{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# Feature Selection\n",
"This material is adapted from the following,\n",
"- [Scikit Learn](http://scikit-learn.org/stable/) \n",
"- [Sebastian Raschka](https://github.com/rasbt/python-machine-learning-book) \n",
"- [Jake Vanderplas](https://github.com/jakevdp/sklearn_tutorial)\n",
"- [Andreas Mueller](http://amueller.github.io) \n",
"- [Kyle Kastner](https://kastnerkyle.github.io/) \n",
"- [Quantopian Research](https://github.com/quantopian/research_public)\n",
"- [Python for Probability, Statistics, and Machine Learning](http://www.springer.com/fr/book/9783319307152), [github](https://github.com/unpingco/Python-for-Probability-Statistics-and-Machine-Learning)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Imports"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
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"text/html": [
""
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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from IPython.core.display import display, HTML\n",
"display(HTML(\"\"))\n",
"\n",
"%load_ext line_profiler\n",
"\n",
"# Ignore Warnings\n",
"def warn(*args, **kwargs):\n",
" pass\n",
"import warnings\n",
"warnings.warn = warn\n",
"\n",
"from helper_functions import tic, toc\n",
"\n",
"\"\"\" Include Parent Directory in Python Path \"\"\"\n",
"import os,sys,inspect\n",
"currentdir = os.path.dirname(os.path.abspath(inspect.getfile(inspect.currentframe())))\n",
"parentdir = os.path.dirname(currentdir)\n",
"sys.path.insert(0,parentdir) "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from IPython.display import Image\n",
"%matplotlib inline\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"%matplotlib inline\n",
"plt.style.use('fivethirtyeight')\n",
"plt.rcParams['figure.figsize'] = (10, 6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Notes for today's class"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Note on imputation\n",
"If you need to impute data, you have several options with Pandas. A very nice purpose-specific library to consider is [FancyImpute](https://pypi.python.org/pypi/fancyimpute/0.0.4). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Note on Categorical/Qualitative Data\n",
"A common way to deal with categorical/qualitative data is to \"onehotencode\" the classes/categories. This is available in scikit-learn."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Training-Test Splitting\n",
"Scikit-Learn provides several \"Cross-Validation\" approaches. For now, it's best to stick to the [train_test_split](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html) function. \n",
"\n",
"More detail on more advanced techniques will be provided in the class on Model Evaluation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Feature Scaling\n",
"Many algorithms benefit from features that are appropriately scaled. Many [scaling functions](http://scikit-learn.org/stable/modules/preprocessing.html) are available in Scikit-Learn. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Feature Selection\n",
"[This](http://blog.datadive.net/selecting-good-features-part-i-univariate-selection/) series of posts provides a comprehensive review of feature selection approaches. \n",
"\n",
"[mlxtend](http://rasbt.github.io/mlxtend/) provides several good [sequential feature selection](http://rasbt.github.io/mlxtend/user_guide/feature_selection/SequentialFeatureSelector/#sequential-feature-selector) algorithms you should be familiar with."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Regularization\n",
"The idea behind regularization is to prefer simpler models for a certain definition of ''simpler'', even if they lead to more errors on the training set.\n",
"\n",
"Regularization can also be viewed as a prior on the distribution from which your data is drawn (most famously Gaussian for least-squares), as a way to punish high values in regression coefficients, and so on.\n",
