.647075334429115,8.0,9.0,9.891790462309455,10.0,8.26203727722168,9.0,1000.0,15.0,10.0 167 | 165,Uniform,17.81143492053908,29.077745461324287,19.0,29.0,29.97775546237104,30.0,18.43553352355957,21.0,1000.0,35.0,30.0 168 | 166,Uniform,25.037523432249692,51.60204156437309,27.0,49.0,50.479728973271236,50.0,27.95118522644043,29.0,1000.0,55.0,50.0 169 | 167,Uniform,30.875326701883157,73.21666786325508,33.0,67.0,71.44787428977018,70.0,36.272926330566406,40.0,1000.0,75.0,70.0 170 | 168,Norm,13.887903339794127,20.0,15.0,20.0,20.24470405323878,20.0,13.968093872070312,15.0,1000.0,20.0,20.0 171 | 169,Norm,13.815426205672747,21.519375298230866,15.0,21.0,20.454393758566095,20.0,14.044336318969727,14.0,1000.0,50.0,20.0 172 | 170,Norm,24.602716566773232,50.0,27.0,48.0,49.292278951099554,50.0,25.35314178466797,27.0,1000.0,50.0,50.0 173 | 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Dataset,MLE,GeoMLE,MIND,DANCo,ESS,PCA,CD,Hein,Num,Dim,RealDim 2 | 0,Sphere,2.9658029913435096,2.9942751239563195,3.0,3.0,3.9234220227500316,4.0,2.7383649349212646,3.0,1000.0,5.0,3.0 3 | 1,Sphere,4.649992163736543,4.588708295313299,5.0,6.0,5.8744954549592965,6.0,4.280256271362305,5.0,1000.0,10.0,5.0 4 | 2,Sphere,8.168119766184349,8.268423276493392,8.0,11.0,11.021198276916795,11.0,8.782669067382812,9.0,1000.0,15.0,10.0 5 | 3,Sphere,19.36738392816978,26.406475811763098,20.0,30.0,31.893584013295154,31.0,20.612667083740234,21.0,1000.0,35.0,30.0 6 | 4,Sphere,28.333053391870497,46.955321229488014,29.0,49.0,51.57965512152485,51.0,29.895282745361328,31.0,1000.0,55.0,50.0 7 | 5,Sphere,35.06823840438664,66.42941149739237,37.0,69.0,70.10999725245276,71.0,40.78301239013672,41.0,1000.0,75.0,70.0 8 | 6,Affine_3to5,3.0661043227854474,3.1547484522421216,3.0,3.0,2.5327030649842674,3.0,3.167365312576294,3.0,1000.0,5.0,3.0 9 | 7,Affine,4.972840149984336,5.0,5.0,5.0,4.9863298603869275,5.0,4.723347187042236,5.0,1000.0,5.0,5.0 10 | 8,Affine,8.981315987520126,10.0,9.0,10.0,10.210354821894224,10.0,8.13756275177002,9.0,1000.0,10.0,10.0 11 | 9,Affine,15.056524671453776,20.0,15.0,20.0,20.45147220382136,20.0,13.744416236877441,14.0,1000.0,20.0,20.0 12 | 10,Nonlinear_4to6,4.063037924251211,4.280303024839654,4.0,5.0,3.232883643269365,5.0,3.709861993789673,4.0,1000.0,6.0,4.0 13 | 11,Nonlinear,4.17153270018565,3.9516913401472795,4.0,5.0,7.211034701466111,8.0,3.977647066116333,4.0,1000.0,8.0,4.0 14 | 12,Nonlinear,6.332210645013337,6.509010761716799,6.0,8.0,10.901715292935519,12.0,5.638318061828613,6.0,1000.0,36.0,6.0 15 | 13,Nonlinear,8.479684165081306,9.25874860938152,8.0,10.0,14.033637936349567,16.0,7.599908351898193,8.0,1000.0,64.0,8.0 16 | 14,Nonlinear,12.37308020159902,14.982277477637071,13.0,15.0,21.51554171003064,24.0,11.206862449645996,12.0,1000.0,72.0,12.0 17 | 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23,Roll,2.021952095755329,1.9228994418455532,2.0,2.0,2.779826025907719,3.0,1.9507354497909546,2.0,1000.0,3.0,2.0 26 | 24,Roll,2.049839975488909,2.195373224880566,2.0,2.0,2.760067083607,3.0,1.8770883083343506,2.0,1000.0,13.0,2.0 27 | 25,Scurve,2.016446392304498,2.04640735850655,2.0,2.0,1.954577304672984,3.0,1.9863978624343872,2.0,1000.0,3.0,2.0 28 | 26,Scurve,2.0015199212844097,2.0254587807745867,2.0,2.0,1.9845090372495062,3.0,1.9777183532714844,2.0,1000.0,13.0,2.0 29 | 27,Moebius,2.083028440218034,1.9231739536138084,2.0,2.0,2.080712449053478,2.0,2.0151240825653076,2.0,1000.0,3.0,2.0 30 | 28,Paraboloid,2.8166497226963103,2.947466098376333,3.0,3.0,1.8237646580209441,1.0,2.049680471420288,2.0,1000.0,12.0,3.0 31 | 29,Paraboloid,4.794693871262201,5.791393331507552,5.0,7.0,1.4912874748945812,1.0,2.9180872440338135,3.0,1000.0,21.0,6.0 32 | 30,Paraboloid,5.951078054730212,8.925959657661704,6.0,8.0,1.3031262472301162,1.0,3.095428466796875,3.0,1000.0,30.0,9.0 33 | 31,Paraboloid,6.496605234530625,11.614549802233713,7.0,8.0,1.224396276958854,1.0,3.1507813930511475,3.0,1000.0,39.0,12.0 34 | 32,Paraboloid,6.793192445240967,13.680685309618319,7.0,9.0,1.1592402436564573,1.0,3.076751708984375,3.0,1000.0,48.0,15.0 35 | 33,Cubic,3.0516984954841493,3.0708652262651084,3.0,4.0,3.993332998764866,4.0,2.7812812328338623,3.0,1000.0,5.0,3.0 36 | 34,Cubic,20.467943671528534,32.36913710022393,22.0,35.0,29.855002353799605,31.0,19.911529541015625,21.0,1000.0,35.0,30.0 37 | 35,Cubic,34.20926766080261,74.23356037049942,36.0,75.0,67.26658419091666,71.0,32.430885314941406,35.0,1000.0,90.0,70.0 38 | 36,Sphere,2.9885863562483252,3.1156223498140125,3.0,3.0,3.951025120996701,4.0,2.9054417610168457,3.0,1000.0,5.0,3.0 39 | 37,Sphere,4.676672637805432,4.956750870386064,5.0,6.0,5.948526384274605,6.0,4.669887542724609,5.0,1000.0,10.0,5.0 40 | 38,Sphere,8.248961025139785,9.02267594865405,8.0,10.0,10.934735264239643,11.0,7.715565204620361,8.0,1000.0,15.0,10.0 41 | 39,Sphere,19.704773861695873,28.419953051603226,20.0,29.0,31.234942107368862,31.0,21.488140106201172,22.0,1000.0,35.0,30.0 42 | 40,Sphere,28.057636946880617,47.718973296137044,29.0,49.0,50.2922591128014,51.0,32.14515686035156,32.0,1000.0,55.0,50.0 43 | 41,Sphere,35.4216798802245,70.01902571489778,37.0,70.0,71.3808351853865,71.0,41.248626708984375,40.0,1000.0,75.0,70.0 44 | 42,Affine_3to5,3.028161861054907,3.1125804447258227,3.0,3.0,2.664925783664277,3.0,2.9321014881134033,3.0,1000.0,5.0,3.0 45 | 43,Affine,5.051436896835055,5.0,5.0,5.0,4.984671781981486,5.0,4.760454177856445,5.0,1000.0,5.0,5.0 46 | 44,Affine,8.960269543801358,10.0,9.0,10.0,9.883525699323222,10.0,8.51689624786377,9.0,1000.0,10.0,10.0 47 | 45,Affine,14.787474901701971,20.0,15.0,19.0,19.596770932289253,20.0,13.597286224365234,15.0,1000.0,20.0,20.0 48 | 46,Nonlinear_4to6,4.003789555464905,4.11282956075842,4.0,6.0,3.1795122523584123,5.0,3.8056347370147705,4.0,1000.0,6.0,4.0 49 | 47,Nonlinear,4.144947198564668,3.9722062737412327,4.0,5.0,7.152557826247026,8.0,3.850205898284912,4.0,1000.0,8.0,4.0 50 | 48,Nonlinear,6.351484543878164,6.114468887469278,6.0,8.0,10.790335766650573,12.0,5.950523853302002,6.0,1000.0,36.0,6.0 