├── .gitignore ├── .travis.yml ├── LICENSE ├── MANIFEST ├── MANIFEST.in ├── README ├── README.md ├── ci ├── .travis_install.sh └── .travis_test.sh ├── docs └── images │ └── pyclust-logo-tentative.png ├── examples ├── .ipynb_checkpoints │ ├── bisecting_kmeans-checkpoint.ipynb │ ├── comp_KM_GMM-checkpoint.ipynb │ ├── compare_kernelKmenas_vs_kmeans-checkpoint.ipynb │ └── kmedoids-checkpoint.ipynb ├── bisecting_kmeans.ipynb ├── compare_GMM_vs_KM.ipynb ├── compare_KM_vs_BKM.ipynb ├── compare_kernelKmenas_vs_kmeans.ipynb ├── data │ ├── data_k5.csv │ └── data_k5.txt └── kmedoids.ipynb ├── pyclust ├── __init__.py ├── _bisect_kmeans.py ├── _gaussian_mixture_model.py ├── _kernel_kmeans.py ├── _kmeans.py ├── _kmedoids.py └── validate │ ├── __init__.py │ └── _internal.py ├── requirements.txt ├── setup.py └── tests ├── test_bi_kmeans.py ├── test_gmm.py ├── test_kernel_kmeans.py ├── test_kmeans.py ├── test_kmedoids.py └── test_silhouette.py /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | 5 | # C extensions 6 | *.so 7 | 8 | # Distribution / packaging 9 | .Python 10 | env/ 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | .eggs/ 17 | lib/ 18 | lib64/ 19 | parts/ 20 | sdist/ 21 | var/ 22 | *.egg-info/ 23 | .installed.cfg 24 | *.egg 25 | 26 | # PyInstaller 27 | # Usually these files are written by a python script from a template 28 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 29 | *.manifest 30 | *.spec 31 | 32 | # Installer logs 33 | pip-log.txt 34 | pip-delete-this-directory.txt 35 | 36 | # Unit test / coverage reports 37 | htmlcov/ 38 | .tox/ 39 | .coverage 40 | .coverage.* 41 | .cache 42 | nosetests.xml 43 | coverage.xml 44 | *,cover 45 | 46 | # Translations 47 | *.mo 48 | *.pot 49 | 50 | # Django stuff: 51 | *.log 52 | 53 | # Sphinx documentation 54 | docs/_build/ 55 | 56 | # PyBuilder 57 | target/ 58 | -------------------------------------------------------------------------------- /.travis.yml: -------------------------------------------------------------------------------- 1 | language: python 2 | virtualenv: 3 | system_site_packages: true 4 | env: 5 | matrix: 6 | - PYTHON_VERSION="2.7" COVERAGE="true" LATEST="true" 7 | - PYTHON_VERSION="2.7" NUMPY_VERSION="1.9.2" SCIPY_VERSION="0.15.1" SKLEARN_VERSION="0.16.1" PANDAS_VERSION="0.16.0" MATPLOTLIB_VERSION="1.4.3" 8 | - PYTHON_VERSION="3.4" LATEST="true" 9 | install: source ./ci/.travis_install.sh 10 | script: bash ./ci/.travis_test.sh 11 | after_success: 12 | # Ignore coveralls failures as the coveralls server is not very reliable 13 | # but we don't want travis to report a failure in the github UI just 14 | # because the coverage report failed to be published. 15 | - if [[ "$COVERAGE" == "true" ]]; then coveralls || echo "failed"; fi 16 | cache: apt 17 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 2, June 1991 3 | 4 | Copyright (C) 1989, 1991 Free Software Foundation, Inc., 5 | 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 6 | Everyone is permitted to copy and distribute verbatim copies 7 | of this license document, but changing it is not allowed. 8 | 9 | Preamble 10 | 11 | The licenses for most software are designed to take away your 12 | freedom to share and change it. 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If this is what you want to do, use the GNU Lesser General 339 | Public License instead of this License. 340 | 341 | -------------------------------------------------------------------------------- /MANIFEST: -------------------------------------------------------------------------------- 1 | # file GENERATED by distutils, do NOT edit 2 | README 3 | README.md 4 | requirements.txt 5 | setup.py 6 | examples/bisecting_kmeans.ipynb 7 | examples/compare_GMM_vs_KM.ipynb 8 | examples/compare_KM_vs_BKM.ipynb 9 | examples/compare_kernelKmenas_vs_kmeans.ipynb 10 | examples/kmedoids.ipynb 11 | pyclust/__init__.py 12 | pyclust/_bisect_kmeans.py 13 | pyclust/_gaussian_mixture_model.py 14 | pyclust/_kernel_kmeans.py 15 | pyclust/_kmeans.py 16 | pyclust/_kmedoids.py 17 | pyclust/validate/__init__.py 18 | pyclust/validate/_internal.py 19 | tests/test_bi_kmeans.py 20 | tests/test_gmm.py 21 | tests/test_kernel_kmeans.py 22 | tests/test_kmeans.py 23 | tests/test_kmedoids.py 24 | tests/test_silhouette.py 25 | -------------------------------------------------------------------------------- /MANIFEST.in: -------------------------------------------------------------------------------- 1 | include README.md requirements.txt 2 | include examples/*.ipynb 3 | recursive-include pyclust *.py 4 | recursive-include tests *.py 5 | -------------------------------------------------------------------------------- /README: -------------------------------------------------------------------------------- 1 | pyclust 2 | ======== 3 | 4 | Clustering Algorithms in Python 5 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | 2 | [![Build Status](https://travis-ci.org/mirjalil/pyclust.svg?branch=master)](https://travis-ci.org/mirjalil/pyclust) 3 | [![Code Health](https://landscape.io/github/mirjalil/pyclust/master/landscape.svg?style=flat)](https://landscape.io/github/mirjalil/pyclust) 4 | [![PyPI version](https://badge.fury.io/py/pyclust.svg)](http://badge.fury.io/py/pyclust) 5 | 6 | 7 | ![pyclust: data clustering in python](https://github.com/mirjalil/pyclust/blob/master/docs/images/pyclust-logo-tentative.png) 8 | 9 | 10 | Documentation: http://mirjalil.github.io/pyclust 11 | 12 | -------------------------------------------------------------------------------- /ci/.travis_install.sh: -------------------------------------------------------------------------------- 1 | #!/bin/bash 2 | # This script is meant to be called by the "install" step defined in 3 | # .travis.yml. See http://docs.travis-ci.com/ for more details. 4 | # The behavior of the script is controlled by environment variabled defined 5 | # in the .travis.yml in the top level folder of the project. 6 | 7 | # License: 3-clause BSD 8 | 9 | set -e 10 | 11 | # Fix the compilers to workaround avoid having the Python 3.4 build 12 | # lookup for g++44 unexpectedly. 13 | export CC=gcc 14 | export CXX=g++ 15 | 16 | # Deactivate the travis-provided virtual environment and setup a 17 | # conda-based environment instead 18 | deactivate 19 | 20 | # Use the miniconda installer for faster download / install of conda 21 | # itself 22 | wget http://repo.continuum.io/miniconda/Miniconda-3.7.0-Linux-x86_64.sh \ 23 | -O miniconda.sh 24 | chmod +x miniconda.sh && ./miniconda.sh -b 25 | export PATH=/home/travis/miniconda/bin:$PATH 26 | conda update --yes conda 27 | 28 | # Configure the conda environment and put it in the path using the 29 | # provided versions 30 | if [[ "$LATEST" == "true" ]]; then 31 | conda create -n testenv --yes python=$PYTHON_VERSION pip nose \ 32 | numpy scipy scikit-learn cython pandas matplotlib 33 | else 34 | conda create -n testenv --yes python=$PYTHON_VERSION pip nose \ 35 | numpy=$NUMPY_VERSION scipy=$SCIPY_VERSION \ 36 | scikit-learn=$SKLEARN_VERSION \ 37 | pandas=$PANDAS_VERSION \ 38 | matplotlib=$MATPLOTLIB_VERSION cython 39 | fi 40 | 41 | source activate testenv 42 | 43 | if [[ "$COVERAGE" == "true" ]]; then 44 | pip install coverage coveralls 45 | fi 46 | 47 | 48 | pip install treelib 49 | 50 | # Build gplearn in the install.sh script to collapse the verbose 51 | # build output in the travis output when it succeeds. 52 | python --version 53 | python -c "import numpy; print('numpy %s' % numpy.__version__)" 54 | python -c "import scipy; print('scipy %s' % scipy.__version__)" 55 | python -c "import sklearn; print('sklearn %s' % sklearn.__version__)" 56 | python -c "import pandas; print('pandas %s' % pandas.__version__)" 57 | python -c "import matplotlib; print('matplotlib %s' % matplotlib.__version__)" 58 | python setup.py build_ext --inplace 59 | -------------------------------------------------------------------------------- /ci/.travis_test.sh: -------------------------------------------------------------------------------- 1 | #!/bin/bash 2 | # This script is meant to be called by the "script" step defined in 3 | # .travis.yml. See http://docs.travis-ci.com/ for more details. 4 | # The behavior of the script is controlled by environment variabled defined 5 | # in the .travis.yml in the top level folder of the project. 