"\n",
"First, let's understand Projection,"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Projection\n",
"\n",
"The concept of projection is key to developing an intuition about regularization. We already have a natural intuition of projection from looking at the shadows of objects on a sunny day. Consider the following figure:\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our aim is to find a point along the blue line (namely, $\\mathbf{x}$) that is closest to the black square (namely, $\\mathbf{y}$). In other words, we want to inflate the gray circle until it just touches the black line. Recall that the circle boundary is the set of points for which\n",
"$$\n",
"\\sqrt{(\\mathbf{y}-\\mathbf{x})^T(\\mathbf{y}-\\mathbf{x})} =\\|\\mathbf{y}-\\mathbf{x} \\| = \\epsilon\n",
"$$\n",
"\n",
" for some value of $\\epsilon$. So we want a point $\\mathbf{x}$ along\n",
"the line that satisfies this for the smallest $\\epsilon$. Then, that point\n",
"will be the closest point on the black line to the black square.\n",
" It may be obvious from the diagram, but the closest point on the line\n",
"occurs where the line segment from the black square to the black line is\n",
"perpedicular to the line. At this point, the gray circle just touches the black\n",
"line.\n",
"\n",
"Given the point $\\mathbf{y}$ (black square) we want to find the $\\mathbf{x}$ along the line that is closest to it. The gray circle is the locus of points within a fixed distance from $\\mathbf{y}$.\n",
"\n",
"The line tangent to the circle is the closest point on the line.\n",
"\n",
"
\n",
"\n",
"We can analytically solve for an arbitrary point along the black line as:\n",
"\n",
"$$\n",
"\\mathbf{x}=\\alpha\\mathbf{v}\n",
"$$\n",
"\n",
"where $\\alpha\\in\\mathbb{R}$ slides the point up and down the line with\n",
" \n",
"$$\n",
"\\mathbf{v} = \\left[ 1,1 \\right]^T\n",
"$$\n",
"\n",
"Formally, $\\mathbf{v}$ is the *subspace* onto which we want to *project* $\\mathbf{y}$. At the closest point, the vector between $\\mathbf{y}$ and $\\mathbf{x}$ (the *error* vector above) is\n",
"perpedicular to the line. This means that\n",
"\n",
"$$\n",
"(\\mathbf{y}-\\mathbf{x} )^T \\mathbf{v} = 0\n",
"$$\n",
"\n",
"and through substitution and basic algebra, we obtain\n",
" \n",
"$$\n",
"\\alpha = \\frac{\\mathbf{y}^T\\mathbf{v}}{ \\|\\mathbf{v} \\|^2}\n",
"$$\n",
"\n",
"The *error* is the distance between $\\alpha\\mathbf{v}$ and $\\mathbf{y}$. This is a right triangle, and we can use the Pythagorean theorem to compute the squared length of this error as\n",
"\n",
"$$\n",
"\\epsilon^2 = \\|( \\mathbf{y}-\\mathbf{x} )\\|^2 = \\|\\mathbf{y}\\|^2 - \\alpha^2 \\|\\mathbf{v}\\|^2 = \\|\\mathbf{y}\\|^2 - \\frac{\\|\\mathbf{y}^T\\mathbf{v}\\|^2}{\\|\\mathbf{v}\\|^2}\n",
"$$\n",
"\n",
"where $ \\|\\mathbf{v}\\|^2 = \\mathbf{v}^T \\mathbf{v} $. Note that since $\\epsilon^2 \\ge 0 $, this also shows that\n",
" \n",
"$$\n",
"\\| \\mathbf{y}^T\\mathbf{v}\\| \\le \\|\\mathbf{y}\\| \\|\\mathbf{v}\\|\n",
"$$\n",
"\n",
"which is the famous and useful Cauchy-Schwarz inequality. Finally, we can assemble all of this into the *projection* operator\n",
"\n",
"$$\n",
"\\mathbf{P}_v = \\frac{1}{\\|\\mathbf{v}\\|^2 } \\mathbf{v v}^T\n",
"$$\n",
"\n",
"With this operator, we can take any $\\mathbf{y}$ and find the closest point on $\\mathbf{v}$ as\n",
"\n",
"$$\n",
"\\mathbf{P}_v \\mathbf{y} = \\mathbf{v} \\left( \\frac{ \\mathbf{v}^T \\mathbf{y} }{\\|\\mathbf{v}\\|^2} \\right)\n",
"$$\n",
"\n",
"where we recognize the term in parenthesis as the $\\alpha$ we computed earlier. It's called an *operator* because it takes a vector ($\\mathbf{y}$) and produces another vector ($\\alpha\\mathbf{v}$). Thus, projection unifies geometry and optimization."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Weighted distance\n",
"\n",
"We can easily extend this projection operator to cases where the measure of\n",
"distance between $\\mathbf{y}$ and the subspace $\\mathbf{v}$ is weighted. We can\n",
