├── README.rst ├── plotting.py ├── chaos_detection.py └── LICENSE /README.rst: -------------------------------------------------------------------------------- 1 | .. image:: https://raw.githubusercontent.com/giotto-ai/giotto-tda/master/doc/images/tda_logo.svg 2 | :width: 850 3 | 4 | Noise-to-signal 5 | =============== 6 | The notebook contains a pipeline to build noise detection features on psuedo-periodic signals. 7 | 8 | We consider the problem of predicting regime changes under noise in time series data. 9 | Access the full story in the `blog post 10 | `_ on towards data science 11 | 12 | Task: 13 | ----- 14 | We consider the problem of predicting regime changes under noise in time series data. 15 | Recover the orange signal from the blue one. 16 | 17 | .. image:: https://miro.medium.com/max/1878/1*RtxU-EpeU_7OULHN6u9MHQ.png 18 | :width: 500 19 | 20 | Below is the Duffing oscilator which is the circuit we used to generate the blue signal. The blue signal is obtained by varying the A parameter in the duffing oscillator. We then add noise to it. 21 | 22 | .. image:: https://miro.medium.com/max/581/1*S2M-M-Yov523gC9qTUR_mQ.png 23 | :width: 500 24 | 25 | Features to isolate the signal: 26 | =============================== 27 | To get an idea of which feature sets are the best to predict regime changes we build four models to perform a binary classification task. Each model is built using a different set of features: two sets of features without TDA, one using only TDA features, and one with all the combined features. 28 | 29 | Performance of TDA features: 30 | ---------------------------- 31 | In the high noise regime TDA features yielded a significant performance boost over standard feature strategies. TDA not only outperforms the standard strategies alone, it provides a clear performance boost on top of standard strategies when the two are combined. 32 | 33 | .. image:: https://miro.medium.com/max/1132/1*_z6KNahraO6nhzBtK2If4g.png 34 | :width: 500 35 | 36 | TDA Features: 37 | ------------- 38 | - Total number of holes: for every time window we calculate a persistence diagram. It allows us to build the Betti surface counts the number of holes present in the data as a function of epsilon and time. 39 | - Relevant holes feature: the relevant holes feature counts the number of holes over a given threshold size (more than 70% of the maximum value). 40 | - Amplitude of the diagram feature: we use the diagram norm as measure of the total persistence of all the holes in the diagram. 41 | - Mean support feature: the mean of the epsilon distances yielding non-zero Betti values in the Betti surface. 42 | - ArgMax feature: the argmax feature is the value of epsilon for which the Betti number was highest for each time window. 43 | - Average lifetime feature: for each dimension we take the average lifetime of a hole in the persistence diagram (=Betti surface at a fixed time). 44 | 45 | .. image:: https://miro.medium.com/max/939/1*yfrKsJqxLKqG-qsJcMTipw.png 46 | :width: 500 47 | 48 | Full pipeline: 49 | -------------- 50 | 51 | .. image:: https://miro.medium.com/max/720/1*ikqaEipVCg3X7os2FsKl6Q.png 52 | 53 | 54 | Feature creation: 55 | ----------------- 56 | In order to create the TDA features, we embed our time-series into a higher dimensional space using the Takens’ embedding. Each step of the rolling window is converted into a single vector in higher-dimensional space (the dimension of which is the size of the window). 57 | 58 | .. image:: https://miro.medium.com/max/4000/1*8JoVsvYk8w5CJRfTUCbA5Q.gif 59 | :width: 500 60 | 61 | 62 | 63 | 64 | 65 | -------------------------------------------------------------------------------- /plotting.py: -------------------------------------------------------------------------------- 1 | """Plot functions """ 2 | 3 | import numpy as np 4 | import plotly.graph_objs as gobj 5 | from giotto.diagrams._utils import _subdiagrams 6 | 7 | 8 | def plot_point_cloud(point_cloud, dimension=None): 9 | """Plot the first 2 or 3 coordinates of the point cloud. 10 | 11 | This function will not work on 1-dimensional arrays. 12 | 13 | Parameters 14 | ---------- 15 | point_cloud : ndarray, shape (n_samples, n_dimensions) 16 | Data points to be represented in a 2D or 3D scatter plot. Only the 17 | first 2 or 3 dimensions will be considered for plotting. 18 | 19 | dimension : int or None, default : ``None`` 20 | This parameter sets the dimension of the resulting plot. If ``None``, 21 | the dimension will be chosen between 2 and 3 depending on 22 | ``n_dimensions`` see Input). 23 | 24 | """ 25 | if dimension is None: 26 | dimension = np.min((3, point_cloud.shape[1])) 27 | 28 | # Check consistency between point_cloud and dimension 29 | if point_cloud.shape[1] < dimension: 30 | raise ValueError("Not enough dimensions available in the input point" 31 | "cloud.") 