51 | 49,Nonlinear,8.374054400890165,9.302116299827736,8.0,10.0,14.229875780656158,16.0,7.610683441162109,8.0,1000.0,64.0,8.0 52 | 50,Nonlinear,12.387136283366944,15.208973605801988,12.0,18.0,22.51523212836146,24.0,10.900484085083008,11.0,1000.0,72.0,12.0 53 | 51,Spiral,1.7586268804373326,1.8910072365929185,1.0,1.0,2.011739255845878,2.0,0.9570624828338623,1.0,1000.0,3.0,1.0 54 | 52,Spiral,1.7962484704523134,1.955172771339445,1.0,1.0,2.0570234178989257,2.0,1.0820579528808594,1.0,1000.0,13.0,1.0 55 | 53,Helix1d,1.0258663765246323,1.0795550150916595,1.0,1.0,2.7197352914556094,3.0,1.0289634466171265,1.0,1000.0,3.0,1.0 56 | 54,Helix1d,1.005891766108069,1.0024569638341816,1.0,1.0,2.7155885691175428,3.0,0.9548850655555725,1.0,1000.0,13.0,1.0 57 | 55,Helix2d,2.8658085325311906,3.0,3.0,3.0,2.3582844842494985,3.0,1.98493230342865,2.0,1000.0,3.0,2.0 58 | 56,Helix2d,2.8295182800800243,3.25352018733773,2.0,3.0,2.3595706339351947,3.0,1.913253664970398,2.0,1000.0,13.0,2.0 59 | 57,Helicoid,2.138481495003851,2.090949824872817,2.0,2.0,2.248949907770779,3.0,2.0748822689056396,2.0,1000.0,3.0,2.0 60 | 58,Helicoid,2.0884609535476324,2.008100837422693,2.0,2.0,2.2992599032294314,3.0,2.0949456691741943,2.0,1000.0,13.0,2.0 61 | 59,Roll,2.0931529284557806,2.577434423575281,2.0,2.0,2.7590034069254923,3.0,1.9331061840057373,2.0,1000.0,3.0,2.0 62 | 60,Roll,2.0520567772162455,2.0989470059280535,2.0,2.0,2.7646173858249035,3.0,2.051841974258423,2.0,1000.0,13.0,2.0 63 | 61,Scurve,2.0316601786088127,2.0077716052997547,2.0,2.0,1.9826615690522371,3.0,2.118140697479248,2.0,1000.0,3.0,2.0 64 | 62,Scurve,2.010922230643805,2.049081434243764,2.0,2.0,1.9965284953378601,3.0,1.9956227540969849,2.0,1000.0,13.0,2.0 65 | 63,Moebius,2.0867872703485246,1.9371853416149847,2.0,2.0,2.1087367492059363,2.0,2.001065969467163,2.0,1000.0,3.0,2.0 66 | 64,Paraboloid,2.8369942688640806,2.9964432096943536,3.0,3.0,1.7918016902734168,1.0,2.190873861312866,2.0,1000.0,12.0,3.0 67 | 65,Paraboloid,4.746246083934058,5.752859304927765,5.0,7.0,1.474066736372035,1.0,3.1879379749298096,3.0,1000.0,21.0,6.0 68 | 66,Paraboloid,5.9216860821187876,8.0803764272321,6.0,8.0,1.3073872740850319,1.0,3.5511221885681152,3.0,1000.0,30.0,9.0 69 | 67,Paraboloid,6.5845257909181765,11.506832448408995,7.0,8.0,1.2152060099839537,1.0,3.7698843479156494,3.0,1000.0,39.0,12.0 70 | 68,Paraboloid,6.830602044900961,14.191404373128549,7.0,9.0,1.1608478185710582,1.0,3.626716136932373,4.0,1000.0,48.0,15.0 71 | 69,Cubic,3.0073630746062934,3.067595708173512,3.0,3.0,3.9558697885909115,4.0,2.9130048751831055,3.0,1000.0,5.0,3.0 72 | 70,Cubic,20.110314532655767,32.506844496414224,21.0,33.0,30.841689919712376,31.0,19.45778465270996,20.0,1000.0,35.0,30.0 73 | 71,Cubic,34.13884636020536,74.51463507861845,37.0,70.0,71.57839339498639,71.0,32.65533447265625,35.0,1000.0,90.0,70.0 74 | 72,Sphere,2.9435981215539244,2.9770400769397956,3.0,3.0,4.035769692223904,4.0,3.156963586807251,3.0,1000.0,5.0,3.0 75 | 73,Sphere,4.610629013570351,4.887104095544266,5.0,6.0,5.938374370744965,6.0,4.41686487197876,5.0,1000.0,10.0,5.0 76 | 74,Sphere,8.24336976007345,8.784370286892415,8.0,10.0,10.945910254131174,11.0,8.411603927612305,8.0,1000.0,15.0,10.0 77 | 75,Sphere,19.589955021306412,30.39258619226731,20.0,29.0,30.9080180708304,31.0,21.5140380859375,22.0,1000.0,35.0,30.0 78 | 76,Sphere,28.355942537634395,49.475927710291316,30.0,49.0,49.93487229948482,51.0,32.687705993652344,32.0,1000.0,55.0,50.0 79 | 77,Sphere,35.66641596931279,71.52291207712031,37.0,71.0,67.77985376907564,71.0,40.4273796081543,39.0,1000.0,75.0,70.0 80 | 78,Affine_3to5,3.063824519113673,3.2693193438611443,3.0,3.0,2.5201518286540914,3.0,2.854018449783325,3.0,1000.0,5.0,3.0 81 | 79,Affine,4.88701348862193,5.0,5.0,5.0,5.02473187576588,5.0,4.768245697021484,5.0,1000.0,5.0,5.0 82 | 80,Affine,9.073632918956053,10.0,9.0,10.0,9.956277480941196,10.0,8.74211597442627,9.0,1000.0,10.0,10.0 83 | 81,Affine,15.03373123275088,20.0,16.0,19.0,20.242330250981187,20.0,13.84654426574707,15.0,1000.0,20.0,20.0 84 | 82,Nonlinear_4to6,4.064227711360667,4.344904675797502,4.0,5.0,3.1576777329376204,5.0,3.8121302127838135,4.0,1000.0,6.0,4.0 85 | 83,Nonlinear,4.163420606966134,3.5929024870729345,4.0,6.0,7.393040716092836,8.0,3.854719638824463,4.0,1000.0,8.0,4.0 86 | 84,Nonlinear,6.337963998512376,6.561815849784519,6.0,8.0,11.084841360885939,12.0,5.818990707397461,6.0,1000.0,36.0,6.0 87 | 85,Nonlinear,8.475018362625525,9.14530408419402,9.0,10.0,14.566592306387088,16.0,7.614221096038818,8.0,1000.0,64.0,8.0 88 | 86,Nonlinear,12.615610387628811,15.58929949558587,13.0,15.0,21.96453790460201,24.0,11.365955352783203,11.0,1000.0,72.0,12.0 89 | 87,Spiral,1.7718126462228443,2.2374791179878017,1.0,1.0,2.0204399060871325,2.0,0.9880959391593933,1.0,1000.0,3.0,1.0 90 | 88,Spiral,1.799443199266377,2.051713802164517,1.0,1.0,2.0584391301731917,2.0,1.002811074256897,1.0,1000.0,13.0,1.0 91 | 89,Helix1d,1.0339991106409268,1.1108559096606345,1.0,1.0,2.6117080118140814,3.0,0.9700276851654053,1.0,1000.0,3.0,1.0 92 | 90,Helix1d,1.0223802770923078,1.0786945273053745,1.0,1.0,2.657363298722605,3.0,0.9591562747955322,1.0,1000.0,13.0,1.0 93 | 91,Helix2d,2.90558175371263,3.0,3.0,3.0,2.352668809519466,3.0,1.9526567459106445,2.0,1000.0,3.0,2.0 94 | 92,Helix2d,2.8309780774117965,3.3470116043776863,2.0,3.0,2.303094825646885,3.0,1.9562110900878906,2.0,1000.0,13.0,2.0 95 | 93,Helicoid,2.090858528034905,1.9769890674250805,2.0,2.0,2.2355722862328338,3.0,1.9997791051864624,2.0,1000.0,3.0,2.0 96 | 94,Helicoid,2.091271620847433,2.032356939099315,2.0,2.0,2.234688190939492,3.0,1.9299160242080688,2.0,1000.0,13.0,2.0 97 | 95,Roll,2.0375951247123694,1.8669134165594552,2.0,2.0,2.733390654946583,3.0,1.98904287815094,2.0,1000.0,3.0,2.0 98 | 96,Roll,2.0406428968987798,1.6203136447965056,2.0,2.0,2.748459106998617,3.0,2.123300790786743,2.0,1000.0,13.0,2.0 99 | 97,Scurve,2.018894450710143,1.9591847190937524,2.0,2.0,1.9757697484419317,3.0,1.967795968055725,2.0,1000.0,3.0,2.0 