"accommodate these weighted distances by re-writing the projection operator as\n",
"\n",
"\n",
"\n",
"\n",
"$$\n",
"\\mathbf{P}_v=\\mathbf{v}\\frac{\\mathbf{v}^T\\mathbf{Q}^T}{\\mathbf{v}^T\\mathbf{Q v}}\n",
"$$\n",
"\n",
" where $\\mathbf{Q}$ is positive definite matrix. In the previous\n",
"case, we started with a point $\\mathbf{y}$ and inflated a circle centered at\n",
"$\\mathbf{y}$ until it just touched the line defined by $\\mathbf{v}$ and this\n",
"point was closest point on the line to $\\mathbf{y}$. The same thing happens\n",
"in the general case with a weighted distance except now we inflate an\n",
"ellipse, not a circle, until the ellipse touches the line.\n",
"\n",
"In the weighted case, the closest point on the line is tangent to the ellipse and is still perpedicular in the sense of the weighted distance.\n",
"\n",
"
\n",
"\n",
"Note that the error vector ($\\mathbf{y}-\\alpha\\mathbf{v}$) is still perpendicular to the line (subspace $\\mathbf{v}$), but in the space of the weighted distance. The difference between the first projection (with the uniform circular distance) and the general case (with the elliptical weighted distance) is the inner product between the two cases. For example, in the first case we have $\\mathbf{y}^T \\mathbf{v}$ and in the weighted case we have $\\mathbf{y}^T \\mathbf{Q}^T \\mathbf{v}$. To move from the uniform circular case to the weighted ellipsoidal case, all we had to do was change all of the vector inner products. Before we finish, we need a formal property of projections:\n",
"\n",
"$$\n",
"\\mathbf{P}_v \\mathbf{P}_v = \\mathbf{P}_v\n",
"$$\n",
"\n",
"known as the *idempotent* property which basically says that once we have projected onto a subspace, subsequent projections leave us in the same subspace. Thus, projection ties a minimization problem (closest point to a line) to an algebraic concept (inner product)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The ℓp Ball\n",
"As the value of p decreases, the size of the corresponding ℓp space also decreases. This can be seen visually when comparing the the size of the spaces of signals, in three dimensions, for which the ℓp norm is less than or equal to one. The volume of these ℓp “balls” decreases with p.\n",
"\n",
"
\n",
"\n",
"The most common choice of regularizers are ℓ1 \n",
"\n",
"
\n",
"\n",
"and ℓ2 \n",
"\n",
"
\n",
"\n",
"Typically ridge or ℓ2 penalties are much better for minimizing prediction error rather than ℓ1 penalties. The reason for this is that when two predictors are highly correlated, ℓ1 regularizer will simply pick one of the two predictors. In contrast, the ℓ2 regularizer will keep both of them and jointly shrink the corresponding coefficients a little bit. Thus, while the ℓ1 penalty can certainly reduce overfitting, you may also experience a loss in predictive power.\n",
"\n",
"ℓ2 penalization is preferable for data that is not at all sparse, i.e. where you do not expect regression coefficients to show a decaying property. In such cases, incorrectly using an ℓ1 penalty for non-sparse data will give you give you a large estimation error. If the true signal is sparse its coefficients have exactly k non-zero elements and approximately sparse if k really large coefficients and with the rest of the coefficients decaying quickly to zero. ℓ1 regularization doesn't merely encourage sparse solutions, but is capable of exact recovery of sparse signals."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Practicel Example of Regularization\n",
"Now that the theoretical foundation of regularization is clear, let's look at an example.\n",
"\n",
"First, let's generate with a 9th order polynomial."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
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8Fh0dx8pdBpAQU3xhCrimBgAAiiegwhRwTQ0AABTP2TNMAdfUAABA8QRUmAKuqQEAgOKZ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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"rng = np.random.RandomState(0)\n",