32 | 33 | if dimension == 2: 34 | layout = { 35 | "title": "Point Cloud", 36 | "width": 800, 37 | "height": 800, 38 | "xaxis1": { 39 | "title": "First coordinate", 40 | "side": "bottom", 41 | "type": "linear", 42 | "ticks": "outside", 43 | "anchor": "x1", 44 | "showline": True, 45 | "zeroline": True, 46 | "showexponent": "all", 47 | "exponentformat": "e" 48 | }, 49 | "yaxis1": { 50 | "title": "Second coordinate", 51 | "side": "left", 52 | "type": "linear", 53 | "ticks": "outside", 54 | "anchor": "y1", 55 | "showline": True, 56 | "zeroline": True, 57 | "showexponent": "all", 58 | "exponentformat": "e" 59 | }, 60 | "plot_bgcolor": "white" 61 | } 62 | 63 | fig = gobj.Figure(layout=layout) 64 | fig.update_xaxes(zeroline=True, linewidth=1, linecolor='black', 65 | mirror=False) 66 | fig.update_yaxes(zeroline=True, linewidth=1, linecolor='black', 67 | mirror=False) 68 | 69 | fig.add_trace(gobj.Scatter(x=point_cloud[:, 0], 70 | y=point_cloud[:, 1], 71 | mode='markers', 72 | marker=dict(size=4, 73 | color=list(range( 74 | point_cloud.shape[0])), 75 | colorscale='Viridis', 76 | opacity=0.8))) 77 | fig.show() 78 | elif dimension == 3: 79 | 80 | scene = { 81 | "xaxis": { 82 | "title": "First coordinate", 83 | "type": "linear", 84 | "showexponent": "all", 85 | "exponentformat": "e" 86 | }, 87 | "yaxis": { 88 | "title": "Second coordinate", 89 | "type": "linear", 90 | "showexponent": "all", 91 | "exponentformat": "e" 92 | }, 93 | "zaxis": { 94 | "title": "Third coordinate", 95 | "type": "linear", 96 | "showexponent": "all", 97 | "exponentformat": "e" 98 | } 99 | } 100 | 101 | fig = gobj.Figure() 102 | fig.update_layout(scene=scene, title="Point cloud") 103 | 104 | fig.add_trace(gobj.Scatter3d(x=point_cloud[:, 0], 105 | y=point_cloud[:, 1], 106 | z=point_cloud[:, 2], 107 | mode='markers', 108 | marker=dict(size=4, 109 | color=list(range( 110 | point_cloud.shape[0])), 111 | colorscale='Viridis', 112 | opacity=0.8))) 113 | 114 | fig.show() 115 | else: 116 | raise ValueError("The value of the dimension is different from 2 or 3") 117 | 118 | 119 | def plot_diagram(diagram, homology_dimensions=None): 120 | """Plot a single persistence diagram. 121 | 122 | Parameters 123 | ---------- 124 | diagram : ndarray, shape (n_points, 3) 125 | The persistence diagram to plot, where the third dimension along axis 1 126 | contains homology dimensions, and the other two contain (birth, death) 127 | pairs to be used as coordinates in the two-dimensional plot. 128 | 129 | homology_dimensions : list of int or None, default: ``None`` 130 | Homology dimensions which will appear on the plot. If ``None``, all 131 | homology dimensions which appear in `diagram` will be plotted. 132 | 133 | """ 134 | if homology_dimensions is None: 135 | homology_dimensions = np.unique(diagram[:, 2]) 136 | 137 | maximum_persistence = np.where(np.isinf(diagram), -np.inf, diagram).max() 138 | 139 | layout = { 140 | "title": "Persistence diagram", 141 | "width": 500, 142 | "height": 500, 143 | "xaxis1": { 144 | "title": "Birth", 145 | "side": "bottom", 146 | "type": "linear", 147 | "range": [0, 1.1 * maximum_persistence], 148 | "ticks": "outside", 149 | "anchor": "y1", 150 | "showline": True, 151 | "zeroline": True, 152 | "showexponent": "all", 153 | "exponentformat": "e" 154 | }, 155 | "yaxis1": { 156 | "title": "Death", 157 | "side": "left", 158 | "type": "linear", 159 | "range": [0, 1.1 * maximum_persistence], 160 | "ticks": "outside", 161 | "anchor": "x1", 162 | "showline": True, 163 | "zeroline": True, 164 | "showexponent": "all", 165 | "exponentformat": "e" 166 | }, 167 | "plot_bgcolor": "white" 168 | } 169 | 170 | fig = gobj.Figure(layout=layout) 171 | fig.update_xaxes(zeroline=True, linewidth=1, linecolor='black', 172 | mirror=False) 173 | fig.update_yaxes(zeroline=True, linewidth=1, linecolor='black', 174 | mirror=False) 175 | 176 | fig.add_trace(gobj.Scatter(x=np.array([-100 * maximum_persistence, 177 | 100 * maximum_persistence]), 178 | y=np.array([-100 * maximum_persistence, 179 | 100 * maximum_persistence]), 180 | mode='lines', 181 | line=dict(dash='dash', width=1, color='black'), 182 | showlegend=False, hoverinfo='none')) 183 | 184 | for i, dimension in enumerate(homology_dimensions): 185 | name = f"H{int(dimension)}" 186 | subdiagram = _subdiagrams(np.asarray([diagram]), [dimension], 187 | remove_dim=True)[0] 188 | diff = (subdiagram[:, 1] != subdiagram[:, 0]) 189 | subdiagram = subdiagram[diff] 190 | fig.add_trace(gobj.Scatter(x=subdiagram[:, 0], y=subdiagram[:, 1], 191 | mode='markers', name=name)) 192 | 193 | fig.show() 194 | 195 | 196 | def plot_landscapes(landscapes, homology_dimensions=None, samplings=None): 197 | """Plot landscapes by homology dimension. 198 | 199 | Parameters 200 | ---------- 201 | landscapes : ndarray, shape (n_homology_dimension, n_layers, n_values) 202 | Collection of ``n_homology_dimension`` discretised persistence 203 | landscapes. Each landscape contains ``n_layers`` layers. Entry i along 204 | axis 0 should be the persistence landscape in homology dimension i. 205 | 206 | homology_dimensions : list of int or None, default: ``None`` 207 | Homology dimensions for which the Betti curves should be plotted. 208 | If ``None``, all available dimensions will be used. 209 | 210 | samplings : ndarray, shape (n_homology_dimension, n_layers, n_values), \ 211 | default: ``None`` 212 | For each homology dimension, (filtration parameter) values to be used 213 | on the x-axis against the corresponding values in `landscapes` on 214 | the y-axis. If ``None``, the samplings will start at 0 with step 1. 