100 | 98,Scurve,2.0394855785893684,2.0409534634521336,2.0,2.0,1.973016339105969,3.0,1.965282917022705,2.0,1000.0,13.0,2.0 101 | 99,Moebius,2.0688640988572558,1.956996043908811,2.0,2.0,2.062364689679282,2.0,1.998818039894104,2.0,1000.0,3.0,2.0 102 | 100,Paraboloid,2.797603254193612,2.9111866189698143,3.0,4.0,1.7996777902245769,1.0,2.2470877170562744,2.0,1000.0,12.0,3.0 103 | 101,Paraboloid,4.719531399533175,5.765130794951456,5.0,7.0,1.462894527735263,1.0,2.571855306625366,2.0,1000.0,21.0,6.0 104 | 102,Paraboloid,5.883909944983074,8.75177599169594,6.0,8.0,1.307882980725593,1.0,2.7569823265075684,3.0,1000.0,30.0,9.0 105 | 103,Paraboloid,6.674222494664453,12.461056178417257,7.0,8.0,1.2243603193075003,1.0,2.694888114929199,3.0,1000.0,39.0,12.0 106 | 104,Paraboloid,7.072726385460186,14.11286781134407,8.0,9.0,1.1656043337861082,1.0,3.125192642211914,3.0,1000.0,48.0,15.0 107 | 105,Cubic,3.0438193501557866,3.110695696552331,3.0,4.0,3.8954329749462047,4.0,2.7367589473724365,3.0,1000.0,5.0,3.0 108 | 106,Cubic,20.253005940282787,31.22928949297475,21.0,33.0,30.785484475117954,31.0,20.103364944458008,21.0,1000.0,35.0,30.0 109 | 107,Cubic,34.23355594828238,74.22503798452055,36.0,79.0,69.25234785051897,71.0,32.58235549926758,34.0,1000.0,90.0,70.0 110 | 108,Sphere,2.9916814026307077,3.047058949080859,3.0,3.0,4.011212661848823,4.0,2.8308277130126953,3.0,1000.0,5.0,3.0 111 | 109,Sphere,4.581922001612302,4.701541140990317,5.0,6.0,5.918809182787733,6.0,4.706301689147949,5.0,1000.0,10.0,5.0 112 | 110,Sphere,8.136443342015072,9.085123691212445,8.0,10.0,11.305816719168746,11.0,8.87562370300293,9.0,1000.0,15.0,10.0 113 | 111,Sphere,19.594033158684315,28.516273918587782,20.0,29.0,30.79881303028232,31.0,20.371749877929688,21.0,1000.0,35.0,30.0 114 | 112,Sphere,28.327145750878937,51.63198441938035,30.0,50.0,50.583098795592136,51.0,30.521337509155273,31.0,1000.0,55.0,50.0 115 | 113,Sphere,34.35296703244641,68.60966190413102,37.0,68.0,70.6051068441357,71.0,41.802734375,42.0,1000.0,75.0,70.0 116 | 114,Affine_3to5,2.979116840041,3.170351788679365,3.0,4.0,2.5202441353146234,3.0,2.8653435707092285,3.0,1000.0,5.0,3.0 117 | 115,Affine,4.926650195804265,5.0,5.0,5.0,5.223136823395108,5.0,4.763138294219971,5.0,1000.0,5.0,5.0 118 | 116,Affine,8.87808078150968,10.0,9.0,10.0,10.015172980003465,10.0,8.51073169708252,9.0,1000.0,10.0,10.0 119 | 117,Affine,14.867264694674958,20.0,15.0,20.0,19.827210883263913,20.0,13.73190975189209,15.0,1000.0,20.0,20.0 120 | 118,Nonlinear_4to6,3.955403441349259,4.0738062268869895,4.0,5.0,3.2156050619812913,5.0,3.651642322540283,4.0,1000.0,6.0,4.0 121 | 119,Nonlinear,4.101021099388289,3.762658848647831,4.0,5.0,7.20756950005997,8.0,3.8756673336029053,4.0,1000.0,8.0,4.0 122 | 120,Nonlinear,6.347475285333237,6.252097996301776,6.0,8.0,11.065734699283293,12.0,5.7338361740112305,6.0,1000.0,36.0,6.0 123 | 121,Nonlinear,8.518316350308616,9.211411444526425,9.0,10.0,14.045648902872722,16.0,7.619960308074951,8.0,1000.0,64.0,8.0 124 | 122,Nonlinear,12.277487932751068,14.716851072386966,12.0,17.0,21.923399894140406,24.0,10.881813049316406,11.0,1000.0,72.0,12.0 125 | 123,Spiral,1.7930407640442059,2.033006330288244,1.0,1.0,2.0584787225680077,2.0,1.014147162437439,1.0,1000.0,3.0,1.0 126 | 124,Spiral,1.7683776585068895,2.0737121391339075,1.0,1.0,2.0562028418563756,2.0,1.0646899938583374,1.0,1000.0,13.0,1.0 127 | 125,Helix1d,1.0134630104260025,1.1267963728530523,1.0,1.0,2.678201168539484,3.0,1.0371644496917725,1.0,1000.0,3.0,1.0 128 | 126,Helix1d,1.0364881641675507,1.1423230544721132,1.0,1.0,2.671656027217426,3.0,0.9746978282928467,1.0,1000.0,13.0,1.0 129 | 127,Helix2d,2.83939256789795,3.0,2.0,3.0,2.3462791058631742,3.0,1.8395017385482788,2.0,1000.0,3.0,2.0 130 | 128,Helix2d,2.880410551739984,3.39156098519958,3.0,3.0,2.290434988003446,3.0,2.0040860176086426,2.0,1000.0,13.0,2.0 131 | 129,Helicoid,2.068734362204152,2.0316016640311094,2.0,2.0,2.198913651029179,3.0,1.9696871042251587,2.0,1000.0,3.0,2.0 132 | 130,Helicoid,2.0632643124901433,1.9408876843810614,2.0,2.0,2.1751222228342773,3.0,1.9130445718765259,2.0,1000.0,13.0,2.0 133 | 131,Roll,2.0550044328062187,2.144445650953972,2.0,2.0,2.7101484550093504,3.0,2.1242623329162598,2.0,1000.0,3.0,2.0 134 | 132,Roll,2.0277260956956664,1.8542832283073345,2.0,2.0,2.7821862321757616,3.0,1.9515671730041504,2.0,1000.0,13.0,2.0 135 | 133,Scurve,2.036501254680639,2.024587345617636,2.0,2.0,1.9793104563201205,3.0,1.9284350872039795,2.0,1000.0,3.0,2.0 136 | 134,Scurve,2.0501030022808964,2.1045251629036676,2.0,2.0,1.958624602536759,3.0,2.0884761810302734,2.0,1000.0,13.0,2.0 137 | 135,Moebius,2.040114745462617,1.8803061336801479,2.0,2.0,2.088400763417765,2.0,1.9533170461654663,2.0,1000.0,3.0,2.0 138 | 136,Paraboloid,2.851812166543113,2.9691298932358023,3.0,3.0,1.7809425224146875,1.0,1.983471155166626,2.0,1000.0,12.0,3.0 139 | 137,Paraboloid,4.771951733248396,5.769746341842997,5.0,7.0,1.468248777677604,1.0,2.7418253421783447,3.0,1000.0,21.0,6.0 140 | 138,Paraboloid,5.975172363735502,8.565950658851545,6.0,7.0,1.3100497841652665,1.0,2.439730644226074,2.0,1000.0,30.0,9.0 141 | 139,Paraboloid,6.71827959997754,11.801240766190428,7.0,9.0,1.2283278673621756,1.0,3.5666258335113525,4.0,1000.0,39.0,12.0 142 | 140,Paraboloid,6.894368824033752,14.363075435961228,7.0,9.0,1.1643339848428675,1.0,4.154123306274414,4.0,1000.0,48.0,15.0 143 | 141,Cubic,3.0857846463572893,3.125682737745631,3.0,4.0,4.048231023848569,4.0,3.0607547760009766,3.0,1000.0,5.0,3.0 144 | 142,Cubic,20.357189073064188,33.7562474793431,21.0,33.0,31.389036436780344,31.0,19.938535690307617,21.0,1000.0,35.0,30.0 145 | 143,Cubic,34.25689682756365,73.03262826057144,36.0,75.0,71.89103399224506,71.0,31.842044830322266,36.0,1000.0,90.0,70.0 146 | 144,Sphere,3.008712876579574,2.987877703502503,3.0,3.0,3.9291082548828555,4.0,2.9546539783477783,3.0,1000.0,5.0,3.0 147 | 145,Sphere,4.571411160690072,4.653315880948018,5.0,5.0,5.816577765891278,6.0,4.59770393371582,5.0,1000.0,10.0,5.0 