6 | 7 | # License: 3-clause BSD 8 | 9 | set -e 10 | 11 | python --version 12 | python -c "import numpy; print('numpy %s' % numpy.__version__)" 13 | python -c "import scipy; print('scipy %s' % scipy.__version__)" 14 | python -c "import sklearn; print('sklearn %s' % sklearn.__version__)" 15 | python -c "import pandas; print('pandas %s' % pandas.__version__)" 16 | python -c "import matplotlib; print('matplotlib %s' % matplotlib.__version__)" 17 | 18 | if [[ "$COVERAGE" == "true" ]]; then 19 | nosetests -s -v --with-coverage --cover-package=tests/test_gmm.py 20 | else 21 | nosetests -s -v tests/test_gmm.py 22 | fi 23 | #make test-doc test-sphinxext 24 | -------------------------------------------------------------------------------- /docs/images/pyclust-logo-tentative.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/vmirly/pyclust/bdb12be4649e70c6c90da2605bc5f4b314e2d07e/docs/images/pyclust-logo-tentative.png -------------------------------------------------------------------------------- /examples/data/data_k5.csv: -------------------------------------------------------------------------------- 1 | x,y,label 2 | 9.3716,-0.4233,4 3 | 10.1449,0.0706,4 4 | -9.7006,4.7697,1 5 | -9.1902,5.4692,1 6 | 7.0868,1.2443,5 7 | -8.8987,6.2341,1 8 | -5.9528,2.9749,2 9 | -11.1316,4.2041,1 10 | -5.0696,5.0548,2 11 | -10.3145,4.4601,1 12 | -9.6497,5.9251,1 13 | -11.1016,-1.1102,3 14 | -10.7579,4.7315,1 15 | -7.0165,4.1340,2 16 | -6.5479,2.4876,2 17 | 11.2710,-0.9987,4 18 | -6.6153,1.7544,2 19 | -9.5631,4.7270,1 20 | -10.0955,3.8709,1 21 | -9.6523,4.7177,1 22 | 9.7840,-0.7195,4 23 | -9.9356,4.7251,1 24 | -9.0083,-2.4628,3 25 | -9.8144,-2.1312,3 26 | -7.7955,1.6824,2 27 | -9.4895,-2.1914,3 28 | -7.5306,0.3740,3 29 | -7.0595,-1.6496,3 30 | 5.8198,0.1317,5 31 | 6.7902,0.7076,5 32 | -10.5252,-3.0888,3 33 | 10.0502,-0.8898,4 34 | -8.6586,-2.4603,3 35 | 10.1325,-0.6966,4 36 | -12.0514,4.4795,1 37 | 10.5645,-0.5806,4 38 | -5.5934,1.2156,2 39 | 8.9211,-0.9387,4 40 | -8.7295,-1.2907,3 41 | -6.5833,2.1517,2 42 | -10.2950,-1.4051,3 43 | -6.3471,2.2745,2 44 | -6.2304,3.6193,2 45 | 6.5262,0.4026,5 46 | -8.5803,-1.7069,3 47 | -9.5816,4.6367,1 48 | -7.0934,2.7715,2 49 | 8.7214,-1.6531,4 50 | -7.3329,1.9659,2 51 | 9.2268,-1.3251,4 52 | 9.2166,-1.5321,4 53 | -10.7638,4.2417,1 54 | -5.2805,4.2142,2 55 | 7.5874,0.2566,5 56 | -9.3804,-2.2324,3 57 | -9.2143,-1.8715,3 58 | -9.8484,5.5779,1 59 | 8.2346,1.7254,5 60 | 10.9436,-0.7238,4 61 | 9.6885,-0.7281,4 62 | -10.2664,-1.9866,3 63 | -8.8969,-3.1654,3 64 | -9.5047,4.7427,1 65 | -9.4616,5.1830,1 66 | 8.6615,-1.9847,4 67 | -8.8223,6.9551,1 68 | -6.7701,5.4426,2 69 | -7.4205,3.5070,2 70 | -8.0293,-2.7058,3 71 | 6.9737,0.9576,5 72 | -8.9639,-1.5780,3 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10.0621,1.0644,4 117 | -6.4314,2.9813,2 118 | -6.3881,3.6334,2 119 | -9.7080,5.7542,1 120 | 11.3255,-1.0922,4 121 | -9.2550,-2.8646,3 122 | -------------------------------------------------------------------------------- /examples/data/data_k5.txt: -------------------------------------------------------------------------------- 1 | x1 x2 label 2 | -4.4791 3.3937 2 3 | 7.8984 -5.8965 3 4 | -9.8639 -7.7490 0 5 | 2.9518 -5.1833 3 6 | -4.1867 3.8343 2 7 | -3.1768 4.3702 2 8 | 5.4088 -5.3447 3 9 | -9.5431 4.6309 1 10 | 4.3218 -5.5438 3 11 | 5.4968 -5.6538 3 12 | -10.6395 4.6339 1 13 | 3.9048 -4.6311 3 14 | -4.8774 -2.4898 4 15 | 4.3310 -6.7243 3 16 | -3.2520 3.2348 2 17 | -4.0318 3.4640 2 18 | 4.9453 -6.1662 3 19 | 5.7822 -5.4181 3 20 | 5.6520 -5.1689 3 21 | -4.6943 -3.2294 4 22 | 4.4173 -5.2402 3 23 | -4.0492 3.1254 2 24 | -8.1458 -8.0735 0 25 | -9.2024 3.5654 1 26 | -8.8864 3.8588 1 27 | -10.0461 -6.8617 0 28 | -3.1254 4.2010 2 29 | 6.1868 -5.9088 3 30 | -10.0851 -7.8282 0 31 | -10.0197 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-5.1673 3 76 | -11.4239 4.6926 1 77 | -5.0557 -2.9554 4 78 | -9.0357 5.9764 1 79 | 5.6075 -5.9669 3 80 | 6.6010 -5.6611 3 81 | -10.2395 4.9487 1 82 | -8.8909 -8.1023 0 83 | -10.3803 4.0075 1 84 | -5.0648 -3.8558 4 85 | -7.3378 -2.3940 4 86 | -9.8274 3.2856 1 87 | -7.7716 -8.6099 0 88 | -9.5704 -10.1851 0 89 | -2.8091 5.2364 2 90 | -3.7752 3.2464 2 91 | -4.2066 -6.1067 4 92 | -4.9114 -3.4216 4 93 | -4.4552 -3.5057 4 94 | -9.1961 4.0429 1 95 | -8.1431 4.0263 1 96 | -9.0886 -8.6273 0 97 | -11.0169 3.4889 1 98 | 5.6792 -5.1388 3 99 | 4.8909 -5.8556 3 100 | 4.7322 -4.0895 3 101 | -9.5160 -7.5866 0 102 | 5.4398 -5.9188 3 103 | -5.2242 -0.0478 4 104 | -8.6125 -7.4585 0 105 | -9.3216 -9.4631 0 106 | -9.7942 -7.3977 0 107 | -3.8286 2.5118 2 108 | -9.2315 -8.0868 0 109 | -2.8642 5.3891 2 110 | -10.9938 4.6405 1 111 | -5.3267 3.7716 2 112 | -4.2468 2.3606 2 113 | -8.7130 -8.3648 0 114 | -8.8329 -8.8046 0 115 | -9.2127 3.2399 1 116 | -6.2019 -4.6130 4 117 | -9.6228 -6.3125 0 118 | -10.6627 6.4633 1 119 | -4.3118 -3.5116 4 120 | -8.3277 4.2822 1 121 | -8.2551 -7.0715 0 122 | 2.9148 -6.8599 3 123 | -9.9834 -9.6528 0 124 | -2.9007 4.3563 2 125 | -9.6864 -7.8579 0 126 | 5.4794 -7.0687 3 127 | -9.8626 5.3823 1 128 | -4.7216 4.4998 2 129 | -7.3743 -7.8252 0 130 | 6.6317 -5.9392 3 131 | 4.4958 -4.6014 3 132 | -9.3933 -8.9807 0 133 | -11.1569 4.7187 1 134 | 5.1866 -6.6096 3 135 | -9.0050 4.1887 1 136 | -4.9271 -4.6270 4 137 | -8.4499 3.7425 1 138 | -10.4434 4.4453 1 139 | 5.3197 -5.7306 3 140 | -5.6644 -3.7406 4 141 | -4.4926 2.9934 2 142 | -4.3424 -4.5848 4 143 | -9.1353 4.7492 1 144 | -4.5283 -4.8782 4 145 | -3.2452 2.6036 2 146 | 5.9346 -6.2940 3 147 | -4.3771 4.8473 2 148 | -3.8048 3.3566 2 149 | -8.3716 -8.0255 0 150 | 5.3566 -7.2207 3 151 | -7.5255 -7.4856 0 152 | -5.5182 -3.8333 4 153 | -4.9309 3.4471 2 154 | -4.0898 3.7194 2 155 | -9.0815 -8.2778 0 156 | 4.3885 -7.0471 3 157 | -6.7164 -4.1545 4 158 | -4.6582 -2.8804 4 159 | 6.5552 -3.4784 3 160 | -10.0585 -7.3565 0 161 | -8.6341 5.8623 1 162 | -10.1693 -7.0268 0 163 | -9.7052 5.3153 1 164 | -9.2413 -9.9978 0 165 | -6.8781 -5.2769 4 166 | -10.5360 4.8153 1 167 | -5.2178 2.5060 2 168 | -5.1568 -2.2503 4 169 | -8.8603 -9.1659 0 170 | 6.1220 -5.9961 3 171 | -4.0345 3.6847 2 172 | 6.5271 -5.0738 3 173 | -4.9300 3.7007 2 174 | -5.6830 2.6654 2 175 | 5.1247 -4.9710 3 176 | -3.2428 2.4205 2 177 | -8.8656 -6.9812 0 178 | -9.6682 4.8939 1 179 | -3.6967 3.5237 2 180 | -9.1200 -9.5740 0 181 | -8.8484 -8.9083 0 182 | -9.5319 3.8516 1 183 | -9.8538 -9.8689 0 184 | -2.7827 4.7249 2 185 | -5.0561 -3.5068 4 186 | -8.8758 4.0565 1 187 | -8.8767 5.4792 1 188 | -5.4080 -4.6670 4 189 | -6.1483 -4.4859 4 190 | 3.3675 -4.6395 3 191 | -5.2386 2.4540 2 192 | -4.1245 -1.6710 4 193 | -4.8915 3.2353 2 194 | -6.6277 2.0789 2 195 | -4.0553 4.1504 2 196 | -4.7384 -2.4468 4 197 | -6.1181 -2.7184 4 198 | -8.8202 5.4299 1 199 | -3.4339 3.4155 2 200 | -8.3427 5.1111 1 201 | -5.2566 -2.2820 4 202 | -------------------------------------------------------------------------------- /examples/kmedoids.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "metadata": { 7 | "collapsed": true 8 | }, 9 | "outputs": [], 10 | "source": [ 11 | "import numpy as np\n", 12 | "import scipy\n", 13 | "import pandas\n", 14 | "import treelib\n", 15 | "import pyclust\n", 16 | "import pandas\n", 17 | "\n", 18 | "import matplotlib\n", 19 | "import matplotlib.pyplot as plt\n", 20 | "%matplotlib inline" 21 | ] 22 | }, 23 | { 24 | "cell_type": "code", 25 | "execution_count": 2, 26 | "metadata": { 27 | "collapsed": false 28 | }, 29 | "outputs": [ 30 | { 31 | "data": { 32 | "text/plain": [ 33 | "'0.1.1'" 34 | ] 35 | }, 36 | "execution_count": 2, 37 | "metadata": {}, 38 | "output_type": "execute_result" 39 | } 40 | ], 41 | "source": [ 42 | "pyclust.