215 | 216 | """ 217 | if homology_dimensions is None: 218 | homology_dimensions = np.arange(0, landscapes.shape[0]) 219 | if samplings is None: 220 | samplings = np.arange(0, landscapes.shape[2]) 221 | layout = { 222 | "xaxis1": { 223 | "side": "bottom", 224 | "type": "linear", 225 | "ticks": "outside", 226 | "anchor": "y1", 227 | "showline": True, 228 | "zeroline": True, 229 | "showexponent": "all", 230 | "exponentformat": "e" 231 | }, 232 | "yaxis1": { 233 | "side": "left", 234 | "type": "linear", 235 | "ticks": "outside", 236 | "anchor": "x1", 237 | "showline": True, 238 | "zeroline": True, 239 | "showexponent": "all", 240 | "exponentformat": "e" 241 | }, 242 | "plot_bgcolor": "white" 243 | } 244 | 245 | for i, dimension in enumerate(homology_dimensions): 246 | layout_dim = layout.copy() 247 | layout_dim['title'] = f"Persistence landscape for homology dimension" \ 248 | f"{int(dimension)}" 249 | fig = gobj.Figure(layout=layout_dim) 250 | fig.update_xaxes(zeroline=True, linewidth=1, linecolor='black', 251 | mirror=False) 252 | fig.update_yaxes(zeroline=True, linewidth=1, linecolor='black', 253 | mirror=False) 254 | 255 | n_layers = landscapes.shape[1] 256 | for layer in range(n_layers): 257 | fig.add_trace(gobj.Scatter(x=samplings, 258 | y=landscapes[i, layer, :], 259 | mode='lines', showlegend=False, 260 | hoverinfo='none', 261 | name=f"layer {layer + 1}")) 262 | 263 | fig.show() 264 | 265 | 266 | def plot_betti_curves(betti_curves, homology_dimensions=None, samplings=None): 267 | """Plot the Betti curves of a single persistence diagram by homology 268 | dimension. 269 | 270 | Parameters 271 | ---------- 272 | betti_curves : ndarray, shape (n_homology_dimension, n_values) 273 | Collection of ``n_homology_dimension`` discretised Betti curves. 274 | Entry i along axis 0 should be the Betti curve in homology dimension i. 275 | 276 | homology_dimensions : list of int or None, default: ``None`` 277 | Homology dimensions for which the Betti curves should be plotted. 278 | If ``None``, all available dimensions will be used. 279 | 280 | samplings : ndarray, shape (n_homology_dimension, n_values), \ 281 | default: ``None`` 282 | For each homology dimension, (filtration parameter) values to be used 283 | on the x-axis against the corresponding values in `betti_curves` on 284 | the y-axis. If ``None``, the samplings will start at 0 with step 1. 285 | 286 | """ 287 | if homology_dimensions is None: 288 | homology_dimensions = np.arange(0, betti_curves.shape[0]) 289 | if samplings is None: 290 | samplings = np.arange(0, betti_curves.shape[1]) 291 | layout = { 292 | "title": "Betti curves", 293 | "xaxis1": { 294 | "title": "Epsilon", 295 | "side": "bottom", 296 | "type": "linear", 297 | "ticks": "outside", 298 | "anchor": "x1", 299 | "showline": True, 300 | "zeroline": True, 301 | "showexponent": "all", 302 | "exponentformat": "e" 303 | }, 304 | "yaxis1": { 305 | "title": "Betti number", 306 | "side": "left", 307 | "type": "linear", 308 | "ticks": "outside", 309 | "anchor": "y1", 310 | "showline": True, 311 | "zeroline": True, 312 | "showexponent": "all", 313 | "exponentformat": "e" 314 | }, 315 | "plot_bgcolor": "white" 316 | } 317 | fig = gobj.Figure(layout=layout) 318 | fig.update_xaxes(zeroline=True, linewidth=1, linecolor='black', 319 | mirror=False) 320 | fig.update_yaxes(zeroline=True, linewidth=1, linecolor='black', 321 | mirror=False) 322 | 323 | for i, dimension in enumerate(homology_dimensions): 324 | fig.add_trace(gobj.Scatter(x=samplings, 325 | y=betti_curves[i, :], 326 | mode='lines', showlegend=False, 327 | hoverinfo='none')) 328 | 329 | 330 | return fig 331 | 332 | 333 | def plot_betti_surfaces(betti_curves, samplings=None, 334 | homology_dimensions=None): 335 | """Plots the Betti surfaces (Betti numbers against time and filtration 336 | parameter) by homology dimension. 337 | 338 | Parameters 339 | ---------- 340 | betti_curves : ndarray, shape (n_samples, n_homology_dimensions, \ 341 | n_values) 342 | ``n_samples`` collections of discretised Betti curves. There are 343 | ``n_homology_dimension`` curves in each collection. Index i along axis 344 | 1 should yield all Betti curves in homology dimension i. 345 | 346 | homology_dimensions : list of int or None, default: ``None`` 347 | Homology dimensions for which the Betti surfaces should be plotted. 348 | If ``None``, all available dimensions will be used. 349 | 350 | samplings : ndarray, shape (n_homology_dimension, n_values), \ 351 | default: ``None`` 352 | For each homology dimension, (filtration parameter) values to be used 353 | on the x-axis against the corresponding values in `betti_curves` on the 354 | y-axis. If ``None``, the samplings will start at 0 with step 1. 