148 | 146,Sphere,8.283797413811229,9.228749571660666,8.0,11.0,10.951853014986975,11.0,7.521526336669922,8.0,1000.0,15.0,10.0 149 | 147,Sphere,19.555541450265412,27.80773334626359,20.0,29.0,31.164120388624468,31.0,20.293460845947266,21.0,1000.0,35.0,30.0 150 | 148,Sphere,28.13666671543808,48.24002205495091,29.0,49.0,49.77079616989833,51.0,31.08838653564453,32.0,1000.0,55.0,50.0 151 | 149,Sphere,35.42907427019873,74.15954843154168,37.0,69.0,71.4288191631308,71.0,38.416175842285156,40.0,1000.0,75.0,70.0 152 | 150,Affine_3to5,3.0007812158037965,3.051998894738058,3.0,3.0,2.6148828524873977,3.0,2.8484303951263428,3.0,1000.0,5.0,3.0 153 | 151,Affine,4.974160487838066,5.0,5.0,5.0,5.027426350307825,5.0,4.728709697723389,5.0,1000.0,5.0,5.0 154 | 152,Affine,8.958626504531948,10.0,9.0,10.0,9.704142225428159,10.0,8.74773120880127,9.0,1000.0,10.0,10.0 155 | 153,Affine,15.096716765308193,20.0,16.0,20.0,19.692806726636075,20.0,14.239279747009277,15.0,1000.0,20.0,20.0 156 | 154,Nonlinear_4to6,3.912958198776363,4.011875381093304,4.0,5.0,3.080662684083166,5.0,3.6981749534606934,4.0,1000.0,6.0,4.0 157 | 155,Nonlinear,4.166817116253112,3.9480647701123295,4.0,5.0,7.312050165488994,8.0,3.889019250869751,4.0,1000.0,8.0,4.0 158 | 156,Nonlinear,6.476344512785582,6.830959190089727,6.0,8.0,10.789174061461235,12.0,6.005344867706299,6.0,1000.0,36.0,6.0 159 | 157,Nonlinear,8.384631803696113,8.904293824507912,8.0,10.0,14.819783878543323,16.0,7.939055442810059,8.0,1000.0,64.0,8.0 160 | 158,Nonlinear,12.272128211551026,15.172232633215932,12.0,15.0,22.83808751038828,24.0,11.27104663848877,12.0,1000.0,72.0,12.0 161 | 159,Spiral,1.7676362381149804,2.2945214581938944,1.0,2.0,2.072690932261638,2.0,1.0191389322280884,1.0,1000.0,3.0,1.0 162 | 160,Spiral,1.7227581499672278,1.9111071718195685,1.0,1.0,2.0799236538427057,2.0,0.9288991093635559,1.0,1000.0,13.0,1.0 163 | 161,Helix1d,1.0404468569845258,1.1587143519578083,1.0,1.0,2.6346907038513923,3.0,1.0179067850112915,1.0,1000.0,3.0,1.0 164 | 162,Helix1d,1.0275103426727512,1.1667217679411952,1.0,1.0,2.6825253071971744,3.0,0.9616995453834534,1.0,1000.0,13.0,1.0 165 | 163,Helix2d,2.8728842666023438,3.0,3.0,3.0,2.372413565095956,3.0,1.8992478847503662,2.0,1000.0,3.0,2.0 166 | 164,Helix2d,2.8536913405862707,3.5995084626125275,3.0,3.0,2.3084501142636022,3.0,1.9498296976089478,2.0,1000.0,13.0,2.0 167 | 165,Helicoid,2.125497266961622,2.056926289846078,2.0,2.0,2.189933179029173,3.0,2.0282177925109863,2.0,1000.0,3.0,2.0 168 | 166,Helicoid,2.114879714474318,2.0315291219475906,2.0,2.0,2.209362791131772,3.0,1.9455223083496094,2.0,1000.0,13.0,2.0 169 | 167,Roll,2.0535907596785354,2.2654420210553425,2.0,2.0,2.7878454535923747,3.0,2.0406086444854736,2.0,1000.0,3.0,2.0 170 | 168,Roll,2.0598585149561965,2.0806529563905163,2.0,2.0,2.7344834227456793,3.0,1.994260311126709,2.0,1000.0,13.0,2.0 171 | 169,Scurve,2.024168932614871,2.0462804190120827,2.0,2.0,1.972045225396105,3.0,1.9489351511001587,2.0,1000.0,3.0,2.0 172 | 170,Scurve,1.9984315830231287,1.9781947157661957,2.0,2.0,1.997352264381174,3.0,2.0597455501556396,2.0,1000.0,13.0,2.0 173 | 171,Moebius,2.111647071621014,1.9665104715608832,2.0,2.0,2.149208195916251,2.0,2.0560061931610107,2.0,1000.0,3.0,2.0 174 | 172,Paraboloid,2.8371474902254543,2.9882679983904845,3.0,3.0,1.810773872182264,1.0,2.073009490966797,2.0,1000.0,12.0,3.0 175 | 173,Paraboloid,4.720080960689353,5.701453365334637,5.0,7.0,1.5101405620991366,1.0,2.572871208190918,2.0,1000.0,21.0,6.0 176 | 174,Paraboloid,5.8639527897831805,8.500408639623547,6.0,8.0,1.3083876873909697,1.0,2.7984800338745117,3.0,1000.0,30.0,9.0 177 | 175,Paraboloid,6.596037873612912,11.567878046029648,7.0,8.0,1.2161038405233102,1.0,3.4374682903289795,3.0,1000.0,39.0,12.0 178 | 176,Paraboloid,6.949489820416153,14.254712133272095,7.0,9.0,1.1663228117063031,1.0,3.699939250946045,3.0,1000.0,48.0,15.0 179 | 177,Cubic,3.068934860225418,3.0821566408293655,3.0,3.0,3.9732910844778964,4.0,2.9265925884246826,3.0,1000.0,5.0,3.0 180 | 178,Cubic,19.99281943114786,33.78676143697462,21.0,32.0,31.346028815842793,31.0,20.009336471557617,20.0,1000.0,35.0,30.0 181 | 179,Cubic,34.102402236261156,76.14667236418778,37.0,75.0,71.84959340647345,71.0,33.28594207763672,37.0,1000.0,90.0,70.0 182 | 180,Sphere,3.027208383582469,3.100218893745966,3.0,3.0,3.9672547078220783,4.0,3.0715229511260986,3.0,1000.0,5.0,3.0 183 | 181,Sphere,4.591581602220439,4.808304350165145,5.0,7.0,5.923666326751542,6.0,4.759364604949951,5.0,1000.0,10.0,5.0 184 | 182,Sphere,8.20358634822697,8.327102213143375,8.0,10.0,11.624220283509619,11.0,8.733025550842285,8.0,1000.0,15.0,10.0 185 | 183,Sphere,19.687228245696453,30.61825950474803,20.0,29.0,31.62847509804295,31.0,21.349191665649414,21.0,1000.0,35.0,30.0 186 | 184,Sphere,28.24352006370218,45.98134295812129,29.0,50.0,50.033200069067696,51.0,29.468063354492188,31.0,1000.0,55.0,50.0 187 | 185,Sphere,34.84641079280347,67.84089754998719,37.0,69.0,67.94685946367947,71.0,36.54821014404297,42.0,1000.0,75.0,70.0 188 | 186,Affine_3to5,3.076528323180595,3.168829953972712,3.0,3.0,2.5981558866960857,3.0,2.971346616744995,3.0,1000.0,5.0,3.0 189 | 187,Affine,5.00011847161844,5.0,5.0,5.0,4.962603438529532,5.0,4.726370334625244,5.0,1000.0,5.0,5.0 190 | 188,Affine,9.017097715854744,10.0,9.0,10.0,10.199889553628886,10.0,8.176755905151367,9.0,1000.0,10.0,10.0 191 | 189,Affine,14.944593770304758,20.0,15.0,20.0,19.654207751729235,20.0,13.964456558227539,15.0,1000.0,20.0,20.0 192 | 190,Nonlinear_4to6,4.0599117964709315,4.241010721286663,4.0,5.0,3.1591888423350025,5.0,3.818222999572754,4.0,1000.0,6.0,4.0 193 | 191,Nonlinear,4.171035574158524,3.90545277377817,4.0,5.0,7.083912724289053,8.0,3.9718191623687744,4.0,1000.0,8.0,4.0 194 | 192,Nonlinear,6.350395772461456,6.56521122756773,6.0,8.0,10.965707992371751,12.0,5.648438453674316,6.0,1000.0,36.0,6.0 195 | 193,Nonlinear,8.462251732548719,8.968189720376655,8.0,10.0,14.942796812236729,16.0,7.729441165924072,7.0,1000.0,64.0,8.0 