__version__" 43 | ] 44 | }, 45 | { 46 | "cell_type": "code", 47 | "execution_count": 3, 48 | "metadata": { 49 | "collapsed": true 50 | }, 51 | "outputs": [], 52 | "source": [ 53 | "def plot_scatter(X, labels=None, centers=None, title=\"Scatter Plot\"):\n", 54 | " \n", 55 | " labels = np.zeros(shape=X.shape[0], dtype=int) if labels is None else labels\n", 56 | " colors = ['b', 'r', 'g', 'm', 'y']\n", 57 | " col_dict = {}\n", 58 | " i = 0\n", 59 | " for lab in np.unique(labels):\n", 60 | " col_dict[lab] = colors[i]\n", 61 | " i += 1 \n", 62 | " \n", 63 | " fig1 = plt.figure(1, figsize=(8,6))\n", 64 | " ax = fig1.add_subplot(1, 1, 1)\n", 65 | "\n", 66 | " for i in np.unique(labels):\n", 67 | " indx = np.where(labels == i)[0]\n", 68 | " plt.scatter(X[indx,0], X[indx,1], color=col_dict[i], marker='o', s=100, alpha=0.5)\n", 69 | "\n", 70 | " if centers is not None:\n", 71 | " plt.scatter(centers[:,0], centers[:,1], color='magenta', marker='*', s=250, alpha=0.5)\n", 72 | " \n", 73 | " plt.setp(ax.get_xticklabels(), rotation='horizontal', fontsize=16)\n", 74 | " plt.setp(ax.get_yticklabels(), rotation='vertical', fontsize=16)\n", 75 | "\n", 76 | " plt.xlabel('$x_1$', size=20)\n", 77 | " plt.ylabel('$x_2$', size=20)\n", 78 | " plt.title(title, size=20)\n", 79 | "\n", 80 | " plt.show()\n" 81 | ] 82 | }, 83 | { 84 | "cell_type": "markdown", 85 | "metadata": {}, 86 | "source": [ 87 | "## Example 1" 88 | ] 89 | }, 90 | { 91 | "cell_type": "code", 92 | "execution_count": 4, 93 | "metadata": { 94 | "collapsed": false 95 | }, 96 | "outputs": [ 97 | { 98 | "data": { 99 | "image/png": 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9y/O8n5r0RaTj3OG880KwX1Wj7XFsDLq6YP16Ne9LZ2WiSd/dt5vZ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\nSUVORK5CYII=\n", 100 | "text/plain": [ 101 | "" 102 | ] 103 | }, 104 | "metadata": {}, 105 | "output_type": "display_data" 106 | } 107 | ], 108 | "source": [ 109 | "m1 = np.array([-2.5, 1.0])\n", 110 | "m2 = np.array([0.0, -3.0])\n", 111 | "m3 = np.array([2.0, 2.0])\n", 112 | "\n", 113 | "X1 = np.random.multivariate_normal(mean=m1, cov=np.eye(2), size=20)\n", 114 | "X2 = np.random.multivariate_normal(mean=m2, cov=np.eye(2), size=30)\n", 115 | "X3 = np.random.multivariate_normal(mean=m3, cov=np.eye(2), size=10)\n", 116 | "\n", 117 | "X = np.vstack((X1, X2, X3))\n", 118 | "\n", 119 | "indx_arr = np.arange(X.shape[0])\n", 120 | "np.random.shuffle(indx_arr)\n", 121 | "\n", 122 | "y = np.hstack((np.zeros(20, dtype=int), np.ones(30, dtype=int), 2*np.ones(10, dtype=int)))\n", 123 | "X = X[indx_arr,:]\n", 124 | "y = y[indx_arr]\n", 125 | "\n", 126 | "plot_scatter(X, labels=None, centers=None, title=\"Scatter Plot\")" 127 | ] 128 | }, 129 | { 130 | "cell_type": "code", 131 | "execution_count": 5, 132 | "metadata": { 133 | "collapsed": false 134 | }, 135 | "outputs": [ 136 | { 137 | "data": { 138 | "image/png": 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xMxoXNHLqilNxvCSDwzQgTaQy1PpgurgU0oevXPoxq5akMrPJuZ4YSnD5zZdz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\nPBya8RsaYHQUDhyAVasm9/O3tMCWLWE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75NbdJAdjjKOT55eSPF68/yDJoyT3knTT8wKn\ns6UPrLKbn0H/0PZ7kptJviyeP8liYW+M8TpJ2j7b4IzACpb2gDO1vZrkVZLPSY6TPE+yl+Qoydck\n+2OMP77ntz1OsjPG+LjBcYG/EHzgXAg+XCy+4QPABAQfACYg+MB5sqUPF4TgA/9V2/tt95KMJC/a\nPtz2TIClPQCYghM+AExA8AFgAoIPABMQfACYgOADwAQEHwAmIPgAMAHBB4AJCD4ATOAHn//1CV8R\nihkAAAAASUVORK5CYII=\n", 139 | "text/plain": [ 140 | "" 141 | ] 142 | }, 143 | "metadata": {}, 144 | "output_type": "display_data" 145 | } 146 | ], 147 | "source": [ 148 | "## Performing KMeans\n", 149 | "kmd = pyclust.KMedoids(n_clusters=3, n_trials=50)\n", 150 | "\n", 151 | "kmd.fit(X)\n", 152 | "\n", 153 | "plot_scatter(X, labels=kmd.labels_, centers=kmd.centers_, title=\"Scatter Plot: KMeans Clustering\")" 154 | ] 155 | }, 156 | { 157 | "cell_type": "markdown", 158 | "metadata": {}, 159 | "source": [ 160 | "## Example 2" 161 | ] 162 | }, 163 | { 164 | "cell_type": "code", 165 | "execution_count": 9, 166 | "metadata": { 167 | "collapsed": false 168 | }, 169 | "outputs": [ 170 | { 171 | "data": { 172 | "image/png": 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fNoYW2ziIRmFvr2p3C/oDkkA1s79DI/rvRAX1dVXt16CFZYZRYZfHlV8MbEHTcE4X9+WZ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\nz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173 | "text/plain": [ 174 | "" 175 | ] 176 | }, 177 | "metadata": {}, 178 | "output_type": "display_data" 179 | } 180 | ], 181 | "source": [ 182 | "s1 = np.array([[0.3, 0.05], [0.05, 0.3]])\n", 183 | "s2 = np.array([[0.6, 0.0], [0.0, 1.1]])\n", 184 | "s3 = np.array([[0.4, -0.05], [-0.02, 0.2]])\n", 185 | "\n", 186 | "m1 = np.array([-2.0, 1.0])\n", 187 | "m2 = np.array([0.0, -3.0])\n", 188 | "m3 = np.array([1.0, 2.0])\n", 189 | "\n", 190 | "X1 = np.random.multivariate_normal(mean=m1, cov=s1, size=100)\n", 191 | "X2 = np.random.multivariate_normal(mean=m2, cov=s2, size=150)\n", 192 | "X3 = np.random.multivariate_normal(mean=m3, cov=s3, size=80)\n", 193 | "\n", 194 | "X = np.vstack((X1, X2, X3))\n", 195 | "\n", 196 | "indx_arr = np.arange(X.shape[0])\n", 197 | "np.random.shuffle(indx_arr)\n", 198 | "\n", 199 | "y = np.hstack((np.zeros(100, dtype=int), np.ones(150, dtype=int), 2*np.ones(80, dtype=int)))\n", 200 | "X = X[indx_arr,:]\n", 201 | "y = y[indx_arr]\n", 202 | "\n", 203 | "## Performing KMedoids\n", 204 | "kmd = pyclust.KMedoids(n_clusters=3, n_trials=50)\n", 205 | "\n", 206 | "kmd.fit(X)\n", 207 | "\n", 208 | "plot_scatter(X, labels=kmd.labels_, centers=kmd.centers_, title=\"Scatter Plot: KMeans Clustering\")" 209 | ] 210 | }, 211 | { 212 | "cell_type": "code", 213 | "execution_count": null, 214 | "metadata": { 215 | "collapsed": true 216 | }, 217 | "outputs": [], 218 | "source": [] 219 | } 220 | ], 221 | "metadata": { 222 | "kernelspec": { 223 | "display_name": "Python 3", 224 | "language": "python", 225 | "name": "python3" 226 | }, 227 | "language_info": { 228 | "codemirror_mode": { 229 | "name": "ipython", 230 | "version": 3 231 | }, 232 | "file_extension": ".py", 233 | "mimetype": "text/x-python", 234 | "name": "python", 235 | "nbconvert_exporter": "python", 236 | "pygments_lexer": "ipython3", 237 | "version": "3.4.3" 238 | } 239 | }, 240 | "nbformat": 4, 241 | "nbformat_minor": 0 242 | } 243 | -------------------------------------------------------------------------------- /pyclust/__init__.py: -------------------------------------------------------------------------------- 1 | # Vahid Mirjalili 08/07/2015 2 | # Unsupervised Data Clustering Algorithms in Python 3 | # Machine Learning Application 4 | 5 | 6 | from ._kmeans import KMeans 7 | from ._bisect_kmeans import BisectKMeans 8 | from ._gaussian_mixture_model import GMM 9 | from ._kmedoids import KMedoids 10 | from ._kernel_kmeans import KernelKMeans 11 | 12 | __version__ = '0.1.18' 13 | -------------------------------------------------------------------------------- /pyclust/_bisect_kmeans.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import treelib 3 | 4 | from . import _kmeans 5 | 6 | 7 | 8 | def _select_cluster_2_split(membs, tree): 9 | leaf_nodes = tree.leaves() 10 | num_leaves = len(leaf_nodes) 11 | if len(leaf_nodes)>1: 12 | sse_arr = np.empty(shape=num_leaves, dtype=float) 13 | labels = np.empty(shape=num_leaves, dtype=int) 14 | 15 | for i,node in enumerate(leaf_nodes): 16 | sse_arr[i] = node.data['sse'] 17 | labels[i] = node.data['label'] 18 | id_max = np.argmax(sse_arr) 19 | clust_id = labels[id_max] 20 | memb_ids = np.where(membs == clust_id)[0] 21 | return(clust_id,memb_ids) 22 | else: 23 | return(0,np.arange(membs.shape[0])) 24 | 25 | 26 | 27 | def _cut_tree(tree, n_clusters, membs): 28 | """ Cut the tree to get desired number of clusters as n_clusters 29 | 2 <= n_desired <= n_clusters 30 | """ 31 | ## starting from root, 32 | ## a node is added to the cut_set or 33 | ## its children are added to node_set 34 | assert(n_clusters >= 2) 35 | assert(n_clusters <= len(tree.leaves())) 36 | 37 | cut_centers = dict() #np.empty(shape=(n_clusters, ndim), dtype=float) 38 | 39 | for i in range(n_clusters-1): 40 | if i==0: 41 | search_set = set(tree.children(0)) 42 | node_set,cut_set = set(), set() 43 | else: 44 | search_set = node_set.union(cut_set) 45 | node_set,cut_set = set(), set() 46 | 47 | if i+2 == n_clusters: 48 | cut_set = search_set 49 | else: 50 | for _ in range(len(search_set)): 51 | n = search_set.pop() 52 | 53 | if n.data['ilev'] is None or n.data['ilev']>i+2: 54 | cut_set.add(n) 55 | else: 56 | nid = n.identifier 57 | if n.data['ilev']-2==i: 58 | node_set = node_set.union(set(tree.children(nid))) 59 | 60 | conv_membs = membs.copy() 61 | for node in cut_set: 62 | nid = node.identifier 63 | label = node.data['label'] 64 | cut_centers[label] = node.data['center'] 65 | sub_leaves = tree.leaves(nid) 66 | for leaf in sub_leaves: 67 | indx = np.where(conv_membs == leaf)[0] 68 | conv_membs[indx] = nid 69 | 70 | return(conv_membs, cut_centers) 71 | 72 | 73 | def _add_tree_node(tree, label, ilev, X=None, size=None, center=None, sse=None, parent=None): 74 | """ Add a node to the tree 75 | if parent is not known, the node is a root 76 | 77 | The nodes of this tree keep properties of each cluster/subcluster: 78 | size --> cluster size as the number of points in the cluster 79 | center --> mean of the cluster 80 | label --> cluster label 81 | sse --> sum-squared-error for that single cluster 82 | ilev --> the level at which this node is split into 2 children 83 | """ 84 | if size is None: 85 | size = X.shape[0] 86 | if (center is None): 87 | center = np.mean(X, axis=0) 88 | if (sse is None): 89 | sse = _kmeans._cal_dist2center(X, center) 90 | 91 | center = list(center) 92 | datadict = { 93 | 'size' : size, 94 | 'center': center, 95 | 'label' : label, 96 | 'sse' : sse, 97 | 'ilev' : None 98 | } 99 | if (parent is None): 100 | tree.create_node(label, label, data=datadict) 101 | else: 102 | tree.create_node(label, label, parent=parent, data=datadict) 103 | tree.get_node(parent).data['ilev'] = ilev 104 | 105 | return(tree) 106 | 107 | 108 | 109 | 110 | def _bisect_kmeans(X, n_clusters, n_trials, max_iter, tol): 111 | """ Apply Bisecting Kmeans clustering 112 | to reach n_clusters number of clusters 113 | """ 114 | membs = np.empty(shape=X.shape[0], dtype=int) 115 | centers = dict() #np.empty(shape=(n_clusters,X.shape[1]), dtype=float) 116 | sse_arr = dict() #-1.0*np.ones(shape=n_clusters, dtype=float) 117 | 118 | ## data structure to store cluster hierarchies 119 | tree = treelib.Tree() 120 | tree = _add_tree_node(tree, 0, ilev=0, X=X) 121 | 122 | km = _kmeans.KMeans(n_clusters=2, n_trials=n_trials, max_iter=max_iter, tol=tol) 123 | for i in range(1,n_clusters): 124 | sel_clust_id,sel_memb_ids = _select_cluster_2_split(membs, tree) 125 | X_sub = X[sel_memb_ids,:] 126 | km.fit(X_sub) 127 | 128 | #print("Bisecting Step %d :"%i, sel_clust_id, km.sse_arr_, km.centers_) 129 | ## Updating the clusters & properties 130 | #sse_arr[[sel_clust_id,i]] = km.sse_arr_ 131 | #centers[[sel_clust_id,i]] = km.centers_ 132 | tree = _add_tree_node(tree, 2*i-1, i, \ 133 | size=np.sum(km.labels_ == 0), center=km.centers_[0], \ 134 | sse=km.sse_arr_[0], parent= sel_clust_id) 135 | tree = _add_tree_node(tree, 2*i, i, \ 136 | size=np.sum(km.labels_ == 1), center=km.centers_[1], \ 137 | sse=km.sse_arr_[1], parent= sel_clust_id) 138 | 139 | pred_labels = km.labels_ 140 | pred_labels[np.where(pred_labels == 1)[0]] = 2*i 141 | pred_labels[np.where(pred_labels == 0)[0]] = 2*i - 1 142 | #if sel_clust_id == 1: 143 | # pred_labels[np.where(pred_labels == 0)[0]] = sel_clust_id 144 | # pred_labels[np.where(pred_labels == 1)[0]] = i 145 | #else: 146 | # pred_labels[np.where(pred_labels == 1)[0]] = i 147 | # pred_labels[np.where(pred_labels == 0)[0]] = sel_clust_id 148 | 149 | membs[sel_memb_ids] = pred_labels 150 | 151 | 152 | for n in tree.leaves(): 153 | label = n.data['label'] 154 | centers[label] = n.data['center'] 155 | sse_arr[label] = n.data['sse'] 156 | 157 | return(centers, membs, sse_arr, tree) 158 | 159 | 160 | 161 | 162 | class BisectKMeans(object): 163 | """ 164 | bisecting KMeans Clustering 165 | 166 | Parameters 167 | ------- 168 | n_clusters: number of clusters (default = 2) 169 | n_trials: number of trial random centroid initialization (default = 10) 170 | max_iter: maximum number of iterations (default = 100) 171 | tol: tolerance (default = 0.0001) 172 | 173 | 174 | Attibutes 175 | ------- 176 | labels_ : cluster labels for each data item 177 | centers_ : cluster centers 178 | sse_arr_ : array of SSE values for each cluster 179 | n_iter_ : number of iterations for the best trial 180 | tree_ : tree hierarchy of bisecting clusters 181 | 182 | Methods 183 | ------- 184 | fit(X): fit the model 185 | fit_predict(X): fit the model and return the cluster labels 186 | """ 187 | 188 | def __init__(self, n_clusters=2, n_trials=10, max_iter=100, tol=0.0001): 189 | assert n_clusters >= 2, 'n_clusters should be >= 2' 190 | self.n_clusters = n_clusters 191 | self.n_trials = n_trials 192 | self.max_iter = max_iter 193 | self.tol = tol 194 | 195 | 196 | def fit(self, X): 197 | """ 198 | """ 199 | self.centers_, self.labels_, self.sse_arr_, self.tree_ = \ 200 | _bisect_kmeans(X, self.n_clusters, self.n_trials, self.max_iter, self.tol) 201 | 202 | 203 | def fit_predict(self, X): 204 | """ 205 | """ 206 | self.fit(X) 207 | return(self.labels_) 208 | 209 | 210 | def cut(self, n_desired): 211 | """ 212 | """ 213 | return(_cut_tree(self.tree_, n_desired, self.labels_)) 214 | -------------------------------------------------------------------------------- /pyclust/_gaussian_mixture_model.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import scipy, scipy.linalg 3 | from . import _kmeans 4 | 5 | Epsilon = 100 * np.finfo(float).eps 6 | Lambda = 0.1 7 | 8 | def _init_mixture_params(X, n_mixtures, init_method): 9 | """ 10 | Initialize mixture density parameters with 11 | equal priors 12 | random means 13 | identity covariance matrices 14 | """ 15 | 16 | init_priors = np.ones(shape=n_mixtures, dtype=float) / n_mixtures 17 | 18 | if init_method == 'kmeans': 19 | km = _kmeans.KMeans(n_clusters = n_mixtures, n_trials=20) 20 | km.fit(X) 21 | init_means = km.centers_ 22 | else: 23 | inx_rand = np.random.choice(X.shape[0], size=n_mixtures) 24 | init_means = X[inx_rand,:] 25 | 26 | 27 | if np.any(np.isnan(init_means)): 28 | raise ValueError("Init means are NaN! ") 29 | 30 | n_features = X.shape[1] 31 | init_covars = np.empty(shape=(n_mixtures, n_features, n_features), dtype=float) 32 | for i in range(n_mixtures): 33 | init_covars[i] = np.eye(n_features) 34 | 35 | return(init_priors, init_means, init_covars) 36 | 37 | 38 | 39 | def __log_density_single(x, mean, covar): 40 | """ This is just a test function to calculate 41 | the normal density at x given mean and covariance matrix. 42 | 43 | Note: this function is not efficient, so 44 | _log_multivariate_density is recommended for use. 45 | """ 46 | n_dim = mean.shape[0] 47 | 48 | dx = x - mean 49 | covar_inv = scipy.linalg.inv(covar) 50 | covar_det = scipy.linalg.det(covar) 51 | 52 | den = np.dot(np.dot(dx.T, covar_inv), dx) + n_dim*np.log(2*np.pi) + np.log(covar_det) 53 | 54 | return(-1/2 * den) 55 | 56 | 57 | def _log_multivariate_density(X, means, covars): 58 | """ 59 | Class conditional density: 60 | P(x | mu, Sigma) = 1/((2pi)^d/2 * |Sigma|^1/2) * exp(-1/2 * (x-mu)^T * Sigma^-1 * (x-mu)) 61 | 62 | log of class conditional density: 63 | log P(x | mu, Sigma) = -1/2*(d*log(2pi) + log(|Sigma|) + (x-mu)^T * Sigma^-1 * (x-mu)) 64 | """ 65 | n_samples, n_dim = X.shape 66 | n_components = means.shape[0] 67 | 68 | assert(means.shape[0] == covars.shape[0]) 69 | 70 | log_proba = np.empty(shape=(n_samples, n_components), dtype=float) 71 | for i, (mu, cov) in enumerate(zip(means, covars)): 72 | try: 73 | cov_chol = scipy.linalg.cholesky(cov, lower=True) 74 | except scipy.linalg.LinAlgError: 75 | try: 76 | cov_chol = scipy.linalg.cholesky(cov + Lambda*np.eye(n_dim), lower=True) 77 | except: 78 | raise ValueError("Triangular Matrix Decomposition not performed!\n") 79 | 80 | cov_log_det = 2 * np.sum(np.log(np.diagonal(cov_chol))) 81 | 82 | try: 83 | cov_solve = scipy.linalg.solve_triangular(cov_chol, (X - mu).T, lower=True).T 84 | except: 85 | raise ValueError("Solve_triangular not perormed!