355 | 356 | """ 357 | if homology_dimensions is None: 358 | homology_dimensions = np.arange(0, betti_curves.shape[1]) 359 | if samplings is None: 360 | samplings = np.arange(0, betti_curves.shape[2]) 361 | 362 | scene = { 363 | "xaxis": { 364 | "title": "Epsilon", 365 | "type": "linear", 366 | "showexponent": "all", 367 | "exponentformat": "e" 368 | }, 369 | "yaxis": { 370 | "title": "Time", 371 | "type": "linear", 372 | "showexponent": "all", 373 | "exponentformat": "e" 374 | }, 375 | "zaxis": { 376 | "title": "Betti number", 377 | "type": "linear", 378 | "showexponent": "all", 379 | "exponentformat": "e" 380 | } 381 | } 382 | if betti_curves.shape[0] == 1: 383 | plot_betti_curves(betti_curves[0], samplings, homology_dimensions) 384 | else: 385 | for i, dimension in enumerate(homology_dimensions): 386 | fig = gobj.Figure() 387 | fig.update_layout(scene=scene, title=f"Betti surface for homology " 388 | f"dimension {int(dimension)}") 389 | fig.add_trace(gobj.Surface(x=samplings, 390 | y=np.arange(betti_curves.shape[0]), 391 | z=betti_curves[:, i, :], 392 | connectgaps=True, hoverinfo='none')) 393 | 394 | fig.show() 395 | -------------------------------------------------------------------------------- /chaos_detection.py: -------------------------------------------------------------------------------- 1 | # General import 2 | import pandas as pd 3 | import numpy as np 4 | import os 5 | import sys 6 | 7 | # Giotto (use 'pip install giotto-learn' if you want to install it) 8 | import giotto as gt 9 | import giotto.time_series as ts 10 | import giotto.diagrams as diag 11 | import giotto.homology as hl 12 | 13 | 14 | # Plotting 15 | import matplotlib.pyplot as plt 16 | from plotting import plot_diagram, plot_landscapes 17 | from plotting import plot_betti_surfaces, plot_betti_curves 18 | from plotting import plot_point_cloud 19 | 20 | # Miscellaneous 21 | from itertools import product 22 | import plotly.express as px 23 | from pandarallel import pandarallel # to parallelize pandas functions 24 | from scipy.fftpack import rfft 25 | from functools import reduce 26 | import openml 27 | from openml.datasets.functions import get_dataset 28 | ####################################################################### 29 | 30 | # A helper function 31 | def concat_dfs(dfs): 32 | return reduce(lambda x, y: pd.concat([x, y]), dfs) 33 | 34 | 35 | def cm2inch(*tupl): 36 | inch = 2.54 37 | if isinstance(tupl[0], tuple): 38 | return tuple(i/inch for i in tupl[0]) 39 | else: 40 | return tuple(i/inch for i in tupl) 41 | 42 | 43 | def create_pred_df(pred, y_test, threshold=0.5, rolling_param=300): 44 | """ 45 | INPUT: 46 | pred: array 47 | y_test: list 48 | threshold: float 49 | rolling_param: int 50 | 51 | OUTPUT: 52 | pred_df: pandas DataFrame 53 | """ 54 | 55 | pred_df = pd.DataFrame() 56 | pred_df['pred'] = pred 57 | pred_df['ref'] = y_test 58 | pred_df['rolling'] = pred_df['pred'].rolling(rolling_param).mean() 59 | pred_df['indicator'] = pred_df['rolling'] > threshold 60 | pred_df = pred_df.dropna() 61 | return pred_df 62 | 63 | 64 | def plot_results(results, noise_level, x_tick_labels=None, return_figure=False, fig_size=(20, 15)): 65 | """ 66 | INPUT: 67 | results: array 68 | noise_level: list 69 | x_tick_labels: list 70 | return_figure: boolean 71 | figsize: in cm, tuple 72 | """ 73 | 74 | fig, ax = plt.subplots(figsize=(cm2inch(fig_size))) 75 | ax.plot(noise_level, results[:,0], '-', label='all features') 76 | ax.plot(noise_level, results[:,1], '-', label='TDA features only') 77 | ax.plot(noise_level, results[:,2], '-', label='no TDA features') 78 | # only features from the dynamical system itself 79 | ax.plot(noise_level, results[:,3], '-', label='intrinsic features only') 80 | ax.set_xlabel('Signal to Noise Ratio') 81 | ax.set_ylabel('Balanced Accuracy') 82 | if x_tick_labels is not None: 83 | ax.set_xticks(np.arange(0, len(x_tick_labels) / 10., 1 / 10)) 84 | ax.set_xticklabels([str(x) for x in np.round(x_tick_labels, 1)]) 85 | ax.legend() 86 | if return_figure == True: 87 | return fig 88 | 89 | 90 | def plot_predictions(pred, y_test): 91 | """ 92 | INPUT: 93 | pred: list 94 | y_test: list 95 | 96 | OUTPUT: 97 | None 98 | """ 99 | 100 | pred_df = create_pred_df(pred, y_test) 101 | fig= plt.figure(figsize=(20, 10)) 102 | plt.plot(y_test, c='blue', label='truth') 103 | plt.plot(pred_df['indicator'], c='red', alpha=0.5, label='prediction', linestyle='solid') 104 | plt.plot(pred_df['rolling'], c='green', alpha=0.5, label='rolling', linestyle='solid') 105 | plt.legend(loc='center left') 106 | 107 | 108 | def convert_to_SNR(time_series, noise_level): 109 | """ 110 | INPUT: 111 | time_series: list of time series 112 | noise_level: list of noise levels 113 | 114 | OUTPUT: 115 | SNR: list with noise levels converted to signal-to-noise ratio 116 | """ 117 | 118 | return [(ts['x'] ** 2).mean() / (noise_level ** 2) for ts in time_series[0]][0] 119 | 120 | 121 | def tda_diagrams(path, 122 | embedding_time_delay, 123 | embedding_dimension, 124 | window_width, 125 | window_stride, 126 | homology_dim=2, 127 | return_betti_surface=False): 128 | """ 129 | INPUT: 130 | path: int (number to OpenML dataset) 131 | embedder_time_delay: int 132 | embedding_dimension: int 133 | window_width: int 134 | window_stride: int 135 | homology_dim: int 136 | return_betti_surface: boolean 137 | 138 | OUTPUT: 139 | X_scaled: persistence diagrams 140 | df_betti_list: List of Betti curve DataFrames 141 | """ 142 | 143 | df = get_dataset(path) 144 | df = df.get_data()[0] 145 | df.rename({'label': 'y', 'coord_0': 'x'}, axis='columns', inplace=True) 146 | df['idx'] = np.arange(len(df)) 147 | 148 | embedder = ts.TakensEmbedding(parameters_type='search', dimension=embedding_dimension, 149 | time_delay=embedding_time_delay, n_jobs=-1) 150 | embedder.fit(df['x']) 151 | embedder_time_delay = embedder.time_delay_ 152 | embedder_dimension = embedder.dimension_ 153 | 154 | print('Optimal embedding time delay based on mutual information: ', embedder_time_delay) 155 | print('Optimal embedding dimension based on false nearest neighbors: ', embedder_dimension) 156 | 157 | X_embedded, y_embedded = embedder.transform_resample(df['x'], df['y']) 158 | sliding_window = ts.SlidingWindow(width=window_width, stride=window_stride) 159 | sliding_window.fit(X_embedded, y_embedded) 160 | 161 | X_windows, y_windows = sliding_window.transform_resample(X_embedded, y_embedded) 162 | 163 | homology_dimensions = [0, 1, 2] 164 | persistenceDiagram = hl.VietorisRipsPersistence(metric='euclidean', max_edge_length=10, 165 | homology_dimensions=homology_dimensions, n_jobs=-1) 166 | 167 | X_diagrams = persistenceDiagram.fit_transform(X_windows[:]) 168 | diagram_scaler = diag.Scaler() 169 | diagram_scaler.fit(X_diagrams) 170 | X_scaled = diagram_scaler.transform(X_diagrams) 171 | 172 | persistent_entropy = diag.PersistenceEntropy() 173 | X_persistent_entropy = persistent_entropy.fit_transform(X_scaled) 174 | 175 | betti_curves = diag.BettiCurve() 176 | betti_curves.fit(X_scaled) 177 | X_betti_curves = betti_curves.transform(X_scaled) 178 | 179 | df_betti_list = [] 180 | for i in homology_dimensions: 181 | df_betti_list.append(pd.DataFrame(X_betti_curves[:, i, :])) 182 | 183 | if return_betti_surface==True: 184 | return (X_scaled, df_betti_list, X_betti_curves) 185 | else: 186 | return (X_scaled, df_betti_list) 187 | 188 | 189 | def num_relevant_holes(X_scaled, homology_dim, theta=0.7): 190 | """ 191 | INPUT: 192 | X_scaled: scaled persistence diagrams, numpy array 193 | homology_dim: dimension of the homology to consider, integer 194 | theta: value between 0 and 1 to be used to calculate the threshold, float 195 | 196 | OUTPUT: 197 | n_rel_holes: list of the number of relevant holes in each time window 198 | """ 199 | 200 | n_rel_holes = [] 201 | 202 | for i in range(X_scaled.shape[0]): 203 | persistence_table = pd.DataFrame(X_scaled[i], columns=['birth', 'death', 'homology']) 204 | persistence_table['lifetime'] = persistence_table['death'] - persistence_table['birth'] 205 | threshold = persistence_table[persistence_table['homology'] == homology_dim]['lifetime'].max() * theta 206 | n_rel_holes.append(persistence_table[(persistence_table['lifetime'] > threshold) 207 | & (persistence_table['homology'] == homology_dim)].shape[0]) 208 | return n_rel_holes 209 | 210 | 211 | def average_lifetime(X_scaled, homology_dim): 212 | """ 213 | INPUT: 214 | X_scaled: scaled persistence diagrams, numpy array 215 | homology_dim: dimension of the homology to consider, integer 216 | 217 | OUTPUT: 218 | avg_lifetime_list: list of average lifetime for each time window 219 | """ 220 | 221 | avg_lifetime_list = [] 222 | 223 | for i in range(X_scaled.shape[0]): 224 | persistence_table = pd.DataFrame(X_scaled[i], columns=['birth', 'death', 'homology']) 225 | persistence_table['lifetime'] = persistence_table['death'] - persistence_table['birth'] 226 | avg_lifetime_list.append(persistence_table[persistence_table['homology'] 227 | == homology_dim]['lifetime'].mean()) 228 | 229 | return avg_lifetime_list 230 | 231 | 232 | def betti_surface_feature(df_betti, betti_rolling=1): 233 | """ 234 | INPUT: 235 | df_betti: pandas dataframe for the betti surface 236 | betti_rolling: rolling_parameter, integer 237 | 238 | OUTPUT: 239 | mean along the epsilon axis of the non-zero elements of the betti surface 240 | """ 241 | 242 | return df_betti.groupby(df_betti.index).apply(lambda g: find_mean_nonzero(g)).rolling(betti_rolling).mean() 243 | 244 | 245 | def betti_surface_argmax(df_betti): 246 | """ 247 | INPUT: 248 | df_betti: pandas dataframe for the betti surface 249 | 250 | OUTPUT: 251 | argmax along the epsilon axis 252 | """ 253 | 254 | return np.argmax(np.array(df_betti), axis=1) 255 | 256 | 257 | def get_persistent_entropy(X_scaled, homology_dim=0): 258 | """ 259 | INPUT: 260 | X_scaled: scaled persistence diagrams, numpy array 261 | homology_dim: dimension of the homology to consider, integer 262 | 263 | OUTPUT: 264 | persistent_entropy: array 265 | """ 266 | 267 | persistent_entropy = diag.PersistenceEntropy() 268 | return persistent_entropy.fit_transform(X_scaled) 269 | 270 | 271 | def calculate_amplitude_feature(X_scaled, metric='wasserstein', order=2): 272 | """ 273 | INPUT: 274 | X_scaled: scaled persistence diagrams, numpy array 275 | metric: Either 'wasserstein' (default), 'landscape', 'betti', 'bottleneck' or 'heat' 276 | order: integer 277 | 278 | OUTPUT: 279 | amplitude: vector with the values for the amplitude feature 280 | """ 281 | 282 | amplitude = diag.Amplitude(metric=metric, order=order) 283 | return amplitude.fit_transform(X_scaled) 284 | 285 | 286 | def create_non_tda_features(path, 287 | fourier_window_size=[], 288 | rolling_mean_size=[], 289 | rolling_max_size=[], 290 | rolling_min_size=[], 291 | mad_size=[], 292 | fourier_coefficients=[]): 293 | """ 294 | INPUT: 295 | path: int (number to OpenML dataset) 296 | fourier_window_size: a list of window sizes. Note: min must be > max(fourier_coefficients) 297 | rolling_mean_size: a list of window sizes 298 | rolling_max_shift: a list of window sizes 299 | rolling_min_shift: a list of window sizes 300 | mad_size: a list of window sizes 301 | fourier_coefficients: a list of all fourier coefficients to include. 