"x = 2 * rng.rand(100) - 1\n",
"\n",
"f = lambda t: 1.2 * t ** 2 + .1 * t ** 3 - .4 * t ** 5 - .5 * t ** 9\n",
"y = f(x) + .4 * rng.normal(size=100)\n",
"\n",
"plt.figure()\n",
"plt.scatter(x, y, s=4);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And now, let's fit a 4th order and a 9th order polynomial to the data. For this we need to engineer features: the n_th powers of x:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Gz1GpVJg/fz4+/PBDJCQk4P3334erqytcXV2Rmpoqxe/j44OvvvrK6C1WHlev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\nA9vq6uo0adKkEb/2S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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.linear_model import LinearRegression\n",
"\n",
"x_test = np.linspace(-1, 1, 100)\n",
"\n",
"plt.figure()\n",
"plt.scatter(x, y, s=4)\n",
"\n",
"X = np.array([x**i for i in range(5)]).T\n",
"X_test = np.array([x_test**i for i in range(5)]).T\n",
"order4 = LinearRegression()\n",
"order4.fit(X, y)\n",
"plt.plot(x_test, order4.predict(X_test), label='4th order')\n",
"\n",
"X = np.array([x**i for i in range(10)]).T\n",
"X_test = np.array([x_test**i for i in range(10)]).T\n",
"order9 = LinearRegression()\n",
"order9.fit(X, y)\n",
"plt.plot(x_test, order9.predict(X_test), label='9th order')\n",
"\n",
"plt.legend(loc='best')\n",
"plt.axis('tight')\n",
"plt.title('Fitting a 4th and a 9th order polynomial')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Intuitively, which model generalizes better? \n",
"\n",
"Let's look at the ground truth:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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zs1VSUiLDMDR69Gjdc889Lu9/6aWXKiUlRampqbrmmmsUFBSkJ554QsOGDfPW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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"plt.scatter(x, y, s=4)\n",
"plt.plot(x_test, f(x_test), label=\"truth\")\n",
"plt.axis('tight')\n",
"plt.title('Ground truth (9th order polynomial)');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Unsupervised Learning"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In **Unsupervised Learning** there is no desired output associated with the data.\n",
"Instead, we are interested in extracting some form of knowledge or model from the given data.\n",
"In a sense, you can think of unsupervised learning as a means of discovering labels from the data itself.\n",
"Unsupervised learning is often harder to understand and to evaluate.\n",
"\n",
"Unsupervised learning comprises tasks such as *dimensionality reduction*, *clustering*, and\n",
"*density estimation*. For example, in the iris data discussed above, we can used unsupervised\n",
"methods to determine combinations of the measurements which best display the structure of the\n",
"data. As we’ll see below, such a projection of the data can be used to visualize the\n",
"four-dimensional dataset in two dimensions. Some more involved unsupervised learning problems are:\n",
"\n",
"- Given detailed observations of distant galaxies, determine which features or combinations of\n",
" features summarize best the information.\n",
"- Given a mixture of two sound sources (for example, a person talking over some music),\n",
" separate the two (this is called the [blind source separation](http://en.wikipedia.org/wiki/Blind_signal_separation) problem).\n",
"- Given a video, isolate a moving object and categorize in relation to other moving objects which have been seen.\n",
"- Given a large collection of news articles, find recurring topics inside these articles.\n",
"- Given a collection of images, cluster similar images together (for example to group them when visualizing a collection)\n",
"\n",
"Sometimes the two may even be combined: e.g. unsupervised learning can be used to find useful\n",
"features in heterogeneous data, and then these features can be used within a supervised\n",
"framework. This is quite common in successful Kaggle solutions."
