Skip to content

Instantly share code, notes, and snippets.

@Z30G0D
Created July 15, 2018 09:27
Show Gist options
  • Save Z30G0D/a52c1654e03df212bfab2842f472b302 to your computer and use it in GitHub Desktop.
Save Z30G0D/a52c1654e03df212bfab2842f472b302 to your computer and use it in GitHub Desktop.
A spectral clustering from scratch
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Spectral Clustering Analysis\n",
"## Spectral Clustering algorithm from scratch .\n",
"\n",
"One of the main fields in Machine learning is the field of unsupservised learning.<br>\n",
"The main idea is to find a pattern in our data without the prior knowledge of labels for example in supervised learning.<br>\n",
"It is usually achieved by clustering our data into groups.<br>\n",
"One of the more popular algorithms is the very popular K means algorithm (or the familiar EM algorithm). In this algorithm we have K centroids adjusted in an iterative process to find our clusters. sounds good right? <br>\n",
"But the main problems are:<br>\n",
"1) It makes assumption on the shape of the data (a round sphere, a radial basis)<br>\n",
"2) It requires multiple restarts at times to find the local minima (i.e. the best clustering)<br>\n",
"\n",
"Spectral Clustering helps to solve these two problems. Using a graph of the data points and <br>\n",
"The stages are:<br>\n",
"1) constructing a similarity graph (KNN graph)<br>\n",
"2) Embed the data points in low dimensional space (spectral embedding) in which the clusters are more obvious with the use of eigenvectors of the graph Laplacian.<br>\n",
"3) A classical Clustering algorithm (e.g. K - means) is applied to partition the embedding"
]
},
{
"cell_type": "code",
"execution_count": 507,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The watermark extension is already loaded. To reload it, use:\n",
" %reload_ext watermark\n",
"2018-07-15T10:27:49+03:00\n",
"\n",
"CPython 3.5.4\n",
"IPython 6.2.1\n",
"\n",
"compiler : MSC v.1900 64 bit (AMD64)\n",
"system : Windows\n",
"release : 10\n",
"machine : AMD64\n",
"processor : Intel64 Family 6 Model 142 Stepping 9, GenuineIntel\n",
"CPU cores : 4\n",
"interpreter: 64bit\n"
]
}
],
"source": [
"%load_ext watermark\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\") \n",
"from IPython.core.display import display, HTML\n",
"\n",
"import time\n",
"\n",
"import pandas as pd\n",
"import pandas_datareader.data as web\n",
"import numpy as np\n",
"\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"%watermark"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exploring the spectral clustering algorithm."
]
},
{
"cell_type": "code",
"execution_count": 511,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x1eb5f0a4a90>"
]
},
"execution_count": 511,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1eb5f04fd30>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.datasets import make_moons\n",
"random_state = 21\n",
"X_mn, y_mn = make_moons(150, noise=.07, random_state=random_state)\n",
"cmap = 'viridis'\n",
"dot_size=50\n",
"\n",
"fig, ax = plt.subplots(figsize=(9,7))\n",
"ax.set_title('Data with ground truth labels ', fontsize=18, fontweight='demi')\n",
"\n",
"ax.scatter(X_mn[:, 0], X_mn[:, 1],c=y_mn,s=dot_size, cmap=cmap)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"clearly, a K means algorithm won't help here since the clusters are not spherical.<br>\n",
"Here is an example of trying to solve this clustering problem using K- means.\n"
]
},
{
"cell_type": "code",
"execution_count": 496,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x1eb5ea26550>"
]
},
"execution_count": 496,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1eb5e9256d8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"kmeans = KMeans(n_clusters=2, random_state=0).fit(X_mn)\n",
"fig, ax = plt.subplots(figsize=(9,7))\n",
"ax.set_title('Data after trying to cluster using Kmeans', fontsize=18, fontweight='demi')\n",
"\n",
"ax.scatter(X_mn[:, 0], X_mn[:, 1],c=kmeans.labels_,s=dot_size, cmap=cmap)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's try to follow the stages of the spectral clustering.<br>\n",
"Let's start with creating the nearest neighbours graph we need:"
]
},
{
"cell_type": "code",