302 | Note: max must be < min(fourier_window_size) 303 | OUTPUT: 304 | df: pandas dataframe with columns: 305 | max_... for rolling max features 306 | min_... for rolling min features 307 | mean_... for rolling mean features 308 | mad_... for rolling mad features 309 | fourier_... for fourier coefficients 310 | """ 311 | 312 | df = get_dataset(path) 313 | df = df.get_data()[0] 314 | df.rename({'label': 'y', 'coord_0': 'x', 'coord_1': 'x_dot'}, axis='columns', inplace=True) 315 | 316 | pandarallel.initialize() 317 | 318 | for r in rolling_max_size: 319 | df['max_' + str(r)] = df['x'].rolling(r).max() 320 | for r in rolling_mean_size: 321 | df['mean_' + str(r)] = df['x'].rolling(r).mean() 322 | for r in rolling_min_size: 323 | df['min_' + str(r)] = df['x'].rolling(r).min() 324 | for r in mad_size: 325 | df['mad_' + str(r)] = df['x'] - df['x'].rolling(r).min() 326 | if (not fourier_coefficients and fourier_window_size) or (not fourier_window_size and fourier_coefficients): 327 | print('Need to specify the fourier coeffcients and the window size') 328 | for n in fourier_coefficients: 329 | df[f'fourier_w_{n}'] = df['x'].rolling(fourier_window_size).parallel_apply(lambda x: rfft(x)[n], 330 | raw=False) 331 | # Remove all rows with NaNs 332 | df.dropna(axis='rows', inplace=True) 333 | return df 334 | 335 | 336 | #Helper function 337 | def find_mean_nonzero(g): 338 | if g.to_numpy().nonzero()[1].any(): 339 | return g.to_numpy().nonzero()[1].mean() 340 | else: 341 | return 0 342 | 343 | 344 | def create_all_features(path, noise_level, return_betti_surface=False): 345 | """ 346 | INPUT: 347 | path: int (number to OpenML dataset) 348 | noise_level: list with all noise levels 349 | return_betti_surface: boolean 350 | 351 | OUTPUT: 352 | df: all features in a dataframe OR 353 | df, X_betti_curves: df and Betti curves 354 | 355 | """ 356 | 357 | df = create_non_tda_features(path=path, 358 | rolling_max_size=[10, 20, 50], 359 | rolling_min_size=[10, 20, 50], 360 | rolling_mean_size=[10, 20, 50], 361 | fourier_coefficients=[1,2], 362 | fourier_window_size=40) 363 | df['idx'] = np.arange(len(df)) 364 | 365 | window_stride = 50 366 | diagrams = tda_diagrams(path=path, 367 | embedding_dimension=14, 368 | embedding_time_delay=5, 369 | window_width=100, 370 | window_stride=window_stride, 371 | return_betti_surface=return_betti_surface) 372 | X_scaled = diagrams[0] 373 | df_betti_list = diagrams[1] 374 | if return_betti_surface == True: 375 | X_betti_curves = diagrams[2] 376 | 377 | num_holes_feature = num_relevant_holes(X_scaled, homology_dim=0, theta=0.7) 378 | avg_lifetime_feature = average_lifetime(X_scaled, homology_dim=0) 379 | betti_feature = [] 380 | for dim in range(3): 381 | betti_feature.append(betti_surface_feature(df_betti_list[dim], betti_rolling=1)) 382 | amplitude_feature = calculate_amplitude_feature(X_scaled, metric='wasserstein', order=2) 383 | 384 | length = len(np.array([[x] * window_stride for x in num_holes_feature]).flatten()) 385 | df.drop(df[df['idx'] < (df.shape[0] - length)].index, axis='rows', inplace=True) 386 | df['num_holes'] = np.array([[x] * window_stride for x in num_holes_feature]).flatten() 387 | df['avg_lifetime'] = np.array([[x] * window_stride for x in avg_lifetime_feature]).flatten() 388 | for dim in range(3): 389 | df[f'betti_{dim}'] = np.array([[x] * window_stride for x in betti_surface_feature(df_betti_list[dim])]).flatten() 390 | for dim in [1,2]: 391 | df[f'betti_argmax_{dim}'] = np.array([[x] * window_stride for x in betti_surface_argmax(df_betti_list[dim])]).flatten() 392 | df['amplitude'] = np.array([[x] * window_stride for x in amplitude_feature]).flatten() 393 | 394 | df.drop('idx', axis = 'columns', inplace=True) 395 | if return_betti_surface == True: 396 | return df, X_betti_curves 397 | else: 398 | return df 399 | 400 | 401 | if __name__ == '__main__': 402 | """ 403 | This only works if the raw data of the Duffing system are available. 404 | """ 405 | main_dir = 'duffing_raw' 406 | noise_level = sys.argv[1:] 407 | noise_level = [x for x in noise_level] 408 | for n in noise_level: 409 | n_sets = 14 410 | fts_train = concat_dfs([create_all_features(os.path.join(main_dir, 411 | f'dataset_{itr}', 412 | f'duffing_{n}.pickle'), noise_level=n) 413 | for itr in range(n_sets)]) 414 | fts_train.to_pickle('train_'+str(n)+'.pickle') 415 | 416 | fts_test = concat_dfs([create_all_features(os.path.join(main_dir, 417 | f'dataset_{itr}', 418 | f'duffing_{n}.pickle'), noise_level=n) 419 | for itr in range(n_sets, 20)]) 420 | fts_test.to_pickle('test_'+str(n)+'.pickle') 421 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Copyright 2019 L2F SA. 2 | Licensed under the GNU Affero General Public License (the "License"); 3 | you may not use this file except in compliance with the License. 