\n") 86 | 87 | log_proba[:, i] = -0.5 * (np.sum(cov_solve ** 2, axis=1) + \ 88 | n_dim * np.log(2 * np.pi) + cov_log_det) 89 | 90 | return(log_proba) 91 | 92 | 93 | 94 | 95 | def _log_likelihood_per_sample(X, means, covars): 96 | """ 97 | Theta = (theta_1, theta_2, ... theta_M) 98 | Likelihood of mixture parameters given data: L(Theta | X) = product_i P(x_i | Theta) 99 | log likelihood: log L(Theta | X) = sum_i log(P(x_i | Theta)) 100 | 101 | and note that p(x_i | Theta) = sum_j prior_j * p(x_i | theta_j) 102 | 103 | 104 | Probability of sample x being generated from component i: 105 | P(w_i | x) = P(x|w_i) * P(w_i) / P(X) 106 | where P(X) = sum_i P(x|w_i) * P(w_i) 107 | 108 | Here post_proba = P/(w_i | x) 109 | and log_likelihood = log(P(x|w_i)) 110 | """ 111 | 112 | logden = _log_multivariate_density(X, means, covars) 113 | 114 | logden_max = logden.max(axis=1) 115 | log_likelihood = np.log(np.sum(np.exp(logden.T - logden_max) + Epsilon, axis=0)) 116 | log_likelihood += logden_max 117 | 118 | post_proba = np.exp(logden - log_likelihood[:, np.newaxis]) 119 | 120 | return (log_likelihood, post_proba) 121 | 122 | 123 | 124 | def _validate_params(priors, means, covars): 125 | """ Validation Check for M.L. paramateres 126 | """ 127 | 128 | for i,(p,m,cv) in enumerate(zip(priors, means, covars)): 129 | if np.any(np.isinf(p)) or np.any(np.isnan(p)): 130 | raise ValueError("Component %d of priors is not valid " % i) 131 | 132 | if np.any(np.isinf(m)) or np.any(np.isnan(m)): 133 | raise ValueError("Component %d of means is not valid " % i) 134 | 135 | if np.any(np.isinf(cv)) or np.any(np.isnan(cv)): 136 | raise ValueError("Component %d of covars is not valid " % i) 137 | 138 | if (not np.allclose(cv, cv.T) or np.any(scipy.linalg.eigvalsh(cv) <= 0)): 139 | raise ValueError("Component %d of covars must be positive-definite" % i) 140 | 141 | 142 | 143 | def _maximization_step(X, posteriors): 144 | """ 145 | Update class parameters as below: 146 | priors: P(w_i) = sum_x P(w_i | x) ==> Then normalize to get in [0,1] 147 | Class means: center_w_i = sum_x P(w_i|x)*x / sum_i sum_x P(w_i|x) 148 | """ 149 | 150 | ### Prior probabilities or class weights 151 | sum_post_proba = np.sum(posteriors, axis=0) 152 | prior_proba = sum_post_proba / (sum_post_proba.sum() + Epsilon) 153 | 154 | ### means 155 | means = np.dot(posteriors.T, X) / (sum_post_proba[:, np.newaxis] + Epsilon) 156 | 157 | ### covariance matrices 158 | n_components = posteriors.shape[1] 159 | n_features = X.shape[1] 160 | covars = np.empty(shape=(n_components, n_features, n_features), dtype=float) 161 | 162 | for i in range(n_components): 163 | post_i = posteriors[:, i] 164 | mean_i = means[i] 165 | diff_i = X - mean_i 166 | 167 | with np.errstate(under='ignore'): 168 | covar_i = np.dot(post_i * diff_i.T, diff_i) / (post_i.sum() + Epsilon) 169 | covars[i] = covar_i + Lambda * np.eye(n_features) 170 | 171 | 172 | _validate_params(prior_proba, means, covars) 173 | return(prior_proba, means, covars) 174 | 175 | 176 | 177 | def _fit_gmm_params(X, n_mixtures, n_init, init_method, n_iter, tol): 178 | """ 179 | """ 180 | 181 | best_mean_loglikelihood = -np.infty 182 | 183 | for _ in range(n_init): 184 | priors, means, covars = _init_mixture_params(X, n_mixtures, init_method) 185 | prev_mean_loglikelihood = None 186 | for i in range(n_iter): 187 | ## E-step 188 | log_likelihoods, posteriors = _log_likelihood_per_sample(X, means, covars) 189 | 190 | ## M-step 191 | priors, means, covars = _maximization_step(X, posteriors) 192 | 193 | ## convergence Check 194 | curr_mean_loglikelihood = log_likelihoods.mean() 195 | 196 | if prev_mean_loglikelihood is not None: 197 | if np.abs(curr_mean_loglikelihood - prev_mean_loglikelihood) < tol: 198 | break 199 | 200 | prev_mean_loglikelihood = curr_mean_loglikelihood 201 | 202 | if curr_mean_loglikelihood > best_mean_loglikelihood: 203 | best_mean_loglikelihood = curr_mean_loglikelihood 204 | best_params = { 205 | 'priors' : priors, 206 | 'means' : means, 207 | 'covars' : covars, 208 | 'mean_log_likelihood' : curr_mean_loglikelihood, 209 | 'n_iter' : i 210 | } 211 | 212 | return(best_params) 213 | 214 | 215 | 216 | 217 | class GMM(object): 218 | """ 219 | Gaussian Mixture Model (GMM) 220 | 221 | Parameters 222 | ------- 223 | 224 | 225 | Attibutes 226 | ------- 227 | labels_ : cluster labels for each data item 228 | 229 | 230 | Methods 231 | ------- 232 | fit(X): fit the model 233 | fit_predict(X): fit the model and return the cluster labels 234 | """ 235 | 236 | def __init__(self, n_clusters=2, n_trials=10, init_method='', max_iter=100, tol=0.0001): 237 | assert n_clusters >= 2, 'n_clusters should be >= 2' 238 | self.n_clusters = n_clusters 239 | self.n_trials = n_trials 240 | self.init_method = init_method 241 | self.max_iter = max_iter 242 | self.tol = tol 243 | 244 | self.converged = False 245 | 246 | 247 | def fit(self, X): 248 | """ Fit mixture-density parameters with EM algorithm 249 | """ 250 | params_dict = _fit_gmm_params(X=X, n_mixtures=self.n_clusters, \ 251 | n_init=self.n_trials, init_method=self.init_method, \ 252 | n_iter=self.max_iter, tol=self.tol) 253 | self.priors_ = params_dict['priors'] 254 | self.means_ = params_dict['means'] 255 | self.covars_ = params_dict['covars'] 256 | 257 | self.converged = True 258 | self.labels_ = self.predict(X) 259 | 260 | 261 | def predict_proba(self, X): 262 | """ 263 | """ 264 | if not self.converged: 265 | raise Exception('Mixture model is not fit yet!! Try GMM.fit(X)') 266 | _, post_proba = _log_likelihood_per_sample(X=X, means=self.means_, covars=self.covars_) 267 | 268 | return(post_proba) 269 | 270 | 271 | def predict(self, X): 272 | """ 273 | """ 274 | post_proba = self.predict_proba(X) 275 | 276 | return(post_proba.argmax(axis=1)) 277 | -------------------------------------------------------------------------------- /pyclust/_kernel_kmeans.py: -------------------------------------------------------------------------------- 1 | ### Theoretical & Algorithmic Discussion 2 | ### with Emad Zahedi 3 | import numpy as np 4 | import scipy, scipy.spatial 5 | 6 | 7 | 8 | def _compute_gram_matrix(X, kernel_type, params): 9 | """ 10 | """ 11 | if kernel_type == 'rbf': 12 | if 'gamma' in params: 13 | gamma = params['gamma'] 14 | else: 15 | gamma = 1.0 / X.shape[1] 16 | 17 | pairwise_dist = scipy.spatial.distance.pdist(X, metric='sqeuclidean') 18 | pairwise_dist = scipy.spatial.distance.squareform(pairwise_dist) 19 | gram_matrix = np.exp( - gamma * pairwise_dist ) 20 | 21 | np.fill_diagonal(gram_matrix, 1) 22 | else: 23 | pass 24 | 25 | return(gram_matrix) 26 | 27 | 28 | 29 | def _kernelized_dist2centers(K, n_clusters, wmemb, kernel_dist): 30 | """ Computin the distance in transformed feature space to 31 | cluster centers. 32 | 33 | K is the kernel gram matrix. 34 | wmemb contains cluster assignment. {0,1} 35 | 36 | Assume j is the cluster id: 37 | ||phi(x_i) - Phi_center_j|| = K_ii - 2 sum w_jh K_ih + 38 | sum_r sum_s w_jr w_js K_rs 39 | """ 40 | n_samples = K.shape[0] 41 | 42 | for j in range(n_clusters): 43 | memb_j = np.where(wmemb == j)[0] 44 | size_j = memb_j.shape[0] 45 | 46 | K_sub_j = K[memb_j][:, memb_j] 47 | 48 | kernel_dist[:,j] = 1 + np.sum(K_sub_j) /(size_j*size_j) 49 | kernel_dist[:,j] -= 2 * np.sum(K[:, memb_j], axis=1) / size_j 50 | 51 | return 52 | 53 | 54 | def _fit_kernelkmeans(K, n_clusters, n_trials, max_iter, converge_tol=0.001): 55 | """ 56 | """ 57 | n_samples = K.shape[0] 58 | kdist = np.empty(shape=(n_samples, n_clusters), dtype=float) 59 | within_distances = np.empty(shape=n_clusters, dtype=float) 60 | 61 | best_within_distances = np.infty 62 | for i in range(n_trials): 63 | membs_prev = np.random.randint(n_clusters, size=n_samples) 64 | 65 | for it in range(max_iter): 66 | kdist.fill(0) 67 | _kernelized_dist2centers(K, n_clusters, membs_prev, kdist) 68 | 69 | membs_curr = np.argmin(kdist, axis=1) 70 | membs_changed_ratio = float(np.sum((membs_curr - membs_prev) != 0)) / n_samples 71 | 72 | if membs_changed_ratio < converge_tol: 73 | break 74 | 75 | membs_prev = membs_curr 76 | 77 | for j in range(n_clusters): 78 | within_distances[j] = np.sum(kdist[np.where(membs_curr == j)[0], j]) 79 | if best_within_distances > within_distances.sum(): 80 | best_within_distances = within_distances.sum() 81 | best_labels = membs_curr 82 | 83 | return(it, best_labels) 84 | 85 | 86 | 87 | class KernelKMeans(object): 88 | """ 89 | """ 90 | 91 | def __init__(self, n_clusters=2, kernel='linear', params={}, n_trials=10, max_iter=100): 92 | assert (kernel in ['linear', 'rbf']) 93 | self.n_clusters = n_clusters 94 | self.kernel_type = kernel 95 | self.n_trials = n_trials 96 | self.max_iter = max_iter 97 | 98 | self.kernel_params = params 99 | self.kernel_matrix_ = None 100 | 101 | 102 | def _set_kernel_matrix(self, X=None, kernel_matrix=None): 103 | """ 104 | """ 105 | if self.kernel_matrix_ is None: 106 | if kernel_matrix is None: 107 | if X is None: 108 | raise("Either X or kernel_matrix is needed!") 