196 | 194,Nonlinear,12.398760630516485,15.325871473798934,12.0,16.0,21.27371286116196,24.0,11.020339965820312,11.0,1000.0,72.0,12.0 197 | 195,Spiral,1.7868750430062652,2.2483506707861274,1.0,1.0,2.0538761615725165,2.0,0.9852169156074524,1.0,1000.0,3.0,1.0 198 | 196,Spiral,1.7648945108485288,1.9215343005946006,1.0,1.0,2.0625709639213623,2.0,0.9786437153816223,1.0,1000.0,13.0,1.0 199 | 197,Helix1d,1.0362055017725569,1.124237906803855,1.0,1.0,2.7031344756354216,3.0,1.0306518077850342,1.0,1000.0,3.0,1.0 200 | 198,Helix1d,1.0117178717988593,1.161418650539833,1.0,1.0,2.6767252408348092,3.0,0.9603040218353271,1.0,1000.0,13.0,1.0 201 | 199,Helix2d,2.8932430280241896,3.0,3.0,3.0,2.31634280013089,3.0,2.049751043319702,2.0,1000.0,3.0,2.0 202 | 200,Helix2d,2.8759773860381626,3.560048369369925,3.0,3.0,2.330911184614789,3.0,2.0790839195251465,2.0,1000.0,13.0,2.0 203 | 201,Helicoid,2.1354084168323593,2.0416406924006343,2.0,2.0,2.3287260127798604,3.0,2.1325552463531494,2.0,1000.0,3.0,2.0 204 | 202,Helicoid,2.121231575275241,2.058643228605642,2.0,2.0,2.267171000227189,3.0,2.1198041439056396,2.0,1000.0,13.0,2.0 205 | 203,Roll,2.0335380862270536,2.482540282359371,2.0,2.0,2.7494226437278795,3.0,2.035492181777954,2.0,1000.0,3.0,2.0 206 | 204,Roll,2.0841648927462697,2.434773374874953,2.0,2.0,2.774631978489926,3.0,1.9859442710876465,2.0,1000.0,13.0,2.0 207 | 205,Scurve,2.01694014667637,1.9670570353810362,2.0,2.0,1.995801422304114,3.0,1.9720598459243774,2.0,1000.0,3.0,2.0 208 | 206,Scurve,1.9990964471713941,2.016165655847971,2.0,2.0,1.9938058616032244,3.0,1.9275847673416138,2.0,1000.0,13.0,2.0 209 | 207,Moebius,2.0793967780309393,1.9469033087248444,2.0,2.0,2.1439488826656334,2.0,1.972975492477417,2.0,1000.0,3.0,2.0 210 | 208,Paraboloid,2.804578920038458,2.9203323254324958,3.0,3.0,1.7770161766010042,1.0,2.447404623031616,2.0,1000.0,12.0,3.0 211 | 209,Paraboloid,4.715452201245487,5.67981780447471,5.0,7.0,1.4713980214656208,1.0,2.316777467727661,2.0,1000.0,21.0,6.0 212 | 210,Paraboloid,5.999327033076288,9.040008391657935,6.0,8.0,1.3089684631300542,1.0,2.823556900024414,3.0,1000.0,30.0,9.0 213 | 211,Paraboloid,6.691068174625885,11.965648453514268,7.0,9.0,1.2205239463701816,1.0,3.115905523300171,3.0,1000.0,39.0,12.0 214 | 212,Paraboloid,6.907107791513007,13.482251106568787,7.0,9.0,1.1659422411309721,1.0,2.310718536376953,2.0,1000.0,48.0,15.0 215 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| 221,Sphere,35.42486839420432,69.54554195710688,37.0,69.0,70.52967642692825,71.0,39.3236083984375,40.0,1000.0,75.0,70.0 224 | 222,Affine_3to5,2.994796495781,3.1447714434504617,3.0,3.0,2.691310914642303,3.0,2.9259660243988037,3.0,1000.0,5.0,3.0 225 | 223,Affine,4.870772883050646,5.0,5.0,5.0,4.988779489723266,5.0,4.649651050567627,5.0,1000.0,5.0,5.0 226 | 224,Affine,8.9205066252749,10.0,9.0,10.0,10.373987275325682,10.0,8.27966022491455,9.0,1000.0,10.0,10.0 227 | 225,Affine,14.932677768504199,20.0,15.0,20.0,19.954226091976324,20.0,13.305989265441895,14.0,1000.0,20.0,20.0 228 | 226,Nonlinear_4to6,4.008294263489492,4.078703000165725,4.0,5.0,3.0463753540380396,5.0,3.676079273223877,4.0,1000.0,6.0,4.0 229 | 227,Nonlinear,4.19867549818456,3.8799834668020217,4.0,5.0,7.528959330306827,8.0,3.8786685466766357,4.0,1000.0,8.0,4.0 230 | 228,Nonlinear,6.37445034661789,6.321978654020311,6.0,8.0,10.623219017315908,12.0,5.841892719268799,6.0,1000.0,36.0,6.0 231 | 229,Nonlinear,8.391177469152195,9.119884625783103,8.0,9.0,14.38061849822592,16.0,7.349371910095215,7.0,1000.0,64.0,8.0 232 | 230,Nonlinear,12.095605305916653,15.272080006633015,12.0,15.0,22.556881998399195,24.0,11.145633697509766,11.0,1000.0,72.0,12.0 233 | 231,Spiral,1.767787548983401,2.093598967720807,1.0,1.0,2.025436091191528,2.0,1.0380127429962158,1.0,1000.0,3.0,1.0 234 | 232,Spiral,1.7716343469124127,1.7626176435562164,1.0,1.0,1.9928660528735955,2.0,1.0548264980316162,1.0,1000.0,13.0,1.0 235 | 233,Helix1d,1.0003722554255088,1.037440642451732,1.0,1.0,2.7193440423383457,3.0,0.931479811668396,1.0,1000.0,3.0,1.0 236 | 234,Helix1d,1.0251330137333219,1.1440247336560008,1.0,1.0,2.6883375244104926,3.0,1.0254392623901367,1.0,1000.0,13.0,1.0 237 | 235,Helix2d,2.9058565833851313,3.0,3.0,3.0,2.2986981543135023,3.0,2.0116467475891113,2.0,1000.0,3.0,2.0 238 | 236,Helix2d,2.8008903304192905,3.721387629960127,2.0,3.0,2.303592050645093,3.0,2.015435218811035,2.0,1000.0,13.0,2.0 239 | 237,Helicoid,2.0708556036358634,1.9805834475758306,2.0,2.0,2.3249275138519967,3.0,2.1174378395080566,2.0,1000.0,3.0,2.0 240 | 238,Helicoid,2.1216590380783367,2.0886671696245913,2.0,2.0,2.1939021319452876,3.0,2.0057427883148193,2.0,1000.0,13.0,2.0 241 | 239,Roll,2.0533019020580787,2.0508110237330155,2.0,2.0,2.746111303625106,3.0,2.039008378982544,2.0,1000.0,3.0,2.0 242 | 240,Roll,2.0167089019951283,1.9075665655504899,2.0,2.0,2.749619184493885,3.0,2.0149295330047607,2.0,1000.0,13.0,2.0 243 | 241,Scurve,2.050605031489731,2.056662691973039,2.0,2.0,1.9977280210741424,3.0,2.0950210094451904,2.0,1000.0,3.0,2.0 244 | 242,Scurve,2.0226465244465768,2.0858093897090035,2.0,2.0,1.9720364972957585,3.0,1.8436980247497559,2.0,1000.0,13.0,2.0 245 | 243,Moebius,2.0867734003066496,2.0162481435111523,2.0,2.0,2.0641435325809443,2.0,1.9653748273849487,2.0,1000.0,3.0,2.0 246 | 244,Paraboloid,2.7799260862778303,2.8226210504000253,3.0,3.0,1.78848146787691,1.0,2.2664737701416016,2.0,1000.0,12.0,3.0 247 | 245,Paraboloid,4.696227890051659,5.66384989170359,5.0,6.0,1.4565781772693798,1.0,3.0938570499420166,3.0,1000.0,21.0,6.0 248 | 246,Paraboloid,5.829499120790941,8.764265264633908,6.0,8.0,1.3121584100089838,1.0,2.7039597034454346,3.0,1000.0,30.0,9.0 249 | 247,Paraboloid,6.668195289831134,11.535950565256792,7.0,8.0,1.2367298073358197,1.0,2.942725658416748,3.0,1000.0,39.0,12.0 250 | 248,Paraboloid,7.016132456094211,14.441691950828584,7.0,9.0,1.1679406405379273,1.0,3.1241471767425537,3.0,1000.0,48.0,15.0 251 | 