4 | You may obtain a copy of the License below or at https://www.gnu.org/licenses/agpl-3.0.html 5 | 6 | Unless required by applicable law or agreed to in writing, software 7 | distributed under the License is distributed on an "AS IS" BASIS, 8 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 9 | See the License for the specific language governing permissions and 10 | limitations under the License. 11 | 12 | GNU AFFERO GENERAL PUBLIC LICENSE 13 | Version 3, 19 November 2007 14 | 15 | Copyright (C) 2007 Free Software Foundation, Inc. 16 | Everyone is permitted to copy and distribute verbatim copies 17 | of this license document, but changing it is not allowed. 18 | 19 | Preamble 20 | 21 | The GNU Affero General Public License is a free, copyleft license for 22 | software and other kinds of works, specifically designed to ensure 23 | cooperation with the community in the case of network server software. 24 | 25 | The licenses for most software and other practical works are designed 26 | to take away your freedom to share and change the works. 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"Knowingly relying" means you have 507 | actual knowledge that, but for the patent license, your conveying the 508 | covered work in a country, or your recipient's use of the covered work 509 | in a country, would infringe one or more identifiable patents in that 510 | country that you have reason to believe are valid. 511 | 512 | If, pursuant to or in connection with a single transaction or 513 | arrangement, you convey, or propagate by procuring conveyance of, a 514 | covered work, and grant a patent license to some of the parties 515 | receiving the covered work authorizing them to use, propagate, modify 516 | or convey a specific copy of the covered work, then the patent license 517 | you grant is automatically extended to all recipients of the covered 518 | work and works based on it. 519 | 520 | A patent license is "discriminatory" if it does not include within 521 | the scope of its coverage, prohibits the exercise of, or is 522 | conditioned on the non-exercise of one or more of the rights that are 523 | specifically granted under this License. You may not convey a covered 524 | work if you are a party to an arrangement with a third party that is 525 | in the business of distributing software, under which you make payment 526 | to the third party based on the extent of your activity of conveying 527 | the work, and under which the third party grants, to any of the 528 | parties who would receive the covered work from you, a discriminatory 529 | patent license (a) in connection with copies of the covered work 530 | conveyed by you (or copies made from those copies), or (b) primarily 531 | for and in connection with specific products or compilations that 532 | contain the covered work, unless you entered into that arrangement, 533 | or that patent license was granted, prior to 28 March 2007. 534 | 535 | Nothing in this License shall be construed as excluding or limiting 536 | any implied license or other defenses to infringement that may 537 | otherwise be available to you under applicable patent law. 538 | 539 | 12. No Surrender of Others' Freedom. 540 | 541 | If conditions are imposed on you (whether by court order, agreement or 542 | otherwise) that contradict the conditions of this License, they do not 543 | excuse you from the conditions of this License. If you cannot convey a 544 | covered work so as to satisfy simultaneously your obligations under this 545 | License and any other pertinent obligations, then as a consequence you may 546 | not convey it at all. For example, if you agree to terms that obligate you 547 | to collect a royalty for further conveying from those to whom you convey 548 | the Program, the only way you could satisfy both those terms and this 549 | License would be to refrain entirely from conveying the Program. 550 | 551 | 13. Remote Network Interaction; Use with the GNU General Public License. 552 | 553 | Notwithstanding any other provision of this License, if you modify the 554 | Program, your modified version must prominently offer all users 555 | interacting with it remotely through a computer network (if your version 556 | supports such interaction) an opportunity to receive the Corresponding 557 | Source of your version by providing access to the Corresponding Source 558 | from a network server at no charge, through some standard or customary 559 | means of facilitating copying of software. This Corresponding Source 560 | shall include the Corresponding Source for any work covered by version 3 561 | of the GNU General Public License that is incorporated pursuant to the 562 | following paragraph. 563 | 564 | Notwithstanding any other provision of this License, you have 565 | permission to link or combine any covered work with a work licensed 566 | under version 3 of the GNU General Public License into a single 567 | combined work, and to convey the resulting work. The terms of this 568 | License will continue to apply to the part which is the covered work, 569 | but the work with which it is combined will remain governed by version 570 | 3 of the GNU General Public License. 