109 | self.kernel_matrix_ = _compute_gram_matrix(X, self.kernel_type, self.kernel_params) 110 | else: 111 | self.kernel_matrix_ = kernel_matrix 112 | 113 | 114 | def fit(self, X, kernel_matrix=None): 115 | """ 116 | """ 117 | self._set_kernel_matrix(X, kernel_matrix) 118 | self.n_iter_, self.labels_ = _fit_kernelkmeans(self.kernel_matrix_, self.n_clusters, self.n_trials, self.max_iter) 119 | 120 | 121 | def fit_predict(self, X): 122 | """ 123 | """ 124 | self.fit(X) 125 | return(self.labels_) 126 | 127 | 128 | ############### Global Kernel K-Means #################### 129 | 130 | 131 | def _fit_global_kernelkmeans(K, n_clusters, max_iter, converge_tol=0.001): 132 | """ 133 | """ 134 | n_samples = K.shape[0] 135 | kdist = np.empty(shape=(n_samples, n_clusters), dtype=float) 136 | within_distances = np.empty(shape=n_clusters, dtype=float) 137 | 138 | best_within_distances = np.infty 139 | for i in range(n_samples): 140 | membs_prev = np.random.randint(n_clusters, size=n_samples) 141 | 142 | for it in range(max_iter): 143 | kdist.fill(0) 144 | _kernelized_dist2centers(K, n_clusters, membs_prev, kdist) 145 | 146 | membs_curr = np.argmin(kdist, axis=1) 147 | membs_changed_ratio = float(np.sum((membs_curr - membs_prev) != 0)) / n_samples 148 | 149 | if membs_changed_ratio < converge_tol: 150 | break 151 | 152 | membs_prev = membs_curr 153 | 154 | for j in range(n_clusters): 155 | within_distances[j] = np.sum(kdist[np.where(membs_curr == j)[0], j]) 156 | if best_within_distances > within_distances.sum(): 157 | best_within_distances = within_distances.sum() 158 | best_labels = membs_curr 159 | 160 | return(it, best_labels) 161 | 162 | class GlobalKernelKMeans(object): 163 | """ 164 | """ 165 | def __init__(self, n_clusters=3, kernel='linear', params={}, n_trials=10, max_iter=100): 166 | self.n_clusters = n_clusters 167 | self.kernel_type = kernel 168 | self.n_trials = n_trials 169 | self.max_iter = max_iter 170 | 171 | self.kernel_params = params 172 | self.kernel_matrix_ = None 173 | 174 | def fit(self, X): 175 | """ 176 | """ 177 | if self.kernel_matrix_ is None: 178 | self.kernel_matrix_ = _compute_gram_matrix(X, self.kernel_type, self.kernel_params) 179 | 180 | 181 | def refit(self, n_clusters): 182 | """ Extend clustering to a larger number of clusters 183 | """ 184 | if n_clusters <= self.n_clusters: 185 | pass 186 | else: 187 | pass 188 | 189 | -------------------------------------------------------------------------------- /pyclust/_kmeans.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import scipy.spatial 3 | 4 | def _kmeans_init(X, n_clusters, method='balanced', rng=None): 5 | """ Initialize k=n_clusters centroids randomly 6 | """ 7 | n_samples = X.shape[0] 8 | if rng is None: 9 | cent_idx = np.random.choice(n_samples, replace=False, size=n_clusters) 10 | else: 11 | #print('Generate random centers using RNG') 12 | cent_idx = rng.choice(n_samples, replace=False, size=n_clusters) 13 | 14 | centers = X[cent_idx,:] 15 | mean_X = np.mean(X, axis=0) 16 | 17 | if method == 'balanced': 18 | centers[n_clusters-1] = n_clusters*mean_X - np.sum(centers[:(n_clusters-1)], axis=0) 19 | 20 | return (centers) 21 | 22 | 23 | def _assign_clusters(X, centers): 24 | """ Assignment Step: 25 | assign each point to the closet cluster center 26 | """ 27 | dist2cents = scipy.spatial.distance.cdist(X, centers, metric='seuclidean') 28 | membs = np.argmin(dist2cents, axis=1) 29 | 30 | return(membs) 31 | 32 | def _cal_dist2center(X, center): 33 | """ Calculate the SSE to the cluster center 34 | """ 35 | dmemb2cen = scipy.spatial.distance.cdist(X, center.reshape(1,X.shape[1]), metric='seuclidean') 36 | return(np.sum(dmemb2cen)) 37 | 38 | def _update_centers(X, membs, n_clusters): 39 | """ Update Cluster Centers: 40 | calculate the mean of feature vectors for each cluster 41 | """ 42 | centers = np.empty(shape=(n_clusters, X.shape[1]), dtype=float) 43 | sse = np.empty(shape=n_clusters, dtype=float) 44 | for clust_id in range(n_clusters): 45 | memb_ids = np.where(membs == clust_id)[0] 46 | 47 | if memb_ids.shape[0] == 0: 48 | memb_ids = np.random.choice(X.shape[0], size=1) 49 | #print("Empty cluster replaced with ", memb_ids) 50 | centers[clust_id,:] = np.mean(X[memb_ids,:], axis=0) 51 | 52 | sse[clust_id] = _cal_dist2center(X[memb_ids,:], centers[clust_id,:]) 53 | return(centers, sse) 54 | 55 | 56 | 57 | def _kmeans_run(X, n_clusters, max_iter, tol): 58 | """ Run a single trial of k-means clustering 59 | on dataset X, and given number of clusters 60 | """ 61 | membs = np.empty(shape=X.shape[0], dtype=int) 62 | centers = _kmeans_init(X, n_clusters) 63 | 64 | sse_last = 9999.9 65 | n_iter = 0 66 | for it in range(1,max_iter): 67 | membs = _assign_clusters(X, centers) 68 | centers,sse_arr = _update_centers(X, membs, n_clusters) 69 | sse_total = np.sum(sse_arr) 70 | if np.abs(sse_total - sse_last) < tol: 71 | n_iter = it 72 | break 73 | sse_last = sse_total 74 | 75 | return(centers, membs, sse_total, sse_arr, n_iter) 76 | 77 | 78 | def _kmeans(X, n_clusters, max_iter, n_trials, tol): 79 | """ Run multiple trials of k-means clustering, 80 | and outputt he best centers, and cluster labels 81 | """ 82 | n_samples, n_features = X.shape[0], X.shape[1] 83 | 84 | centers_best = np.empty(shape=(n_clusters,n_features), dtype=float) 85 | labels_best = np.empty(shape=n_samples, dtype=int) 86 | for i in range(n_trials): 87 | centers, labels, sse_tot, sse_arr, n_iter = _kmeans_run(X, n_clusters, max_iter, tol) 88 | if i==0: 89 | sse_tot_best = sse_tot 90 | sse_arr_best = sse_arr 91 | n_iter_best = n_iter 92 | centers_best = centers.copy() 93 | labels_best = labels.copy() 94 | if sse_tot < sse_tot_best: 95 | sse_tot_best = sse_tot 96 | sse_arr_best = sse_arr 97 | n_iter_best = n_iter 98 | centers_best = centers.copy() 99 | labels_best = labels.copy() 100 | 101 | return(centers_best, labels_best, sse_arr_best, n_iter_best) 102 | 103 | 104 | class KMeans(object): 105 | """ 106 | KMeans Clustering 107 | 108 | Parameters 109 | ------- 110 | n_clusters: number of clusters (default = 2) 111 | n_trials: number of trial random centroid initialization (default = 10) 112 | max_iter: maximum number of iterations (default = 100) 113 | tol: tolerance (default = 0.0001) 114 | 115 | 116 | Attibutes 117 | ------- 118 | labels_ : cluster labels for each data item 119 | centers_ : cluster centers 120 | sse_arr_ : array of SSE values for each cluster 121 | n_iter_ : number of iterations for the best trial 122 | 123 | 124 | Methods 125 | ------- 126 | fit(X): fit the model 127 | fit_predict(X): fit the model and return the cluster labels 128 | """ 129 | 130 | def __init__(self, n_clusters=2, n_trials=10, max_iter=100, tol=0.001): 131 | 132 | self.n_clusters = n_clusters 133 | self.n_trials = n_trials 134 | self.max_iter = max_iter 135 | self.tol = tol 136 | 137 | def fit(self, X): 138 | """ Apply KMeans Clustering 139 | X: dataset with feature vectors 140 | """ 141 | self.centers_, self.labels_, self.sse_arr_, self.n_iter_ = \ 142 | _kmeans(X, self.n_clusters, self.max_iter, self.n_trials, self.tol) 143 | 144 | 145 | def fit_predict(self, X): 146 | """ Apply KMeans Clustering, 147 | and return cluster labels 148 | """ 149 | self.fit(X) 150 | return(self.labels_) 151 | -------------------------------------------------------------------------------- /pyclust/_kmedoids.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import scipy.spatial 3 | 4 | from . import _kmeans as kmeans 5 | 6 | 7 | 8 | def _update_centers(X, membs, n_clusters, distance): 9 | """ Update Cluster Centers: 10 | calculate the mean of feature vectors for each cluster. 11 | 12 | distance can be a string or callable. 