249,Cubic,3.053949619977264,3.2185130975713228,3.0,4.0,3.95831703926558,4.0,2.9916296005249023,3.0,1000.0,5.0,3.0 252 | 250,Cubic,19.932402745042477,31.98560754027122,21.0,32.0,32.251046412977644,31.0,19.37272071838379,21.0,1000.0,35.0,30.0 253 | 251,Cubic,33.93140537480208,75.08723873934935,36.0,72.0,67.89323277001243,71.0,31.34124183654785,34.0,1000.0,90.0,70.0 254 | 252,Sphere,2.9955139712275662,3.0425044716136234,3.0,3.0,3.937742542940842,4.0,2.8821611404418945,3.0,1000.0,5.0,3.0 255 | 253,Sphere,4.688423277739854,4.783238666784499,5.0,6.0,6.037040011171584,6.0,4.824970722198486,5.0,1000.0,10.0,5.0 256 | 254,Sphere,8.354867024478107,9.133057423669394,8.0,10.0,10.541517299266536,11.0,8.820335388183594,9.0,1000.0,15.0,10.0 257 | 255,Sphere,19.70275998997594,28.823119925514103,21.0,29.0,30.99826971954194,31.0,20.34808921813965,23.0,1000.0,35.0,30.0 258 | 256,Sphere,28.231606958722285,48.97284842417361,30.0,49.0,49.312463978525464,51.0,31.00775718688965,33.0,1000.0,55.0,50.0 259 | 257,Sphere,34.81949315732714,67.53108996271042,37.0,71.0,71.688539734973,71.0,39.667789459228516,42.0,1000.0,75.0,70.0 260 | 258,Affine_3to5,3.0420874040683357,3.1504310217683806,3.0,3.0,2.5480050784401445,3.0,2.9829838275909424,3.0,1000.0,5.0,3.0 261 | 259,Affine,4.921179876753286,5.0,5.0,5.0,5.124613438677902,5.0,4.802973747253418,5.0,1000.0,5.0,5.0 262 | 260,Affine,8.935738230234884,10.0,9.0,10.0,9.951162752588314,10.0,8.566828727722168,9.0,1000.0,10.0,10.0 263 | 261,Affine,14.682592162047772,20.0,15.0,20.0,20.088884687909488,20.0,13.744309425354004,14.0,1000.0,20.0,20.0 264 | 262,Nonlinear_4to6,4.009416745477706,4.031813847795715,4.0,5.0,3.060569101943558,5.0,3.8363053798675537,4.0,1000.0,6.0,4.0 265 | 263,Nonlinear,4.08538353638159,3.7588804772178737,4.0,5.0,7.221472309271105,8.0,3.823915481567383,4.0,1000.0,8.0,4.0 266 | 264,Nonlinear,6.357131356063904,6.577586301940085,6.0,8.0,10.97454229824964,12.0,5.939971446990967,6.0,1000.0,36.0,6.0 267 | 265,Nonlinear,8.386179574882696,9.086976114717075,8.0,10.0,14.127571885864809,16.0,7.57902193069458,8.0,1000.0,64.0,8.0 268 | 266,Nonlinear,12.42370754438499,15.036794167209257,12.0,17.0,21.5481208501311,24.0,11.40723991394043,11.0,1000.0,72.0,12.0 269 | 267,Spiral,1.7527015327504027,1.9914201484339447,1.0,1.0,2.041469526638065,2.0,0.9610950946807861,1.0,1000.0,3.0,1.0 270 | 268,Spiral,1.7541402139570919,1.7804613169382901,1.0,1.0,2.070209799208121,2.0,1.0550600290298462,1.0,1000.0,13.0,1.0 271 | 269,Helix1d,1.0253994397254607,1.1252435929260545,1.0,1.0,2.7298819209596052,3.0,0.97653728723526,1.0,1000.0,3.0,1.0 272 | 270,Helix1d,1.0128588213965615,0.9381749656003385,1.0,1.0,2.6953530056549297,3.0,0.9686862826347351,1.0,1000.0,13.0,1.0 273 | 271,Helix2d,2.829621753459437,2.7149657252991872,3.0,3.0,2.3542778516522485,3.0,2.008883237838745,2.0,1000.0,3.0,2.0 274 | 272,Helix2d,2.850014473220015,3.457625689515546,2.0,3.0,2.3390072531244277,3.0,1.9721744060516357,2.0,1000.0,13.0,2.0 275 | 273,Helicoid,2.100301120620609,1.9989846893709085,2.0,2.0,2.182961716985499,3.0,2.014737129211426,2.0,1000.0,3.0,2.0 276 | 274,Helicoid,2.099864027220343,2.080683427822655,2.0,2.0,2.1817924578640926,3.0,2.0062949657440186,2.0,1000.0,13.0,2.0 277 | 275,Roll,2.020583687602598,2.076448501074238,2.0,2.0,2.7295673295442873,3.0,1.953583836555481,2.0,1000.0,3.0,2.0 278 | 276,Roll,2.046136467530154,2.191417514566503,2.0,2.0,2.7315326114453944,3.0,1.9294028282165527,2.0,1000.0,13.0,2.0 279 | 277,Scurve,1.9707193945660353,1.9450634188374174,2.0,2.0,1.9661563412603098,3.0,1.9871721267700195,2.0,1000.0,3.0,2.0 280 | 278,Scurve,2.050571010152466,2.017814782355019,2.0,2.0,1.982734872206962,3.0,2.1109142303466797,2.0,1000.0,13.0,2.0 281 | 279,Moebius,2.0955421734918414,1.9702268540492316,2.0,2.0,2.1723566800598033,2.0,1.9827839136123657,2.0,1000.0,3.0,2.0 282 | 280,Paraboloid,2.826659511718738,3.0381159329074405,3.0,3.0,1.7865639035806131,1.0,2.314101219177246,2.0,1000.0,12.0,3.0 283 | 281,Paraboloid,4.73496815420243,5.749572114421951,5.0,6.0,1.482682511675802,1.0,2.6436049938201904,3.0,1000.0,21.0,6.0 284 | 282,Paraboloid,5.851714219847509,8.250712179144513,6.0,8.0,1.3142913980630893,1.0,3.0644114017486572,3.0,1000.0,30.0,9.0 285 | 283,Paraboloid,6.709497021061836,12.04673469761547,7.0,9.0,1.2338312138362046,1.0,3.0295004844665527,3.0,1000.0,39.0,12.0 286 | 284,Paraboloid,6.80797768637442,13.369907476038302,7.0,9.0,1.1538184169924819,1.0,3.6850991249084473,3.0,1000.0,48.0,15.0 287 | 285,Cubic,3.014999907650399,3.0797983956004105,3.0,3.0,4.1076919513783,4.0,2.797050952911377,3.0,1000.0,5.0,3.0 288 | 286,Cubic,19.732101574735314,31.416928489027654,20.0,32.0,31.515296105158516,31.0,19.48583221435547,20.0,1000.0,35.0,30.0 289 | 287,Cubic,33.81688062717952,77.63054589002793,36.0,75.0,71.7535059828306,71.0,32.09937286376953,35.0,1000.0,90.0,70.0 290 | 288,Sphere,3.0643615138944567,3.13977470450539,3.0,3.0,3.9621915982512244,4.0,3.0560643672943115,3.0,1000.0,5.0,3.0 291 | 289,Sphere,4.642115494938936,4.596897056567838,5.0,6.0,6.024564499376385,6.0,4.80794095993042,5.0,1000.0,10.0,5.0 292 | 290,Sphere,8.225716362175008,8.49256827110551,9.0,11.0,10.845065727704931,11.0,9.424631118774414,9.0,1000.0,15.0,10.0 293 | 291,Sphere,19.32184934601243,27.631748410793023,20.0,29.0,30.737084895409307,31.0,21.004993438720703,21.0,1000.0,35.0,30.0 294 | 292,Sphere,28.403617727671982,49.82868480085674,29.0,49.0,50.43499243553703,51.0,28.2808895111084,31.0,1000.0,55.0,50.0 295 | 293,Sphere,35.34271300777438,67.2033619377258,37.0,70.0,69.77915272349762,71.0,38.78868103027344,39.0,1000.0,75.0,70.0 296 | 294,Affine_3to5,3.0356283623375098,3.1994573201265393,3.0,3.0,2.6166283184814842,3.0,3.018522024154663,3.0,1000.0,5.0,3.0 297 | 295,Affine,4.975489527673147,5.0,5.0,5.0,4.988999466857544,5.0,4.6331610679626465,5.0,1000.0,5.0,5.0 298 | 296,Affine,8.941396863975745,10.0,9.0,10.0,10.190355865048726,10.0,8.117391586303711,9.0,1000.0,10.0,10.0 299 | 297,Affine,14.638309015473968,20.0,15.0,19.0,20.659782956731885,20.0,13.761070251464844,14.0,1000.0,20.0,20.0 