"execution_count": 428,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.neighbors import radius_neighbors_graph\n",
"from sklearn.neighbors import kneighbors_graph"
]
},
{
"cell_type": "code",
"execution_count": 472,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(150, 150)"
]
},
"execution_count": 472,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = radius_neighbors_graph(X_mn,0.4,mode='distance', metric='minkowski', p=2, metric_params=None, include_self=False)\n",
"# A = kneighbors_graph(X_mn, 2, mode='connectivity', metric='minkowski', p=2, metric_params=None, include_self=False)\n",
"A = A.toarray()\n",
"A.shape"
]
},
{
"cell_type": "code",
"execution_count": 473,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[0. , 0. , 0. , 0. , 0.23955829],\n",
" [0. , 0. , 0. , 0. , 0. ],\n",
" [0. , 0. , 0. , 0. , 0. ],\n",
" [0. , 0. , 0. , 0. , 0. ],\n",
" [0.23955829, 0. , 0. , 0. , 0. ]])"
]
},
"execution_count": 473,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A[:5,:5]"
]
},
{
"cell_type": "code",
"execution_count": 474,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1eb5d443978>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(9,7))\n",
"ax.set_title('5 first datapoints', fontsize=18, fontweight='demi')\n",
"ax.set_xlim(-1, 2)\n",
"ax.set_ylim(-1,1)\n",
"ax.scatter(X_mn[:5, 0], X_mn[:5, 1],s=dot_size, cmap=cmap)\n",
"for i in range(5):\n",
" ax.annotate(i, (X_mn[i,0],X_mn[i,1]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So we have here our adjacency matrix (50x50), which depicts the distances between each point to another,we set a limit to connect only the 25 nearest points, so all other weights (between the point will be zero.<br>\n",
"Let's take a look at the relationship of the first 5 data points.<br>\n",
"The diagonal in the matrix is zero since every point is not connected to itself. Notice that it is also symmetrical from the nature of our data (e.g. weight between point 1 and 2 is the same as 2 and 1).<br>\n",
"Every number represents the weight (the distance) between the two points, as you can see points 1 and 2 are very close and the weight is 0.2143.<br>\n",
"But point 0 and point 3 are quite far away so the weight is 0 (in simple words, point 0 is not one of the closest 25 points to point 3).<br>\n",
"<br>\n",
"\n",
"Ok, so we are done with building our nearest neighbours graph (equivelent to our adjacency matrix), <br>\n",
"Let's move on to our Laplacian.<br>\n",
"The Laplacian is defined as the L=D-A where A is our adjecency matrix we just saw and D is a diagonal matrix.<br>\n",
"D is the \"degree matrix\" , every cell in the diagonal is the sum of the weights for that point. <br>\n",
"For example,D(1,1) is the sum of all weights between point 1 and all other points (so it is the sum of row number 1 in the adjacency matrix).<br>\n",
"The same for D(2,2) and so on. D(I,J) when I is different than J is 0."
]
},
{
"cell_type": "code",
"execution_count": 475,
"metadata": {},
"outputs": [],
"source": [
"from scipy.sparse import csgraph\n",
"from sklearn.cluster import KMeans\n",
"L = csgraph.laplacian(A, normed=False)"
]
},
{
"cell_type": "code",
"execution_count": 476,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([[ 3.8892734 , -0. , -0. , -0. , -0.23955829],\n",
" [-0. , 3.40126844, -0. , -0. , -0. ],\n",
" [-0. , -0. , 3.00486906, -0. , -0. ],\n",
" [-0. , -0. , -0. , 3.45831612, -0. ],\n",
" [-0.23955829, -0. , -0. , -0. , 4.06569259]]),)"
]
},
"execution_count": 476,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"L[:5,:5],"
]
},
{
"cell_type": "code",
"execution_count": 477,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([3.8892734 , 3.40126844])"
]
},
"execution_count": 477,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"B = np.sum(A,axis=0)\n",
"B[:2]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So I used the built in function of scipy for laplacian, as you can see the Laplacian values on the diagonal are the degree matrix, and the rest are the weights from the adjacency matrix with the minus sign due to our formula.<br>\n",
"\n",
"Next we are going to embed the data points in a low dimensional space(spectral embedding), in which the clusters are more *obvious* with the use of eigenvectors of the graph laplacian."