13 | """ 14 | centers = np.empty(shape=(n_clusters, X.shape[1]), dtype=float) 15 | sse = np.empty(shape=n_clusters, dtype=float) 16 | for clust_id in range(n_clusters): 17 | memb_ids = np.where(membs == clust_id)[0] 18 | X_clust = X[memb_ids,:] 19 | 20 | dist = np.empty(shape=memb_ids.shape[0], dtype=float) 21 | for i,x in enumerate(X_clust): 22 | dist[i] = np.sum(scipy.spatial.distance.cdist(X_clust, np.array([x]), distance)) 23 | 24 | inx_min = np.argmin(dist) 25 | centers[clust_id,:] = X_clust[inx_min,:] 26 | sse[clust_id] = dist[inx_min] 27 | return(centers, sse) 28 | 29 | 30 | 31 | def _kmedoids_run(X, n_clusters, distance, max_iter, tol, rng): 32 | """ Run a single trial of k-medoids clustering 33 | on dataset X, and given number of clusters 34 | """ 35 | membs = np.empty(shape=X.shape[0], dtype=int) 36 | centers = kmeans._kmeans_init(X, n_clusters, method='', rng=rng) 37 | 38 | sse_last = 9999.9 39 | n_iter = 0 40 | for it in range(1,max_iter): 41 | membs = kmeans._assign_clusters(X, centers) 42 | centers,sse_arr = _update_centers(X, membs, n_clusters, distance) 43 | sse_total = np.sum(sse_arr) 44 | if np.abs(sse_total - sse_last) < tol: 45 | n_iter = it 46 | break 47 | sse_last = sse_total 48 | 49 | return(centers, membs, sse_total, sse_arr, n_iter) 50 | 51 | 52 | def _kmedoids(X, n_clusters, distance, max_iter, n_trials, tol, rng): 53 | """ Run multiple trials of k-medoids clustering, 54 | and output he best centers, and cluster labels 55 | """ 56 | n_samples, n_features = X.shape[0], X.shape[1] 57 | 58 | centers_best = np.empty(shape=(n_clusters,n_features), dtype=float) 59 | labels_best = np.empty(shape=n_samples, dtype=int) 60 | for i in range(n_trials): 61 | centers, labels, sse_tot, sse_arr, n_iter = \ 62 | _kmedoids_run(X, n_clusters, distance, max_iter, tol, rng) 63 | if i==0: 64 | sse_tot_best = sse_tot 65 | sse_arr_best = sse_arr 66 | n_iter_best = n_iter 67 | centers_best = centers.copy() 68 | labels_best = labels.copy() 69 | if sse_tot < sse_tot_best: 70 | sse_tot_best = sse_tot 71 | sse_arr_best = sse_arr 72 | n_iter_best = n_iter 73 | centers_best = centers.copy() 74 | labels_best = labels.copy() 75 | 76 | return(centers_best, labels_best, sse_arr_best, n_iter_best) 77 | 78 | 79 | class KMedoids(object): 80 | """ 81 | KMedoids Clustering 82 | 83 | K-medoids clustering take the cluster centroid as the medoid of the data points, 84 | as opposed to the average of data points in a cluster. As a result, K-medoids 85 | gaurantees that the cluster centroid is among the cluster members. 86 | 87 | The medoid is defined as the point that minimizes the total within-cluster distances. 88 | 89 | K-medoids is more robust to outliers (the reason for this is similar to why 90 | median is more robust to mean). 91 | 92 | K-medoids is computationally more expensive, since it involves computation of all 93 | the pairwise distances in a cluster. 94 | 95 | 96 | Parameters 97 | ------- 98 | n_clusters: number of clusters (default = 2) 99 | n_trials: number of trial random centroid initialization (default = 10) 100 | max_iter: maximum number of iterations (default = 100) 101 | tol: tolerance (default = 0.0001) 102 | 103 | 104 | Attibutes 105 | ------- 106 | labels_ : cluster labels for each data item 107 | centers_ : cluster centers 108 | sse_arr_ : array of SSE values for each cluster 109 | n_iter_ : number of iterations for the best trial 110 | 111 | 112 | Methods 113 | ------- 114 | fit(X): fit the model 115 | fit_predict(X): fit the model and return the cluster labels 116 | """ 117 | 118 | def __init__(self, n_clusters=2, distance='euclidean', 119 | n_trials=10, max_iter=100, tol=0.001, random_state=None): 120 | 121 | self.n_clusters = n_clusters 122 | self.n_trials = n_trials 123 | self.max_iter = max_iter 124 | self.tol = tol 125 | self.distance = distance 126 | self.random_state = random_state 127 | self.rng = np.random.RandomState(random_state) 128 | 129 | def fit(self, X): 130 | """ Apply KMeans Clustering 131 | X: dataset with feature vectors 132 | """ 133 | self.centers_, self.labels_, self.sse_arr_, self.n_iter_ = \ 134 | _kmedoids(X, self.n_clusters, self.distance, self.max_iter, self.n_trials, self.tol, self.rng) 135 | 136 | 137 | def fit_predict(self, X): 138 | """ Apply KMeans Clustering, 139 | and return cluster labels 140 | """ 141 | self.fit(X) 142 | return(self.labels_) 143 | -------------------------------------------------------------------------------- /pyclust/validate/__init__.py: -------------------------------------------------------------------------------- 1 | # Vahid Mirjalili 08/07/2015 2 | # Unsupervised Data Clustering Algorithms in Python 3 | # Machine Learning Application 4 | 5 | from ._internal import Silhouette 6 | 7 | __version__ = '0.1.6' 8 | -------------------------------------------------------------------------------- /pyclust/validate/_internal.py: -------------------------------------------------------------------------------- 1 | import scipy, scipy.spatial 2 | import numpy as np 3 | 4 | import sys 5 | 6 | def _cal_silhouette_score(X, y, sample_size, metric): 7 | """ 8 | """ 9 | n_samples = X.shape[0] 10 | if sample_size is not None: 11 | assert(1 < sample_size < n_samples) 12 | rand_inx = np.random.choice(X.shape[0], size=sample_size) 13 | X_samp, y_samp = X[rand_inx], y[rand_inx] 14 | 15 | else: 16 | X_samp, y_samp = X, y 17 | 18 | n_clust_samp = len(np.unique(y_samp)) 19 | pair_dist = scipy.spatial.distance.pdist(X_samp, metric=metric) 20 | 21 | pair_dist_matrix = scipy.spatial.distance.squareform(pair_dist) 22 | 23 | ## Compute average intra-cluster distances 24 | ## for each of the selected samples 25 | a_arr = _intra_cluster_distances(pair_dist_matrix, y_samp, np.arange(y_samp.shape[0])) 26 | 27 | ## Compute Avg. Distabces to the Neighboring Clusters 28 | b_arr = _neighboring_cluster_distances(pair_dist_matrix, y_samp, np.arange(y_samp.shape[0])) 29 | 30 | comb_arr = np.vstack((a_arr, b_arr)) 31 | return((b_arr-a_arr)/np.max(comb_arr, axis=0), a_arr, b_arr) 32 | 33 | 34 | def _intra_cluster_distances(dist_matrix, y, ilist): 35 | """ 36 | """ 37 | n_samples = y.shape[0] 38 | if type(ilist) == type(list()): 39 | n_inx = len(ilist) 40 | elif type(ilist) == type(np.array([])): 41 | n_inx = ilist.shape[0] 42 | else: 43 | raise Exception("ilist must be iterable!") 44 | 45 | mean_intra_distances = np.empty(shape=n_inx, dtype=float) 46 | for i,inx in enumerate(ilist): 47 | mask = y == y[inx] 48 | mask[inx] = False 49 | if np.sum(mask)>0: 50 | mean_intra_distances[i] = np.mean(dist_matrix[inx][mask]) #/(np.sum(mask) - 1.0) 51 | else: 52 | mean_intra_distances[i] = 0.0 53 | #sys.stderr.write("mask size: %d AvgIntraDist %f\n"%(np.sum(mask), mean_intra_distances[i])) 54 | return(mean_intra_distances) 55 | 56 | 57 | 58 | def _neighboring_cluster_distances(dist_matrix, y, ilist): 59 | """ 60 | """ 61 | n_samples = y.shape[0] 62 | if type(ilist) == type(list()): 63 | n_inx = len(ilist) 64 | elif type(ilist) == type(np.array([])): 65 | n_inx = ilist.shape[0] 66 | else: 67 | raise Exception("ilist must be iterable!") 68 | 69 | min_clust_distances = np.empty(shape=n_inx, dtype=float) 70 | for i,inx in enumerate(ilist): 71 | y_inx = y[inx] 72 | dist_row_inx = dist_matrix[inx] 73 | dist_2_clusters = [np.mean(dist_row_inx[y == j]) for j in set(y) if not j == y_inx] 74 | min_clust_distances[i] = np.min(dist_2_clusters) 75 | 76 | #sys.stderr.write("mask size: %d Nearest Cluster %f\n"%(np.sum(mask),min_clust_distances[i])) 77 | return(min_clust_distances) 78 | 79 | 80 | class Silhouette(object): 81 | """ 82 | """ 83 | def __init__(self): 84 | self.n_labels_ = None 85 | 86 | def score(self, X, labels, sample_size=None, metric='euclidean'): 87 | self.sample_scores, self.a_, self.b_ = _cal_silhouette_score(X, labels, sample_size, metric) 88 | self.score = np.mean(self.sample_scores) 89 | 90 | return(self.score, self.a_, self.b_) 91 | -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | numpy >= 1.9.2 2 | scipy >= 0.15.1 3 | treelib >= 1.3.1 4 | -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | from distutils.core import setup 2 | 3 | 4 | setup(name = "pyclust", 5 | version = "0.1.18", 6 | description = "Data Clustering Algorithms in Python", 7 | author = "Vahid Mirjalili", 8 | author_email = "vmirjalily@gmail.com", 9 | url = "https://github.com/mirjalil/pyclust", 10 | 11 | packages = ['pyclust', 'pyclust.validate'], 12 | 13 | #install_requires=['numpy>=1.9.2', 14 | # 'scipy>=0.15.1', 15 | # 'treelib>=1.3.1'], 16 | 17 | #package *needs* these files. 18 | package_data = {'pyclust':[]}, 19 | classifiers = [ 20 | "Programming Language :: Python", 21 | "Programming Language :: Python :: 3", 22 | "Intended Audience :: Information Technology", 23 | "Operating System :: OS Independent", 24 | ], 25 | 26 | scripts = [], 27 | long_description = """ 28 | 29 | 30 | Contact 31 | ============= 32 | 33 | email: vmirjalily@gmail.com 34 | Twitter: https://twitter.com/vmirly 35 | 36 | URL for this project: https://github.com/mirjalil/pyclust 37 | 38 | """, 39 | #classifiers = [], 40 | license='GPLv3', 41 | platforms='any', 42 | ) 43 | 44 | 45 | -------------------------------------------------------------------------------- /tests/test_bi_kmeans.