300 | 298,Nonlinear_4to6,4.005703524841171,4.060279012946528,4.0,6.0,3.1685762687261847,5.0,3.772655963897705,4.0,1000.0,6.0,4.0 301 | 299,Nonlinear,4.190299762443525,3.926864790533505,4.0,5.0,7.106905242866779,8.0,4.053131103515625,4.0,1000.0,8.0,4.0 302 | 300,Nonlinear,6.263368901713227,6.1314859165870965,6.0,7.0,11.41841000989455,12.0,5.8362507820129395,6.0,1000.0,36.0,6.0 303 | 301,Nonlinear,8.324034695719524,9.391369691872978,8.0,10.0,14.541295715936888,16.0,7.72850227355957,8.0,1000.0,64.0,8.0 304 | 302,Nonlinear,12.401531528787443,14.657241107476585,12.0,16.0,22.589766198020985,24.0,10.698650360107422,11.0,1000.0,72.0,12.0 305 | 303,Spiral,1.799230948947642,2.248703165178092,1.0,1.0,2.0557529255742306,2.0,1.0165438652038574,1.0,1000.0,3.0,1.0 306 | 304,Spiral,1.7426167201385012,1.8541852209778658,1.0,1.0,2.0613419383876583,2.0,1.033031702041626,1.0,1000.0,13.0,1.0 307 | 305,Helix1d,1.020585940429027,1.0691368140916262,1.0,1.0,2.711129843828568,3.0,0.9981676340103149,1.0,1000.0,3.0,1.0 308 | 306,Helix1d,1.034608595724586,1.1185710593788345,1.0,1.0,2.6822069843193006,3.0,1.0053379535675049,1.0,1000.0,13.0,1.0 309 | 307,Helix2d,2.807489383574948,3.0,2.0,3.0,2.304358914583216,3.0,1.9578251838684082,2.0,1000.0,3.0,2.0 310 | 308,Helix2d,2.8736850037488186,3.5134312187292505,2.0,3.0,2.3319130784349644,3.0,1.8439863920211792,2.0,1000.0,13.0,2.0 311 | 309,Helicoid,2.126584113265523,2.0952669917325686,2.0,2.0,2.2195619962491584,3.0,2.105626106262207,2.0,1000.0,3.0,2.0 312 | 310,Helicoid,2.071876974971419,2.0216503034236832,2.0,2.0,2.2729446594654688,3.0,1.9572125673294067,2.0,1000.0,13.0,2.0 313 | 311,Roll,2.018973155177934,1.9158399880912065,2.0,2.0,2.78013616126145,3.0,1.97622549533844,2.0,1000.0,3.0,2.0 314 | 312,Roll,2.049299170692064,2.229089789824393,2.0,2.0,2.7999417491335357,3.0,1.942459225654602,2.0,1000.0,13.0,2.0 315 | 313,Scurve,2.0148195681926344,2.0360065634059477,2.0,2.0,1.9887339734596432,3.0,2.0459868907928467,2.0,1000.0,3.0,2.0 316 | 314,Scurve,2.017843906476827,2.0671245130665,2.0,2.0,1.9584385229150754,3.0,2.017350196838379,2.0,1000.0,13.0,2.0 317 | 315,Moebius,2.1100160028888837,1.9834970632020095,2.0,2.0,2.1720168180587205,2.0,1.99403977394104,2.0,1000.0,3.0,2.0 318 | 316,Paraboloid,2.838739300745487,2.9812369955386036,3.0,3.0,1.7867167084547488,1.0,2.153740644454956,2.0,1000.0,12.0,3.0 319 | 317,Paraboloid,4.741460480748037,5.670171060916473,5.0,7.0,1.4826340234042263,1.0,2.2389845848083496,2.0,1000.0,21.0,6.0 320 | 318,Paraboloid,5.862774486440219,8.682937782713958,6.0,8.0,1.3096457403270605,1.0,3.311833143234253,3.0,1000.0,30.0,9.0 321 | 319,Paraboloid,6.47033782794489,11.605784251385037,7.0,8.0,1.2252147045110784,1.0,3.162842035293579,3.0,1000.0,39.0,12.0 322 | 320,Paraboloid,6.927171431178355,14.110006337713276,7.0,9.0,1.1610327773162583,1.0,2.7435824871063232,2.0,1000.0,48.0,15.0 323 | 321,Cubic,3.1007097062441034,3.2089671279716034,3.0,4.0,3.9771293646004815,4.0,2.9002301692962646,3.0,1000.0,5.0,3.0 324 | 322,Cubic,20.01931347943842,30.642814415606598,21.0,31.0,31.785355418267812,31.0,20.26667594909668,21.0,1000.0,35.0,30.0 325 | 323,Cubic,33.62766565175205,73.54959521207971,36.0,74.0,69.80085683763525,71.0,31.43366050720215,34.0,1000.0,90.0,70.0 326 | 324,Sphere,3.0044506972597276,3.0913260269194347,3.0,3.0,4.048219284487116,4.0,2.899837017059326,3.0,1000.0,5.0,3.0 327 | 325,Sphere,4.728665658484506,4.899396033974952,5.0,6.0,5.88983489491552,6.0,4.59906530380249,5.0,1000.0,10.0,5.0 328 | 326,Sphere,8.220437860099572,8.443541594677388,8.0,10.0,11.168550220882848,11.0,8.451441764831543,9.0,1000.0,15.0,10.0 329 | 327,Sphere,19.63629310142389,29.321859899855617,20.0,29.0,30.590566705879517,31.0,21.240093231201172,21.0,1000.0,35.0,30.0 330 | 328,Sphere,28.61144804454233,50.00311268851761,29.0,48.0,51.11061397902123,51.0,28.967777252197266,31.0,1000.0,55.0,50.0 331 | 329,Sphere,36.042424958306405,71.13294496641842,38.0,70.0,71.81328647753521,71.0,39.506465911865234,41.0,1000.0,75.0,70.0 332 | 330,Affine_3to5,3.0271643933072427,3.1858960738819913,3.0,3.0,2.6107884317246484,3.0,2.940922260284424,3.0,1000.0,5.0,3.0 333 | 331,Affine,4.893914639397854,5.0,5.0,5.0,4.995819097325253,5.0,4.741634368896484,5.0,1000.0,5.0,5.0 334 | 332,Affine,8.995952575454323,10.0,9.0,10.0,9.71779100324284,10.0,8.275619506835938,9.0,1000.0,10.0,10.0 335 | 333,Affine,14.905403510287892,20.0,16.0,19.0,20.220375557964434,20.0,13.725573539733887,15.0,1000.0,20.0,20.0 336 | 334,Nonlinear_4to6,4.028001406657169,4.087569451808198,4.0,5.0,3.09833260911985,5.0,3.890782356262207,4.0,1000.0,6.0,4.0 337 | 335,Nonlinear,4.095762865969628,3.7723353468967225,4.0,5.0,7.14674523617343,8.0,3.9020445346832275,4.0,1000.0,8.0,4.0 338 | 336,Nonlinear,6.2530003403534185,6.088203834441965,6.0,8.0,10.822015294968546,12.0,5.787625312805176,6.0,1000.0,36.0,6.0 339 | 337,Nonlinear,8.624657095866791,9.14000912273082,9.0,10.0,14.855393509080114,16.0,7.6600117683410645,8.0,1000.0,64.0,8.0 340 | 338,Nonlinear,12.330481928079573,14.629034806066688,13.0,14.0,21.844627449842907,24.0,10.984440803527832,11.0,1000.0,72.0,12.0 341 | 339,Spiral,1.7462428617554453,2.1254479982455567,1.0,1.0,2.020414315762477,2.0,1.0353726148605347,1.0,1000.0,3.0,1.0 342 | 340,Spiral,1.715035251686395,1.7885457454334248,1.0,1.0,2.022542843396603,2.0,0.9780269861221313,1.0,1000.0,13.0,1.0 343 | 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2,0.2850560846560846,0.15375802469135802,0.2572934744268078,0.243736860670194,0.38105784832451506,0.4249065255731922,0.3192232804232804,0.36748359788359786,0.02 5 | 3,0.2895354497354497,0.1769283950617284,0.2958007054673721,0.3789537918871252,0.3842134038800705,0.4260176366843033,0.39106137566137567,0.43496931216931217,0.03 6 | 4,0.3282761904761905,0.22653439153439156,0.3649456790123457,0.47090652557319224,0.38706208112874785,0.42700176366843035,0.4457449735449735,0.5011068783068783,0.04 7 | 5,0.376494885361552,0.2739012345679012,0.42085361552028216,0.49864409171075835,0.3882853615520282,0.4295837742504409,0.4985940035273369,0.5374179894179894,0.05 8 | -------------------------------------------------------------------------------- /paper/result/result_noise_mpe_new.csv: -------------------------------------------------------------------------------- 1 | MLE,GeoMLE,MIND,DANCo,ESS,PCA,CD,Hein,noise 2 | 0,0.2687622574955908,0.13158765432098765,0.24680035273368603,0.16593544973544974,0.38375308641975303,0.4237954144620811,0.19084726631393298,0.18027865961199294,0.0 3 | 1,0.2687622574955908,0.1271710758377425,0.263921340388007,0.20445396825396825,0.38101022927689593,0.4237954144620811,0.23428924162257495,0.2783611992945326,0.01 4 | 2,0.2673590828924162,0.17137425044091711,0.2853492063492063,0.22751746031746034,0.38228218694885363,0.4260176366843033,0.3288991181657848,0.3663767195767196,0.02 5 | 3,0.26665214002267573,0.16520727040816327,0.29264774659863946,0.26219281462585037,0.3813081065759637,0.42531533446712017,0.394094387755102,0.43648171768707483,0.03 6 | 4,0.31538342151675486,0.2246652557319224,0.33233650793650793,0.30844514991181654,0.3856514991181657,0.42790970017636687,0.43354497354497357,0.5092550264550265,0.04 7 | 5,0.3193082892416226,0.27636261022927694,0.3899746031746032,0.3582589065255732,0.3863753086419753,0.4309911816578483,0.4826712522045855,0.5348239858906526,0.05 8 | -------------------------------------------------------------------------------- /paper/result/result_noise_std.csv: -------------------------------------------------------------------------------- 1 | MLE,GeoMLE,MIND,DANCo,ESS,PCA,CD,Hein,noise 2 | 0,0.016786251001565444,0.013162429532947353,0.012667591943601071,0.010433447789732627,0.034352399063823785,0.033914982949080456,0.015942284024210985,0.015525458590994386,0.0 3 | 1,0.01687919209884618,0.01654902053178338,0.014907170336393955,0.014415849555723191,0.03437209556786778,0.033914982949080456,0.023925648534043345,0.03227758816919596,0.01 4 | 2,0.01806850218674539,0.017597103590411358,0.019422522355030336,0.02444709652042134,0.03444021658895642,0.03390779632250655,0.03844616440545855,0.05167986281501356,0.02 5 | 3,0.017946603032672547,0.019077650820485775,0.02495689003677085,0.0466412823330911,0.03448112750330485,0.03390044631747289,0.04901784072145023,0.06035550380377816,0.03 6 | 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2,0.017867274653664746,0.018259259639472832,0.01841612277346496,0.018656563842744715,0.03440017989565459,0.03390044631747289,0.0415082795675866,0.05165056776988977,0.02 5 | 3,0.018091349350564122,0.018073063275971423,0.018332169296735836,0.021511896566431193,0.03459182601444027,0.03405670592458059,0.05023938518950365,0.060647084649723994,0.03 6 | 4,0.018654591942592006,0.02185743515574005,0.020127950398249692,0.025377203492790868,0.03429626157648437,0.03380444821885487,0.05183285852571681,0.06493639305664249,0.04 7 | 5,0.01849563648141103,0.029013828464024203,0.025593981024104935,0.030485941780337096,0.03445951605223555,0.03366171413731226,0.05647173761082323,0.06794561173673748,0.05 8 | -------------------------------------------------------------------------------- /paper/result/result_sphere.csv: -------------------------------------------------------------------------------- 1 | Dataset,MLE,GeoMLE,MIND,DANCo,ESS,PCA,CD,Hein,Num,Dim,RealDim 2 | 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123,Sphere,2.9191019535064697,39.362680435180664,1.6175878047943115,29.19823980331421,2.2821359634399414,0.003746509552001953,3.067751169204712,3.078775405883789,7500.0,11.0,10.0 126 | 124,Sphere,3.322096824645996,40.72757291793823,1.187157392501831,21.015491247177124,2.5832936763763428,0.003945589065551758,3.4909427165985107,3.4849853515625,8000.0,11.0,10.0 127 | 125,Sphere,3.6784493923187256,40.121463775634766,1.2542474269866943,22.082627296447754,2.790487051010132,0.004172563552856445,3.918764591217041,3.917865514755249,8500.0,11.0,10.0 128 | 126,Sphere,3.910421848297119,45.50800919532776,1.3599655628204346,23.472126483917236,3.2502498626708984,0.004328250885009766,4.380611181259155,4.3776044845581055,9000.0,11.0,10.0 129 | 127,Sphere,4.271763801574707,44.641743898391724,1.5446174144744873,25.056960105895996,3.5391383171081543,0.004548311233520508,4.871017217636108,4.873099088668823,9500.0,11.0,10.0 130 | 128,Sphere,4.583971738815308,44.29523491859436,1.562039852142334,26.05546522140503,3.92533802986145,0.004743099212646484,5.386534214019775,5.387058258056641,10000.0,11.0,10.0 131 | -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | numpy>=1.13.1 2 | scikit-learn>=0.18 3 | pandas>=0.19 4 | 5 | # If you don't want to work with real data, you should to comment below packages. 6 | 7 | # scipy 8 | # zipfile 9 | # PIL 10 | # io 11 | # os 12 | -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | from setuptools import setup 2 | 3 | setup(name='geomle', 4 | version='1.0', 5 | description='Intrinsic dimension', 6 | url='https://github.com/premolab/GeoMLE', 7 | author='Mokrov, Gomtsyan, Panov, Yanovich', 8 | author_email='panov.maxim@gmail.com ', 9 | license='MIT', 10 | packages=['geomle'], 11 | install_requires=[ 12 | 'numpy>=1.13.1', 13 | 'scikit-learn>=0.18', 14 | 'pandas>=0.19', 15 | ], 16 | zip_safe=False) -------------------------------------------------------------------------------- /tests/test_geomle.py: -------------------------------------------------------------------------------- 1 | import pytest 2 | from geomle import DataGenerator, mle, geomle 3 | 4 | def test_mle(): 5 | DG = DataGenerator() 6 | data = DG.gen_data('Sphere', 1000, 2, 1) 7 | res = mle(data)[0].mean() 8 | assert abs(res - 1) < 0.2 9 | 10 | def test_geomle(): 11 | DG = DataGenerator() 12 | data = DG.gen_data('Sphere', 1000, 2, 1) 13 | res = geomle(data).mean() 14 | assert abs(res - 1) < 0.2 15 | --------------------------------------------------------------------------------