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"## Principal Component Analysis (PCA)\n",
"Principal Component Analysis (PCA) is a dimension reduction technique that can find the combinations of variables that explain the most variance.\n",
"\n",
"The following links provide insight into PCA:\n",
"- [PCA Explained Visually](http://setosa.io/ev/principal-component-analysis/)\n",
"- [Eigenvectors/Eigenvalues explained Visually](http://setosa.io/ev/eigenvectors-and-eigenvalues/)\n",
"\n",
"### Key Equation: $Ax = \\lambda b ~~ \\text{for} ~~ n \\times n $\n",
"\n",
"PCA is an orthogonal linear transformation that transforms the data to a new coordinate system such that the greatest variance by some projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on. This is an Unsupervised Learning Techniques - Which means we don't have a target variable.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For example, given the following points,"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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rJvnlzO4jZ9QzdvZ4CvHljF94VakslTXVQKERRAEARcMPlRgn1RArH2DtSBcq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\nx4JFMWV0Ziru6KKpuDvaIlm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bTJWTfIWXdIF9IDatB147rVvWRSw9Tq5twZlCq9ttoMn3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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"np.random.seed(1)\n",
"X = np.dot(np.random.random(size=(2, 2)), np.random.normal(size=(2, 200))).T\n",
"plt.plot(X[:, 0], X[:, 1], 'o')\n",
"plt.axis('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"PCA can be used to find the 2 pricipal components that capture the most variance in the point cloud. In particular, think of PCA as fitting an elipse to the data."
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,\n",
" svd_solver='auto', tol=0.0, whiten=False)"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.decomposition import PCA\n",
"pca = PCA(n_components=2)\n",
"pca.fit(X)"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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cT5TtHltoJYSMes/XnI21Vs+fSWloMiuVe4+s1dBkVs+fSS3qnM19ODOeKb6P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\nPvrokL/fsmXLgJ9vv/123X777dkcAgoUH9rzp7OzM9Hr8/nnn7fU63P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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X[:, 0], X[:, 1], 'o', alpha=0.5)\n",
"for length, vector in zip(pca.explained_variance_, pca.components_):\n",
" v = vector * 3 * np.sqrt(length)\n",
" plt.plot([0, v[0]], [0, v[1]], '-k', lw=3)\n",
"plt.axis('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"PCA can then be used to retain some desired percentage of variance, while projecting the data down to the 1st component."
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"clf = PCA(0.95) # keep 95% of variance\n",
"X_trans = clf.fit_transform(X)"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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6hdYp8IzSvqHREHAKIogCAAC0wXB+/rWxS2kotCHt6djcDXibqiQ6J33607ND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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X_new = clf.inverse_transform(X_trans)\n",
"plt.plot(X[:, 0], X[:, 1], 'o', alpha=0.2)\n",
"plt.plot(X_new[:, 0], X_new[:, 1], 'ob', alpha=0.8)\n",
"plt.axis('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## How to choose the number of components\n",
"Choosing the most informative number of components can be challenging. Several approaches exist to help.\n",
"\n",
"One approach is to plot the number of components vs the explained variance."
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Fi9tVEEJDg8utPz//tbbvc0iSzh3SVT8bn0sgAAAA8IOT2rzs1Vdf1bp169TQ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\n1hrvIzY2Vnv37tVzzz2nW2+9VZK0detWjRo1SjExMbrhhhv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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.datasets import load_digits\n",
"digits = load_digits()\n",
"X = digits.data\n",
"y = digits.target\n",
"\n",
"sns.set()\n",
"pca = PCA().fit(X)\n",
"plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
"plt.xlabel('number of components')\n",
"plt.ylabel('cumulative explained variance');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Alternatively, for visual data, it might be helpful to plot the information content for an increasing number of components."