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import pyclust 3 | 4 | import treelib 5 | 6 | d1 = np.random.uniform(low=-2, high=2, size=(20,2)) 7 | d2 = np.random.uniform(low=2, high=4, size=(10,2)) 8 | d3 = np.random.uniform(low=-4, high=-2, size=(10,2)) 9 | da = np.vstack((d1,d2,d3)) 10 | 11 | 12 | def test_bisect3(): 13 | bkm = pyclust.BisectKMeans(n_clusters=4) 14 | 15 | bkm.fit(da) 16 | 17 | print(bkm.labels_) 18 | 19 | leaf_nodes = bkm.tree_.leaves() 20 | for node in leaf_nodes: 21 | print(node.data) 22 | 23 | 24 | bkm.tree_.show(line_type='ascii') 25 | 26 | print("Orig: ", np.unique(bkm.labels_)) 27 | print("Cut2: ", np.unique(bkm.cut(2)[0])) 28 | print("Cut3: ", np.unique(bkm.cut(3)[0])) 29 | print("Cut4: ", np.unique(bkm.cut(4)[0])) 30 | 31 | 32 | def test_bisect10(): 33 | nsamp = 20 34 | da = np.random.multivariate_normal(mean=(-2,0), cov=[[0.12,0],[0,0.12]], size=nsamp) 35 | ya = np.ones(shape=nsamp, dtype=int) 36 | 37 | db = np.random.multivariate_normal(mean=(-3,1), cov=[[0.08,0.05],[0.05,0.08]], size=nsamp) 38 | yb = 2*np.ones(shape=nsamp, dtype=int) 39 | 40 | dc = np.random.multivariate_normal(mean=(-3,-1), cov=[[0.08,-0.05],[-0.05,0.08]], size=nsamp) 41 | yc = 3*np.ones(shape=nsamp, dtype=int) 42 | 43 | dd = np.random.multivariate_normal(mean=(-1,1), cov=[[0.08,-0.05],[-0.05,0.08]], size=nsamp) 44 | yd = 4*np.ones(shape=nsamp, dtype=int) 45 | 46 | de = np.random.multivariate_normal(mean=(-1,-1), cov=[[0.08,0.05],[0.05,0.08]], size=nsamp) 47 | ye = 5*np.ones(shape=nsamp, dtype=int) 48 | 49 | df = np.random.multivariate_normal(mean=(3,0.6), cov=[[0.05,0.0],[0.0,0.05]], size=nsamp) 50 | yf = 6*np.ones(shape=nsamp, dtype=int) 51 | 52 | dg = np.random.multivariate_normal(mean=(3,-0.6), cov=[[0.05,0.0],[0.0,0.05]], size=nsamp) 53 | yg = 7*np.ones(shape=nsamp, dtype=int) 54 | 55 | X = np.vstack((da, db, dc, dd, de, df, dg)) 56 | y = np.hstack((ya, yb, yc, yd, ye, yf, yg)) 57 | 58 | 59 | bkm = pyclust.BisectKMeans(n_clusters=10) 60 | 61 | bkm.fit(X) 62 | 63 | leaf_nodes = bkm.tree_.leaves() 64 | for node in leaf_nodes: 65 | print(node.data) 66 | 67 | bkm.tree_.show(line_type='ascii') 68 | 69 | print("Orig: ", np.unique(bkm.labels_)) 70 | print("Cut2: ", np.unique(bkm.cut(2)[0])) 71 | print("Cut3: ", np.unique(bkm.cut(3)[0])) 72 | print("Cut4: ", np.unique(bkm.cut(4)[0])) 73 | 74 | print("Cut5: ", np.unique(bkm.cut(5)[0])) 75 | print("Cut6: ", np.unique(bkm.cut(6)[0])) 76 | print("Cut7: ", np.unique(bkm.cut(7)[0])) 77 | 78 | test_bisect10() 79 | 80 | test_bisect3() 81 | -------------------------------------------------------------------------------- /tests/test_gmm.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import scipy, scipy.linalg 3 | import sys 4 | 5 | import pyclust 6 | 7 | 8 | s1 = np.array([[0.3, 0.2], [0.7, 0.5]]) 9 | s2 = np.array([[0.6, 0.0], [0.0, 1.1]]) 10 | 11 | m1 = np.array([0.0, 0.0]) 12 | m2 = np.array([2.0, -3.0]) 13 | 14 | X1 = np.random.multivariate_normal(mean=m1, cov=s1, size=200) 15 | X2 = np.random.multivariate_normal(mean=m2, cov=s2, size=300) 16 | 17 | X = np.vstack((X1, X2)) 18 | 19 | #np.savetxt("/tmp/test", X) 20 | 21 | def test_gmm(): 22 | gmm = pyclust.GMM(n_clusters=2) 23 | 24 | gmm.fit(X) 25 | print(gmm.priors_) 26 | print(gmm.means_) 27 | print(gmm.covars_) 28 | 29 | 30 | print(gmm.predict(X)) 31 | 32 | test_gmm() 33 | -------------------------------------------------------------------------------- /tests/test_kernel_kmeans.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import pyclust 3 | 4 | 5 | d1 = np.random.uniform(low=0, high=3, size=(20,2)) 6 | d2 = np.random.uniform(low=3, high=5, size=(20,2)) 7 | d = np.vstack((d1,d2)) 8 | from scipy.sparse import issparse 9 | 10 | def test_kernelkmeans(): 11 | kg = pyclust._kernel_kmeans._compute_gram_matrix(d, kernel_type='rbf', params={}) 12 | 13 | #print(kg[0,:]) 14 | #print(kg[19,:]) 15 | 16 | w = np.random.randint(2, size=20) 17 | wmemb_old = w 18 | 19 | kdist = np.zeros(shape=(20,2), dtype=float) 20 | 21 | #res = pyclust._kernel_kmeans._fit_kernelkmeans(kg, 2, 100) 22 | 23 | kkm = pyclust.KernelKMeans(n_clusters=2, kernel='rbf') 24 | kkm.fit_predict(d) 25 | print("Converged after %d iterations"%kkm.n_iter_) 26 | print(kkm.labels_) 27 | 28 | test_kernelkmeans() 29 | -------------------------------------------------------------------------------- /tests/test_kmeans.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import pyclust 3 | 4 | 5 | d1 = np.random.uniform(low=0, high=2, size=(10,2)) 6 | d2 = np.random.uniform(low=0, high=4, size=(10,2)) 7 | d = np.vstack((d1,d2)) 8 | 9 | print(d.shape) 10 | cent = pyclust._kmeans._kmeans_init(d, 2) 11 | #d2c = scipy.spatial.distance.cdist(d, cent, metric='euclidean') 12 | 13 | print(cent) 14 | 15 | membs = pyclust._kmeans._assign_clusters(d, cent) 16 | 17 | print(membs) 18 | 19 | cent_upd = pyclust._kmeans._update_centers(d, membs, n_clusters=2) 20 | 21 | print(cent_upd) 22 | 23 | print(pyclust._kmeans._kmeans_run(d, n_clusters=2, max_iter=20, tol=0.0001)) 24 | 25 | km = pyclust.KMeans(n_clusters=2) 26 | 27 | km.fit(d) 28 | 29 | print("Centers: ", km.centers_) 30 | print("Labels: ", km.labels_) 31 | print("SSE: ", km.sse_arr_) 32 | print("N_ITER: ", km.n_iter_) 33 | 34 | ## Checking the random-number generator 35 | #rng = np.random.RandomState(1234) 36 | print('\n\n*** Testing RandomState: ***') 37 | for i in range(3): 38 | rng = np.random.RandomState(1234) 39 | print(pyclust._kmeans._kmeans_init(d, 2, rng=rng)) 40 | print() 41 | -------------------------------------------------------------------------------- /tests/test_kmedoids.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import pyclust 3 | 4 | 5 | d1 = np.random.uniform(low=0, high=2, size=(10,2)) 6 | d2 = np.random.uniform(low=0, high=4, size=(10,2)) 7 | d = np.vstack((d1,d2)) 8 | 9 | print(d.shape) 10 | cent = pyclust._kmeans._kmeans_init(d, 2) 11 | #d2c = scipy.spatial.distance.cdist(d, cent, metric='euclidean') 12 | 13 | print(cent) 14 | 15 | membs = pyclust._kmeans._assign_clusters(d, cent) 16 | 17 | print(membs) 18 | 19 | cent_upd = pyclust._kmedoids._update_centers(d, membs, n_clusters=2, distance='euclidean') 20 | 21 | print(cent_upd) 22 | 23 | 24 | rng = np.random.RandomState(1234) 25 | print(pyclust._kmedoids._kmedoids_run(d, n_clusters=2, distance='euclidean', max_iter=20, tol=0.001, rng=rng)) 26 | 27 | kmd = pyclust.KMedoids(n_clusters=2) 28 | 29 | kmd.fit(d) 30 | 31 | print("Centers: ", kmd.centers_) 32 | print("Labels: ", kmd.labels_) 33 | print("SSE: ", kmd.sse_arr_) 34 | print("N_ITER: ", kmd.n_iter_) 35 | 36 | 37 | print('\n\n*** Testing RandomState: ***') 38 | for i in range(3): 39 | kmd2 = pyclust.KMedoids(n_clusters=2, random_state=123) 40 | kmd2.fit(d) 41 | print("Centers: ", kmd2.centers_) 42 | print("Labels: ", kmd2.labels_) 43 | print("SSE: ", kmd2.sse_arr_) 44 | print("N_ITER: ", kmd2.n_iter_) 45 | print() 46 | 47 | -------------------------------------------------------------------------------- /tests/test_silhouette.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import scipy, scipy.linalg 3 | import sys 4 | 5 | import pyclust, pyclust.validate 6 | from sklearn.metrics import silhouette_score, silhouette_samples 7 | 8 | s1 = np.array([[0.3, 0.2], [0.7, 0.5]]) 9 | s2 = np.array([[0.6, 0.0], [0.0, 1.1]]) 10 | 11 | m1 = np.array([0.0, 0.0]) 12 | m2 = np.array([2.0, -3.0]) 13 | 14 | X1 = np.random.multivariate_normal(mean=m1, cov=s1, size=200) 15 | X2 = np.random.multivariate_normal(mean=m2, cov=s2, size=300) 16 | 17 | X = np.vstack((X1, X2)) 18 | 19 | #X = np.array([[-1,0],[0,0],[-1,-1],[2,0],[2,1],[3,0]]) 20 | #X = np.array([[-1,0],[0,0],[0,0],[2,0],[2,0],[3,0]]) 21 | #ypred = np.array([1,1,1,2,2,2]) 22 | ypred = np.hstack((np.zeros(shape=200), np.ones(shape=300))) 23 | print(ypred.shape) 24 | 25 | #np.savetxt("/tmp/test", X) 26 | 27 | def test_gmm(): 28 | sil = pyclust.validate.Silhouette() 29 | sil_score = sil.score(X, ypred, sample_size=None) 30 | 31 | print(sil_score[0]) 32 | 33 | print(sil.sample_scores[:10]) 34 | 35 | print(silhouette_score(X, ypred, sample_size=None)) 36 | 37 | print(silhouette_samples(X, ypred)[:10]) 38 | test_gmm() 39 | --------------------------------------------------------------------------------