]
},
{
"cell_type": "code",
"execution_count": 513,
"metadata": {},
"outputs": [],
"source": [
"eigval, eigvec = np.linalg.eig(L)\n",
"kmeans = KMeans(n_clusters=2, random_state=0).fit(eigvec)\n",
"# kmeans"
]
},
{
"cell_type": "code",
"execution_count": 516,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"((array([0], dtype=int64),),\n",
" (array([6], dtype=int64),),\n",
" 0.03098972875873049,\n",
" (array([1], dtype=int64),))"
]
},
"execution_count": 516,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.where(eigval == np.partition(eigval, 1)[1]) "
]
},
{
"cell_type": "code",
"execution_count": 485,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.33920652e-15, 3.09897288e-02, 1.26309658e-01, 1.61499165e-01,\n",
" 4.43825692e-01, 5.82521350e-01, 6.74514701e+00, 1.01824273e+00,\n",
" 1.16903130e+00, 1.34766710e+00, 6.32972566e+00, 6.20550519e+00,\n",
" 1.58755522e+00, 1.69464645e+00, 5.94723886e+00, 5.94017533e+00,\n",
" 5.84882863e+00, 5.77774310e+00, 5.71152497e+00, 5.44922770e+00])"
]
},
"execution_count": 485,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eigval[:20]"
]
},
{
"cell_type": "code",
"execution_count": 486,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-8.16496581e-02, -6.50452416e-02, -9.54270622e-02, -4.81422791e-02,\n",
" 4.70127577e-02, 9.73107702e-03, 2.22259737e-06, 1.60521800e-01,\n",
" 2.98776353e-02, 5.33885832e-02, -3.68793655e-02, 6.82503362e-04,\n",
" 1.54935573e-01, -5.09990254e-03, -5.17998325e-02, 1.47600468e-02,\n",
" -4.16481280e-02, 2.55500671e-02, 1.10182626e-01, 9.15063934e-03,\n",
" 1.96342780e-02, 7.97045058e-04, 5.58115113e-03, 1.86976586e-03,\n",
" 5.34649687e-02, -1.00826049e-01, 5.74619881e-03, 3.98974570e-02,\n",
" -3.16111655e-02, -2.32944319e-02, -2.81643434e-02, -2.11019304e-02,\n",
" 7.77073393e-02, 2.16993895e-04, -1.26997019e-03, 2.20672792e-02,\n",
" 4.40736621e-03, 2.35474216e-02, 4.78082842e-03, -2.39693108e-02,\n",
" -5.15340866e-03, -8.32125285e-03, 8.75436352e-04, 4.08518755e-03,\n",
" 2.19015849e-03, 2.09198351e-02, 5.45501946e-03, 4.02612385e-02,\n",
" -8.05743144e-04, -1.68807867e-02, -1.10066937e-02, -3.63346249e-02,\n",
" 9.09916819e-03, -2.12209831e-02, 5.99716228e-03, -1.34853665e-02,\n",
" 3.13444156e-02, 2.02405064e-01, -1.17525543e-03, 9.37524974e-03,\n",
" -3.48824567e-02, 1.37094238e-01, -2.17500362e-03, 5.33319353e-03,\n",
" -1.14105521e-02, -3.42873542e-02, 6.36925763e-03, 1.03946038e-02,\n",
" 4.69246214e-03, 7.25242927e-04, -2.15797694e-03, 2.23012531e-03,\n",
" -2.53297322e-02, -2.51860376e-02, -2.76696358e-01, -1.01897715e-02,\n",
" 1.16767502e-02, -3.75195462e-02, -4.90234268e-03, 6.46867471e-05,\n",
" 1.82772560e-03, -1.69459029e-02, 1.82498227e-01, 6.21168298e-02,\n",
" 5.69399593e-03, 2.79000907e-02, 6.01747346e-03, 5.63966233e-03,\n",
" 1.11450098e-01, 3.46826353e-02, -2.40791456e-02, -3.49755785e-03,\n",
" 1.82725047e-02, 1.24137213e-01, 2.89703129e-02, -5.62588126e-03,\n",
" -1.96163029e-01, -1.11079754e-01, -2.83998683e-01, -1.70743703e-02,\n",
" 8.86861399e-02, 1.09969014e-02, 7.52828451e-02, -1.85444553e-03,\n",