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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YhgIqE2QtkwkRuJjCGUucyrAYgQv5Rcx3GVuPJPM5GddGo5G+ys1LQGI4hv4W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f2fPa5C3eACDph65AILv//vvDXxQQyPwLKrzxjeqXl5dx/PhxHD9+HHNzc5lHfi49X7r8n6km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HkmH7K/rPhyH7uFb8h/s+IrpBXyXesYeH294GsRsxZxAPow9USyrrZZPsxVDZ04czXaIuM0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\n6ope48s4eVXop2ydgsP6D7O3w+NAM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2syKZYnW6FvWwWZRBu/uVWH6ARQsOSDvvY4FovZ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e/F9C5asyVtnQvmo8THwpeFANiuM4Tc4F9V3iS+cBBDP0xDefzwfKXHTXbVPCV/huDHxV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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(8, 8, figsize=(8, 8))\n",
"fig.subplots_adjust(hspace=0.1, wspace=0.1)\n",
"\n",
"for i, ax in enumerate(axes.flat):\n",
" pca = PCA(i + 1).fit(X)\n",
" im = pca.inverse_transform(pca.transform(X[20:21]))\n",
"\n",
" ax.imshow(im.reshape((8, 8)), cmap='binary')\n",
" ax.text(0.95, 0.05, 'n = {0}'.format(i + 1), ha='right',\n",
" transform=ax.transAxes, color='green')\n",
" ax.set_xticks([])\n",
" ax.set_yticks([])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Clustering: K-means\n",
"\n",
"Observations that are homogeneous with respect to a given criterion are referred to as ''clusters'' in the data.\n",
"\n",
"Note that these clusters will uncover relevent hidden structure of the data only if the criterion used highlights it."
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import stats\n",
"\n",
"# use seaborn plotting defaults\n",
"import seaborn as sns; sns.set()"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"K Means is an algorithm for **unsupervised clustering**: that is, finding clusters in data based on the data attributes alone (not the labels).\n",
"\n",
"K Means is a relatively easy-to-understand algorithm. It searches for cluster centers which are the mean of the points within them, such that every point is closest to the cluster center it is assigned to.\n",
"\n",
"Let's look at how KMeans operates on the simple clusters we looked at previously. To emphasize that this is unsupervised, we'll not plot the colors of the clusters:"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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pk0MlCfjsZ1V88IOALFuXNLg1iAcwK/WwN6lVr+dua4vhhRcCGB0FBgaMhx/Z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\n/w/HGJXgBPuv3AAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.datasets.samples_generator import make_blobs\n",
"X, y = make_blobs(n_samples=300, centers=4,\n",
" random_state=0, cluster_std=0.60)\n",
"plt.scatter(X[:, 0], X[:, 1], s=50);"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"By eye, it is relatively easy to pick out the four clusters. If you were to perform an exhaustive search for the different segmentations of the data, however, the search space would be exponential in the number of points."
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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UCyHEZCOf7KIp+hq43L4xSShi6JiA45loPUHAd2sEKYDvFvMckHYHykB2HRaavZRmL2ts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DzC99wDkUh5v/KcHPyePYi88jzZ/7iCzFv/jbYlj/jFF6e0KWjbFn3ZUpC1s0JizJ+HvnJlhWVi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\ntp7oDOgUPZzuQkREREQUYxjSiYiIiIhiDEM6EREREVGMYUgnI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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.cluster import KMeans\n",
"est = KMeans(4) # 4 clusters\n",
"est.fit(X)\n",
"y_kmeans = est.predict(X)\n",
"plt.scatter(X[:, 0], X[:, 1], c=y_kmeans, s=50, cmap='rainbow');"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"The algorithm identifies the four clusters of points in a manner very similar to what we would do by eye!"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"Using *Expectation-Maximization* is another approach to finding clusters in the data. It (often) converges to the optimal cluster centers.\n",
"\n",
"*Expectation-Maximization* is a two-step approach which works as follows:\n",
"\n",
"1. Guess some cluster centers\n",
"2. Repeat until converged\n",
" A. Assign points to the nearest cluster center\n",
" B. Set the cluster centers to the mean \n",
"\n",
"Let's quickly visualize this process:"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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N/ojE8VVWdlSJUlOB3mDXat6/38eSJ5qOx+5PTV65zqTi/ijjb4hgpqjJ7zwa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RAAAg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\nEEKkGAnpQgghhBBCpJj/Dzz//GJk/n/VAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from fig_code import plot_kmeans_interactive\n",
"plot_kmeans_interactive();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### KMeans Caveats\n",
"\n",
"The convergence of this algorithm is not guaranteed; for that reason, scikit-learn by default uses a large number of random initializations and finds the best results.\n",
"\n",
"Also, the number of clusters must be set beforehand... there are other clustering algorithms for which this requirement may be lifted."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The \"elbow\" method\n",
"Another approach is to find the optimal number of clusters using the elbow method."
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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wDKtjAQAAIEB4VR4ee+wxjRs3TjfffLP69Onj60zoRmNT4vW3j8+rsuaiTn1e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\nERER2YThgYiIiIiIbMLwQERERERENvn/pvoIrtq28eUAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"distortions = []\n",
"for i in range(1, 11):\n",
" km = KMeans(n_clusters=i, \n",
" init='k-means++', \n",
" n_init=10, \n",
" max_iter=300, \n",
" random_state=0)\n",
" km.fit(X)\n",
" distortions.append(km.inertia_)\n",
"plt.plot(range(1, 11), distortions, marker='o')\n",
"plt.xlabel('Number of clusters')\n",
"plt.ylabel('Distortion')\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Silhouette Plots\n",
"Alternatively, one can find the number of clusters through visualizing the number of clusterings/categories."
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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lpVPHWmuttfKNb3wjQ4cO7Xhs9uzZefOb39yV0gCgxwgPQF/UpQDxjW98I9OmTUuSPPLI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\nBgComLElGokAAQB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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from matplotlib import cm\n",
"from sklearn.metrics import silhouette_samples\n",
"\n",
"km = KMeans(n_clusters=3, \n",
" init='k-means++', \n",
" n_init=10, \n",
" max_iter=300,\n",
" tol=1e-04,\n",
" random_state=0)\n",
"y_km = km.fit_predict(X)\n",
"\n",
"cluster_labels = np.unique(y_km)\n",
"n_clusters = cluster_labels.shape[0]\n",
"silhouette_vals = silhouette_samples(X, y_km, metric='euclidean')\n",
"y_ax_lower, y_ax_upper = 0, 0\n",
"yticks = []\n",
"for i, c in enumerate(cluster_labels):\n",
" c_silhouette_vals = silhouette_vals[y_km == c]\n",
" c_silhouette_vals.sort()\n",
" y_ax_upper += len(c_silhouette_vals)\n",
" color = cm.jet(float(i) / n_clusters)\n",
" plt.barh(range(y_ax_lower, y_ax_upper), c_silhouette_vals, height=1.0, \n",
" edgecolor='none', color=color)\n",
"\n",
" yticks.append((y_ax_lower + y_ax_upper) / 2.)\n",
" y_ax_lower += len(c_silhouette_vals)\n",
" \n",
"silhouette_avg = np.mean(silhouette_vals)\n",
"plt.axvline(silhouette_avg, color=\"red\", linestyle=\"--\") \n",
"\n",
"plt.yticks(yticks, cluster_labels + 1)\n",
"plt.ylabel('Cluster')\n",
"plt.xlabel('Silhouette coefficient')\n",
"\n",
"plt.tight_layout()"
]
},
{
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"execution_count": null,
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"outputs": [],
"source": []
}
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