571 | 572 | 14. Revised Versions of this License. 573 | 574 | The Free Software Foundation may publish revised and/or new versions of 575 | the GNU Affero General Public License from time to time. Such new versions 576 | will be similar in spirit to the present version, but may differ in detail to 577 | address new problems or concerns. 578 | 579 | Each version is given a distinguishing version number. If the 580 | Program specifies that a certain numbered version of the GNU Affero General 581 | Public License "or any later version" applies to it, you have the 582 | option of following the terms and conditions either of that numbered 583 | version or of any later version published by the Free Software 584 | Foundation. If the Program does not specify a version number of the 585 | GNU Affero General Public License, you may choose any version ever published 586 | by the Free Software Foundation. 587 | 588 | If the Program specifies that a proxy can decide which future 589 | versions of the GNU Affero General Public License can be used, that proxy's 590 | public statement of acceptance of a version permanently authorizes you 591 | to choose that version for the Program. 592 | 593 | Later license versions may give you additional or different 594 | permissions. However, no additional obligations are imposed on any 595 | author or copyright holder as a result of your choosing to follow a 596 | later version. 597 | 598 | 15. Disclaimer of Warranty. 599 | 600 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 601 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 602 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 603 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 604 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 605 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 606 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 607 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 608 | 609 | 16. Limitation of Liability. 610 | 611 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 612 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 613 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 614 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 615 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 616 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 617 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 618 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 619 | SUCH DAMAGES. 620 | 621 | 17. Interpretation of Sections 15 and 16. 622 | 623 | If the disclaimer of warranty and limitation of liability provided 624 | above cannot be given local legal effect according to their terms, 625 | reviewing courts shall apply local law that most closely approximates 626 | an absolute waiver of all civil liability in connection with the 627 | Program, unless a warranty or assumption of liability accompanies a 628 | copy of the Program in return for a fee. 629 | 630 | END OF TERMS AND CONDITIONS 631 | 632 | How to Apply These Terms to Your New Programs 633 | 634 | If you develop a new program, and you want it to be of the greatest 635 | possible use to the public, the best way to achieve this is to make it 636 | free software which everyone can redistribute and change under these terms. 637 | 638 | To do so, attach the following notices to the program. It is safest 639 | to attach them to the start of each source file to most effectively 640 | state the exclusion of warranty; and each file should have at least 641 | the "copyright" line and a pointer to where the full notice is found. 642 | 643 | 644 | Copyright (C) 645 | 646 | This program is free software: you can redistribute it and/or modify 647 | it under the terms of the GNU Affero General Public License as published 648 | by the Free Software Foundation, either version 3 of the License, or 649 | (at your option) any later version. 650 | 651 | This program is distributed in the hope that it will be useful, 652 | but WITHOUT ANY WARRANTY; without even the implied warranty of 653 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 654 | GNU Affero General Public License for more details. 655 | 656 | You should have received a copy of the GNU Affero General Public License 657 | along with this program. If not, see . 658 | 659 | Also add information on how to contact you by electronic and paper mail. 660 | 661 | If your software can interact with users remotely through a computer 662 | network, you should also make sure that it provides a way for users to 663 | get its source. For example, if your program is a web application, its 664 | interface could display a "Source" link that leads users to an archive 665 | of the code. There are many ways you could offer source, and different 666 | solutions will be better for different programs; see section 13 for the 667 | specific requirements. 668 | 669 | You should also get your employer (if you work as a programmer) or school, 670 | if any, to sign a "copyright disclaimer" for the program, if necessary. 671 | For more information on this, and how to apply and follow the GNU AGPL, see 672 | . 673 | --------------------------------------------------------------------------------