" -9.73768013e-02, -1.07807805e-01, 8.50681309e-03, -9.38863607e-04,\n",
" -2.21056367e-01, 8.71098790e-03, -2.00519220e-02, 2.44932588e-03,\n",
" 1.02038260e-01, -1.92226220e-03, -8.91487552e-02, 2.98278921e-03,\n",
" -2.80350971e-03, -3.68953136e-02, -9.28778583e-02, 2.43549654e-01,\n",
" 7.04125552e-02, 3.88148980e-02, -1.15973050e-01, 1.29561345e-01,\n",
" 2.78475838e-02, -5.13183711e-02, -5.04928427e-02, 3.02499381e-02,\n",
" 1.03263819e-03, 7.40261079e-02, -1.76110314e-04, -9.42524231e-02,\n",
" 1.02318067e-01, -4.45222007e-02, 2.86821874e-01, -3.71298188e-02,\n",
" 4.53556511e-02, 5.04896393e-02, -1.03813502e-01, 7.43530699e-02,\n",
" 1.67786078e-02, 2.55783942e-01, -5.21683190e-02, 1.92178721e-01,\n",
" -1.95698596e-01, 4.19184692e-02, -3.93452755e-02, -6.84873646e-02,\n",
" -1.58221172e-02, -1.73192584e-01])"
]
},
"execution_count": 486,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eigvec[3]"
]
},
{
"cell_type": "code",
"execution_count": 491,
"metadata": {},
"outputs": [],
"source": [
"y_spec =eigvec[:,1].copy()\n",
"y_spec[y_spec < 0] = 0\n",
"y_spec[y_spec > 0] = 1"
]
},
{
"cell_type": "code",
"execution_count": 492,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(numpy.ndarray, (150,), (150,))"
]
},
"execution_count": 492,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"type(y_spec),y_mn.shape,y_spec.shape"
]
},
{
"cell_type": "code",
"execution_count": 517,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x1eb5f0e3550>"
]
},
"execution_count": 517,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1eb5f008128>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(9,7))\n",
"ax.set_title('Data after spectral clustering from scratch', fontsize=18, fontweight='demi')\n",
"ax.scatter(X_mn[:, 0], X_mn[:, 1],c=y_spec ,s=dot_size, cmap=cmap)"
]
},
{
"cell_type": "code",
"execution_count": 519,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x1eb5f3d9e80>"
]
},
"execution_count": 519,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1eb5f124898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.cluster import SpectralClustering\n",
"\n",
"model = SpectralClustering(n_clusters=2, affinity='nearest_neighbors',\n",
" assign_labels='kmeans')\n",
"\n",
"labelsS = model.fit_predict(X_mn)\n",
"\n",
"fig, ax = plt.subplots(figsize=(9,7))\n",
"ax.set_title('Built in sklearn spectral clustering', fontsize=18, fontweight='demi')\n",
"plt.scatter(X_mn[:, 0], X_mn[:, 1], c=labelsS, s=dot_size, cmap=cmap)"
]
},
{
"cell_type": "code",
"execution_count": 424,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"SpectralClustering(affinity='nearest_neighbors', assign_labels='kmeans',\n",
" coef0=1, degree=3, eigen_solver=None, eigen_tol=0.0, gamma=1.0,\n",
" kernel_params=None, n_clusters=2, n_init=10, n_jobs=1,\n",
" n_neighbors=10, random_state=None)"
]
},
"execution_count": 424,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python (myenv)",
"language": "python",
"name": "myenv"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment