{ "metadata": { "name": "", "signature": "sha256:dd30ba84dcd243ecd5fcac7b764cb95fad07af9bc1acb834cb68880f19f7e9be" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Cool Examples\n", "\n", "The first example serve as a reminder of the powerful capabilities of IPython and Scientific Python.\n", "The next two examples demonstrate the data science philosphy of quanitifying well known knowledge and get insights into the data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [Timeseries Classification: KNN & DTW](http://nbviewer.ipython.org/github/markdregan/K-Nearest-Neighbors-with-Dynamic-Time-Warping/blob/master/K_Nearest_Neighbor_Dynamic_Time_Warping.ipynb)\n", "\n", "\n", "- [Messi is impossible](http://fivethirtyeight.com/features/lionel-messi-is-impossible/)\n", "\n", "\n", "- [Bagel Price Analysis](http://www.seriouseats.com/2014/07/bagelnomics-best-bagel-pricing-nyc.html)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Machine Learning Using Scikits-Learn" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Goals\n", "This is a tutorial on how to build machine learning systems and analyze their performance.\n", "We are not going to discuss the details of the learning algorithms and how they work.\n", "We will focus on understanding their behavior and analyze their performance.\n", "\n", "#### Advice\n", "Refer to [Coursera Online course](https://www.coursera.org/course/ml) on machine learning as offered by Andrew Ng.\n", "It contains easy to digest description of linear regression, logistic regression, neural network, support vector machines, k-means and PCA." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Imports" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "from __future__ import print_function" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.html.widgets import interact, RadioButtonsWidget, IntSliderWidget, TextWidget" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "import matplotlib.pyplot as plt\n", "from matplotlib.colors import ListedColormap" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "import matplotlib\n", "matplotlib.rcParams.update({\n", " \"lines.linewidth\": 2.0,\n", " \"examples.download\": True,\n", " \"axes.edgecolor\": \"#bcbcbc\",\n", " \"patch.linewidth\": 0.5,\n", " \"legend.fancybox\": True,\n", " \"axes.color_cycle\": [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\", \"#CF4457\", \"#188487\", \"#E24A33\"],\n", " \"axes.facecolor\": \"#eeeeee\",\n", " \"axes.labelsize\": \"large\",\n", " \"axes.grid\": True,\n", " \"patch.edgecolor\": \"#eeeeee\",\n", " \"axes.titlesize\": \"x-large\",\n", " \"svg.embed_char_paths\": \"path\",\n", " \"examples.directory\": \"\"\n", "})" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note**: This tutorial is tested under this version of Scikits-learn" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import sklearn\n", "print(\"Scikits-learn version is\", sklearn.__version__)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Scikits-learn version is 0.15.2\n" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cheat Sheet\n", "\n", "At the end of this tutorial will you learn so many algorithms for the first time, print this cheat sheet and keep it above your desk to guide you selecting the appropriate technique and model for your analysis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Regression\n", "\n", "[LinearRegression](http://en.wikipedia.org/wiki/Least_squares), in it\u2019s simplest form, fits a linear model to the data set by adjusting a set of parameters in order to make the sum of the squared residuals of the model as small as possible.\n", "\n", "Linear models assumes that:\n", "\n", "$y = X\\beta + \\epsilon$\n", "\n", "- $X \\in \\mathbb{R}^{m\\times d}$: data,\n", "- $y \\in \\mathbb{R}^{m}$: target variable,\n", "- $\\beta \\in \\mathbb{R}^{d}$: Coefficients,\n", "- $\\epsilon \\in \\mathbb{R}^d$: Observation noise\n", "\n", "Search for $\\beta$ that minimizes $||y - X\\beta||_2^2$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Diabetes dataset\n", "\n", "Given the patient blood enzymes levels, we would like to predict the insulin in his blood stream. Notice, that our target variable is **continuous**, therefore, we need to use a regression model.\n", "\n", "I am going to choose one feature $X_2$ to simplify the visualization of the model parameters. The original dataset has 10 features ($X_1-X_{10}$).\n", "\n", "Description of the diabetes dataset is available at [UCI machine learning repository](https://archive.ics.uci.edu/ml/datasets/Diabetes). " ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.datasets import load_diabetes" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The feature array $X$ is a matrix where each row represents an example." ] }, { "cell_type": "code", "collapsed": false, "input": [ "diabetes = load_diabetes()\n", "features = diabetes.data[:, 2][:, np.newaxis]\n", "X1 = features\n", "y1 = diabetes.target" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Data fitting\n", "\n", "Try to change the `slope` and `bias` to reduce the residual sum of squares (error).\n", "What is the smallest value you can produce?\n", "Our goal in regression is to learn {`slope`, `bias`} that minimizes the error term.\n", "\n", "Notice, that we are asumming that the data fits a line, that does not have to be true. Howeover, we would like to find the best solution under this assumption." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_line(slope, bias):\n", " plt.scatter(X1, y1, color='y')\n", " plt.xlabel(\"$X_2$\", fontsize=20); plt.ylabel(\"$y$\", fontsize=20)\n", " _ = plt.title(\"$y\\,\\,vs\\,\\,X_2$\", fontsize=20)\n", " predictions = slope * X1 + bias\n", " plt.plot(X1, predictions, color='blue', linewidth=3)\n", " print(\"Slope = {}, Bias = {}\".format(slope, bias))\n", " print(\"Residual sum of squares: %.2f\"\n", " % np.mean((predictions - y1) ** 2))\n", "\n", "_ = interact(plot_line,\n", " slope=IntSliderWidget(min=0, max=2000, step=50, value=1000),\n", " bias=IntSliderWidget(min=0, max=300, step=30, value=100))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Slope = 1150, Bias = 100\n", "Residual sum of squares: 11639.87\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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CoFUsBIIUyO1AFnN96ss+MbEEiYklMBo/QEjIWK/GkBpq4m5qWqE4B7zcHwujgaA1hREf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\nGITCkwGnA37SpLeh08VxtgQ2m98F4Cxtf+XKfqS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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Linear Model" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.linear_model import LinearRegression" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- `bias` term is called also `intercept`.\n", "- If the features vary significantly in range, it pays off to `normalize` the data as a preprocessing step." ] }, { "cell_type": "code", "collapsed": false, "input": [ "model = LinearRegression()\n", "model = model.fit(X1, y1)\n", "predictions = model.predict(X1)\n", "print(\"Model is trained with the following params: {}\".format(model.get_params()))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Model is trained with the following params: {'copy_X': True, 'normalize': False, 'fit_intercept': True}\n" ] } ], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "print(\"Slope = {}, Bias = {}\".format(model.coef_[0], model.intercept_))\n", "# The mean square error\n", "print(\"Residual sum of squares: %.2f\"\n", " % np.mean((predictions - y1) ** 2))\n", "# Explained variance score: 1 is perfect prediction\n", "print('Variance score: %.2f' % model.score(X1, y1))\n", "\n", "# Plot outputs\n", "plt.scatter(X1, y1, color='y')\n", "plt.plot(X1, predictions, color='blue', linewidth=3)\n", "plt.xlabel(\"$X_2$\", fontsize=20); plt.ylabel(\"$y$\", fontsize=20)\n", "_ = plt.title(\"$y\\,\\,vs\\,\\,X_2$\", fontsize=20)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Slope = 949.435260384, Bias = 152.133484163\n", "Residual sum of squares: 3890.46\n", "Variance score: 0.34\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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CaaknuuvQoa9D+nvW1n6Mzs4alJTkICOjgnO8QP7eUmy/+24C/vrX2z0PDvuv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\nfnbJFfYk6O1XYROOSdgbrgmZz58klp6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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Classification" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Iris Dataset\n", "\n", "The Iris flower data set or Fisher's Iris data set is a multivariate data set introduced by Sir Ronald Fisher (1936) as an example of discriminant analysis. The data set consists of 50 samples from each of three species of Iris (Iris setosa, Iris virginica and Iris versicolor).\n", "\n", "Four features were measured from each sample: the length and the width of the sepals and petals, in centimetres.\n", "\n", "Notice, that we want to predict a categorial variable (**discrete** variable).\n", "We need to assign every reading a specific class.\n", "To simplify the visualization, I will choose the first two variables, sepal length and width." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn import datasets\n", "from sklearn.linear_model import LogisticRegression" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "iris = datasets.load_iris()\n", "X2 = iris.data[:, :2] # we only take the first two features.\n", "Y2 = iris.target" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.figure(1, figsize=(6, 4.5))\n", "plt.xlabel('Sepal length'); plt.ylabel('Sepal width')\n", "_ = plt.scatter(X2[:, 0], X2[:, 1], c=Y2, edgecolors='k', cmap=plt.cm.RdYlGn)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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EBBAXF0f16tWxsbEpoIT6l9c6CVFICIIgvAXemoprUSchTU6Z7ty+zaxRY1k6YzYJCQm5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\nvDCZTBw+fJiIiAiSk5O1iiaEEKISml1JjBkzhn379vHLL7/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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice, that regardless of what we are trying to do, scikits-learn has the same sequence of operations:\n", "1. **Instantiate** the model with the appropriate parameters.\n", "1. **Fit** the model to the data, the feature and the labels.\n", "1. **Predict** the target variable." ] }, { "cell_type": "code", "collapsed": false, "input": [ "model = LogisticRegression(C=1e5)\n", "model = model.fit(X2, Y2)\n", "predictions = model.predict(X2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Accuracy\n", "\n", "We are evaluating on the same data we used to fit the model with!\n", "This mean that our model is performing perdictions on data points it already saw.\n", "This gives an upper bound of the real performance of the model.\n", "We will discuss later on how to do proper evaluation." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.metrics import accuracy_score" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "print(\"Performance of our classifier is {:.2f}%\".format(accuracy_score(Y2, predictions)*100))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Performance of our classifier is 80.67%\n" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Decision boundary\n", "\n", "We will use `meshgrid` and `pcolormesh` to visualize how the model splits the spatial regions among classes." ] }, { "cell_type": "code", "collapsed": false, "input": [ "h2 = .02 # step size in the mesh\n", "x_min2, x_max2 = X2[:, 0].min() - .5, X2[:, 0].max() + .5\n", "y_min2, y_max2 = X2[:, 1].min() - .5, X2[:, 1].max() + .5\n", "xx2, yy2 = np.meshgrid(np.arange(x_min2, x_max2, h2), np.arange(y_min2, y_max2, h2))\n", "Z2 = model.predict(np.c_[xx2.ravel(), yy2.ravel()])\n", "# Put the result into a color plot\n", "Z2 = Z2.reshape(xx2.shape)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "now, we will add the original classes of our flowers." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.figure(1, figsize=(6, 4.5))\n", "plt.pcolormesh(xx2, yy2, Z2, cmap=plt.cm.YlOrBr)\n", "plt.xlabel('Sepal length'); plt.ylabel('Sepal width')\n", "plt.xlim(xx2.min(), xx2.max()); plt.ylim(yy2.min(), yy2.max())\n", "_ = plt.scatter(X2[:, 0], X2[:, 1], c=Y2, edgecolors='k', cmap=plt.cm.BrBG)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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4sZER9nqODW3KF1UQM4QLr7qB+rpalr37Gn0a870KBnkW+FGEY40Ix1xbx4n6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\nhIWFdXrzkAwEvhXIAaA7knMNpM5y1PM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"text": [ "" ] } ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As the model is linear, the boundaries are linear.\n", "We made an assumption that the data is linearly separable.\n", "The decision boundary shows that it is easier to split the first class from the other two." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Model Complexity\n", "\n", "Choosing the right model in machine learning is an art.\n", "Complex models tend to memorize the data they saw and not generalize very well to new instances.\n", "Simple models tend to over-generalize and not capture all data intricacies.\n", "It requires experience and understanding of the various tradeoffs between algorithm capacity and data quality to reach the right model.\n", "\n", "Various points could change the model capacity:\n", "\n", "- **Choice of features**: In general, more features increase the model capacity.\n", " - Automatic features: We can generate extra features automatically, using polynomial features.\n", " \n", " - Domain knowledge: Given our expertise in the problem we can synthesize new features. For example, trying to detect if a word is a verb or not, we can add a feature detecting if the suffix of the current word is `ed`.\n", "\n", "\n", "\n", "- **Feature preprocessing**: preprocessing steps as normalization or dimensionality reduction could simplify numerical optimization leading to better models.\n", "\n", "\n", "\n", "- **Choice of algorithm**: Some models like logistic regression has linear decision boundaries, while others like SVM with RBF kernel or Neural network has non-linear (complex curvature) decision boundaries.\n", "\n", "\n", "\n", "- **Regularization**: We can lower the model capacity by imposing constraints on the optimization methods while trying to learn the model parameters.Two common constraints/penalties are $L_1$ ([LASSO regression](http://en.wikipedia.org/wiki/Least_squares#Lasso_method)) and $L_2$ ([ridge regression](http://en.wikipedia.org/wiki/Tikhonov_regularization)).\n", "\n", "While we learn the model's parameters directly from data, the above choices has to be set by the data scientist.\n", "We call these choices **hyperparameters** to distinguish them from parameters learned from the data.\n", "Through this tutorial, we will learn how to analyze these choices and setup an environment to pick them autotmatically driven by data analysis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Polynomial features\n", "We can synthesize new features by introducing interactions between the current features.\n", "If we are using currently $x_1$ and $x_2$, we can introduce a new feature $x_1x_2$.\n", "\n", "Given that our feature set is {$x_1$, $x_2$} using the Preprocessing stage `PolynomialFeatures` will introduce the following features:\n", "- Degree 1: $x_1$, $x_2$\n", "- Degree 2: $x_1$, $x_2$, $x_1^2$, $x_2^2$, $x_1x_2$\n", "- Degree 3: $x_1$, $x_2$, $x_1^2$, $x_2^2$, $x_1x_2$, $x_1^3$, $x_2^3$, $x_1^2x_2$, $x_1x_2^2$\n", "\n", "**Notes**:\n", "- Be aware that the number of features in the output array scales polynomially in the number of features of the input array, and exponentially in the degree.\n", "- High degrees can cause overfitting." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.pipeline import Pipeline\n", "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.linear_model import LinearRegression" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 21 }, { "cell_type": "code", "collapsed": false, "input": [ "np.random.seed(0)\n", "n_samples = 20\n", "true_fun = lambda X: np.cos(1.5 * np.pi * X)\n", "X3 = np.sort(np.random.rand(n_samples))\n", "y3 = true_fun(X3) + np.random.randn(n_samples) * 0.15" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 22 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can stage two operations, in this case, generating features and training a regressor using the class *Pipeline*. Notice, lines 9 and 10." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def regressor(degree):\n", " plt.figure(figsize=(6, 4.5))\n", " ax = plt.subplot(1, 1, 1)\n", " plt.setp(ax, xticks=(), yticks=())\n", "\n", " polynomial_features = PolynomialFeatures(degree=degree,\n", " include_bias=False)\n", " linear_regression = LinearRegression()\n", " pipeline = Pipeline([(\"polynomial_features\", polynomial_features),\n", " (\"linear_regression\", linear_regression)])\n", " pipeline.fit(X3[:, np.newaxis], y3)\n", "\n", " plt.plot(X3, pipeline.predict(X3[:, np.newaxis]), label=\"Model\")\n", " plt.plot(X3, true_fun(X3), label=\"True function\")\n", " plt.scatter(X3, y3, label=\"Samples\")\n", " plt.xlabel(\"$x$\", fontsize=20); plt.ylabel(\"$y=cos(1.5\\pi x)$\", fontsize=20); plt.xlim((0, 1)); plt.ylim((-1.5, 1.5))\n", " plt.legend(loc=\"best\")\n", " plt.title(\"Degree %d\" % degree)" ], "language": "python", "metadata": { "code_folding": [] }, "outputs": [], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note:** Increasing model complexity does not imply necessarily producing better models." ] }, { "cell_type": "code", "collapsed": false, "input": [ "_ = interact(regressor, degree=IntSliderWidget(min=1, max=60, step=1, value=1))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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dO3cWKNE/q2rVqvz+++/8/vvvr1xHSeP8QTdqLJ6ELEk0/msH28b78TAhTddh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\n4yfDLss72uDz0zIc3mmdtfhJ77GE7di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"text": [ "" ] } ], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example demonstrates the problems of **underfitting** and **overfitting**.\n", "Moreover, we can use linear regression with polynomial features to approximate nonlinear functions.\n", "The models have polynomial features of different degrees.\n", "\n", "The plot shows the function that we want to approximate, which is a part of the cosine function ($y=cos(1.5\\pi x)$) and the learned function.\n", "\n", "We can vary the degree of the polynomial features, to change the model capacity.\n", "We can see that a linear function (polynomial with degree 1) is not sufficient to fit the training samples.\n", "This is called **underfitting**.\n", "A polynomial of degree 2-7 approximates the true function almost perfectly.\n", "However, for higher degrees (degree 7) the model will **overfit** the training data, i.e. it learns the noise of the training data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Choice of Classifiers\n", "\n", "We can change model capacity by changing the algorithm used to learn the decision boundaries.\n", "Models vary by their upper bound capacity to represent data.\n", "Non-linear classifiers and models tend to overfit to data quickly and require regualization to lower their capacity.\n", "\n", "The following demonstration is a comparison of several classifiers in scikit-learn on synthetic datasets.\n", "The point of this example is to illustrate the nature of decision boundaries of different classifiers.\n", "This should be taken with a grain of salt, as the intuition conveyed by these examples does not necessarily carry over to real datasets.\n", "Particularly in high-dimensional spaces, data can more easily be separated linearly and the simplicity of classifiers such as naive Bayes and linear SVMs might lead to better generalization than is achieved by other classifiers.\n", "The plots show training points in solid colors and testing points semi-transparent.\n", "The lower right shows the classification accuracy on the test set." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.cross_validation import train_test_split\n", "from sklearn.preprocessing import StandardScaler\n", "from sklearn.datasets import make_moons, make_circles, make_classification\n", "from sklearn.neighbors import KNeighborsClassifier\n", "from sklearn.svm import SVC\n", "from sklearn.tree import DecisionTreeClassifier\n", "from sklearn.ensemble import RandomForestClassifier, AdaBoostClassifier\n", "from sklearn.naive_bayes import GaussianNB\n", "from sklearn.lda import LDA\n", "from sklearn.qda import QDA" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Classifiers Choice\n", "\n", "Parameters as {`C`, `kernel`, `max_depth`, `n_estimators`, `max_features`} are hyperparameters. They are set manually in this example" ] }, { "cell_type": "code", "collapsed": false, "input": [ "clfs_names = [\"Nearest Neighbors\", \"Linear SVM\", \"RBF SVM\", \"Decision Tree\",\n", " \"Random Forest\", \"AdaBoost\", \"Naive Bayes\", \"LDA\", \"QDA\"]\n", "clfs = [KNeighborsClassifier(3),\n", " SVC(kernel=\"linear\", C=0.025),\n", " SVC(gamma=2, C=1),\n", " DecisionTreeClassifier(max_depth=5),\n", " RandomForestClassifier(max_depth=5, n_estimators=10, max_features=1),\n", " AdaBoostClassifier(),\n", " GaussianNB(),\n", " LDA(),\n", " QDA()]\n", "classifiers = dict(zip(clfs_names, clfs))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Datasets" ] }, { "cell_type": "code", "collapsed": false, "input": [ "X, y = make_classification(n_features=2, n_redundant=0, n_informative=2,\n", " random_state=1, n_clusters_per_class=1)\n", "rng = np.random.RandomState(2)\n", "X += 2 * rng.uniform(size=X.shape)\n", "linearly_separable = (X, y)\n", "\n", "ds_names = ['moons', 'circles', 'iris 2 flowers', 'sandwitches']\n", "ds = [make_moons(noise=0.3, random_state=0),\n", " make_circles(noise=0.2, factor=0.5, random_state=1),\n", " (iris.data[:, :2], iris.target == 0),\n", " linearly_separable\n", " ]\n", "datasets = dict(zip(ds_names, ds))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "cm = plt.cm.RdBu\n", "cm_bright = ListedColormap(['#FF0000', '#0000FF'])\n", "h = 0.2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Plot dataset" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_ds(ds_name):\n", " ds = datasets[ds_name]\n", " X, y = ds\n", " X = StandardScaler().fit_transform(X)\n", " X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4)\n", "\n", " x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n", " y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n", " xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n", " np.arange(y_min, y_max, h))\n", "\n", " # just plot the dataset first\n", " ax = plt.subplot(1, 2, 1)\n", " # Plot the training points\n", " ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)\n", " # and testing points\n", " ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6)\n", " ax.set_xlim(xx.min(), xx.max())\n", " ax.set_ylim(yy.min(), yy.max())\n", " ax.set_title(ds_name)\n", " return ds, xx ,yy" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 29 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Build classifier" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def classify(dataset_name, classifier_name):\n", " clf = classifiers[classifier_name]\n", " figure = plt.figure(figsize=(10, 5))\n", " (X,y), xx, yy = plot_ds(dataset_name)\n", " X = StandardScaler().fit_transform(X)\n", " X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4)\n", "\n", " ax = plt.subplot(1, 2, 2)\n", " clf.fit(X_train, y_train)\n", " score = clf.score(X_test, y_test)\n", "\n", " # Plot the decision boundary. For that, we will assign a color to each\n", " # point in the mesh [x_min, m_max]x[y_min, y_max].\n", " if hasattr(clf, \"decision_function\"):\n", " Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])\n", " else:\n", " Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]\n", "\n", " # Put the result into a color plot\n", " Z = Z.reshape(xx.shape)\n", " ax.contourf(xx, yy, Z, cmap=cm, alpha=.8)\n", "\n", " # Plot also the training points\n", " ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright)\n", " # and testing points\n", " ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright,\n", " alpha=0.6)\n", "\n", " ax.set_xlim(xx.min(), xx.max())\n", " ax.set_ylim(yy.min(), yy.max())\n", " ax.set_title(classifier_name)\n", " ax.text(xx.max() - .3, yy.min() + .3, ('Accuracy=%.2f' % score).lstrip('0'),\n", " size=15, horizontalalignment='right')" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 30 }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.html.widgets import interact, RadioButtonsWidget, IntSliderWidget, TextWidget, DropdownWidget" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 31 }, { "cell_type": "code", "collapsed": false, "input": [ "_ = interact(classify,\n", " classifier_name=DropdownWidget(values=clfs_names),\n", " dataset_name=RadioButtonsWidget(values=ds_names))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Twr9cSdyA9rMjRjpPbowYk7e95xZv7bi5vSFFk5EQcXHU/P73je0Eap59Fq1P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"text": [ "" ] } ], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Darker areas means that the classifier is more confident in its own prediction than lighter areas.\n", "Notice, that there is no classifier that outperforms others on all datasets. This fact is known to be \"**No Free Lunch**\" theorem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regularization\n", "\n", "In statistics and machine learning, regularization methods reduce the model complexity, in particular to prevent overfitting by penalizing models with extreme parameter values.\n", "The most common variants in machine learning are $L_1$ and $L_2$ regularization, which can be added to learning algorithms that minimize a loss function $E(X, Y)$ by instead minimizing $E(X, Y) + \\alpha \u2016w\u2016$, where w is the model's weight vector, $\u2016\u00b7\u2016$ is either the $L_1$ norm or the squared $L_2$ norm, and $\\alpha=1/C$ (See Line 6) is a free parameter that needs to be tuned empirically.\n", "\n", "This method applies to many models. When applied in linear regression, the resulting models are termed ridge regression or lasso, but regularization is also employed in (binary and multiclass) logistic regression, neural nets, support vector machines, conditional random fields and some matrix decomposition methods. $L_2$ regularization may also be called \"weight decay\", in particular in the setting of neural nets." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn import svm" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 33 }, { "cell_type": "code", "collapsed": false, "input": [ "def svm_classify(alpha):\n", " xx, yy = np.meshgrid(np.linspace(3, 9, 500),\n", " np.linspace(1, 5, 500))\n", " X, Y = (iris.data[:, :2], iris.target == 2)\n", " # fit the model\n", " clf = svm.SVC(C=1.0/alpha, gamma=5)\n", " clf.fit(X, Y)\n", "\n", " plt.scatter(X[:, 0], X[:, 1], s=30, c=Y, cmap=plt.cm.Paired)\n", " # plot the decision function for each datapoint on the grid\n", " Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])\n", " Z = Z.reshape(xx.shape)\n", "\n", " plt.imshow(Z, interpolation='nearest',\n", " extent=(xx.min(), xx.max(), yy.min(), yy.max()), aspect='auto',\n", " origin='lower', cmap=plt.cm.PuOr_r)\n", " contours = plt.contour(xx, yy, Z, levels=[0], linewidths=2,\n", " linetypes='--')\n", " plt.scatter(X[:, 0], X[:, 1], s=30, c=Y, cmap=plt.cm.Paired)\n", " plt.axis([3, 9, 1, 5])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 34 }, { "cell_type": "code", "collapsed": false, "input": [ "_ = interact(svm_classify, alpha=DropdownWidget(values=[3, 1, 0.3, 1e-1, 1e-2, 1e-3, 1e-6]))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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YvnMtOAeGDZb88u59G8C5wOB+4wAAu/dKL3dQ37HgjsC+A5vAHWBAr9EQjsCB2m3gDkdZ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\nI25fB1fzEe08FMXH2A9DxzAz6xKte1DvPNNIufC5F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"text": [ "" ] } ], "prompt_number": 35 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Choose the following values for $\\alpha$:\n", " - 3.0\n", " - 0.1\n", " - 0.001\n", " \n", "Notice the difference in the complexity of the decision boundary, which boundary you prefer?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Model Selection\n", "\n", "We saw that we can vary the model capacity by changing the feature set, classificaion algorithm, or adding constraints on learned parameters through regularization.\n", "To select the best setting to model data, we need to agree on which criterion we want to optimize for.\n", "\n", "The following example shows how the model perform differently on **training data** (instances used to fit the model) compared to **testing data** (new unseen instances at the training time).\n", "Ultimately, we care about the model performance on new unseen instances, as we already the true answers of the training data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "np.random.seed(0)\n", "n_samples = 15\n", "true_fun = lambda X: np.cos(1.5 * np.pi * X)\n", "X4 = np.sort(np.random.rand(n_samples))\n", "y4 = true_fun(X4) + np.random.randn(n_samples) * 0.15" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 36 }, { "cell_type": "code", "collapsed": false, "input": [ "def regressor2(degree):\n", " if not degree:\n", " return\n", " degree = int(degree)\n", " fig, axes = plt.subplots(1, 3, sharey=False)\n", " fig.set_size_inches((18,6))\n", " polynomial_features = PolynomialFeatures(degree=degree,\n", " include_bias=False)\n", " linear_regression = LinearRegression()\n", " pipeline = Pipeline([(\"polynomial_features\", polynomial_features),\n", " (\"linear_regression\", linear_regression)])\n", " pipeline.fit(X4[:, np.newaxis], y4)\n", "\n", " train_predictions = pipeline.predict(X4[:, np.newaxis])\n", " Y_train = true_fun(X4)\n", " train_err = np.mean((train_predictions - Y_train) ** 2)\n", " \n", "\n", " X_test = np.linspace(0, 1, 100)\n", " test_predictions = pipeline.predict(X_test[:, np.newaxis]) \n", " Y_test = true_fun(X_test)\n", " test_err = np.mean((test_predictions - Y_test) ** 2)\n", "\n", " axes[0].plot(X4, Y_train)\n", " axes[0].set_title(\"True function\")\n", " axes[1].plot(X4, train_predictions)\n", " axes[1].set_title(\"Seen samples\")\n", " \n", " axes[1].text(0, 0, ('Error=%.2f' % train_err),\n", " size=15, horizontalalignment='left', verticalalignment='bottom')\n", "\n", " axes[2].plot(X_test, test_predictions)\n", " axes[2].text(0, 0, ('Error=%.2f' % test_err),\n", " size=15, horizontalalignment='left', verticalalignment='bottom')\n", "\n", " _ = axes[2].set_title(\"Unseen samples\")\n", " return test_err, train_err" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 37 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this demo, we vary one hyperparameter (degree of polynormial feature)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "_ = interact(regressor2, degree=TextWidget(value=\"1\"))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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OM1flEi1fUdxci83UKsy7zx/3+DmgqKIas7cm4EJusYGi0y+RzmHmqkwi5dpc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\no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"text": [ "" ] } ], "prompt_number": 38 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sweeping the hyperparameter" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def regressor3(degree):\n", " polynomial_features = PolynomialFeatures(degree=degree,\n", " include_bias=False)\n", " linear_regression = LinearRegression()\n", " pipeline = Pipeline([(\"polynomial_features\", polynomial_features),\n", " (\"linear_regression\", linear_regression)])\n", " pipeline.fit(X4[:, np.newaxis], y4)\n", " train_predictions = pipeline.predict(X4[:, np.newaxis])\n", " Y_train = true_fun(X4)\n", " train_err = np.mean((train_predictions - Y_train) ** 2)\n", " X_test = np.linspace(0, 1, 100)\n", " test_predictions = pipeline.predict(X_test[:, np.newaxis]) \n", " Y_test = true_fun(X_test)\n", " test_err = np.mean((test_predictions - Y_test) ** 2)\n", " return test_err, train_err" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 39 }, { "cell_type": "code", "collapsed": false, "input": [ "degrees = range(1, 8)\n", "errors = np.array([regressor3(d) for d in degrees])\n", "plt.plot(degrees, errors[:, 0], marker='^', c='r', label='Testing samples')\n", "plt.plot(degrees, errors[:, 1], marker='o', c='b', label='Training samples')\n", "plt.yscale('log')\n", "plt.xlabel(\"degree\"); plt.ylabel(\"Error\")\n", "_ = plt.legend(loc='best')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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jcIoBd5aYP38+V65cEWcUgiCUmtu8ebh/8AGytzdpO3ZgDAqyd0g2V/CMYty4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\ntGrVipiYGA4fPkxCQgITJkygdu3aRER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"text": [ "" ] } ], "prompt_number": 40 }, { "cell_type": "markdown", "metadata": {}, "source": [ "By sweeping the degree we discover two regions of model performance:\n", "\n", " - **Underfitting** (degree < 3): Characterized by the fact that the testing error will get lower if we increase the model capacity.\n", "\n", "\n", " - **Overfitting** (degree > 3): Characterized by the fact the testing will get higher if we increase the model capacity. Note, that the training error is getting lower or just staying the same!." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Observing the training error will give the wrong impression about the model performance.\n", "It is not hard to build a model that has 0 errors or 100% accuracy, by building a lookup table that stores the label/value of each problem instance in the training dataset.\n", "\n", "This observation leads us to realize the importance of evaluating the model performance on unseen data.\n", "\n", "Given constant size dataset, we should split *randomly* the dataset into two parts:\n", "1. **Training dataset**\n", "1. **Testing dataset**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Grid Search" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Grid search is the process of searching for the optimal set of hyperparameters by evaluating all possible combinations of hyperparameters on a cross-validation dataset.\n", "We split the training dataset further into:\n", "\n", "1. **Training dataset**\n", "1. **Cross-validation dataset**\n", "\n", "Note, we never use the testing dataset during training or model selection.\n", "Samples from the testing dataset should neven seen by the model till the final evaluation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following example will illustrate on how to pick the right model for our previous cosine curve fitting problem.\n", "\n", "Ridge regression is a linear regression that allows us to add $L_2$ regularization." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.grid_search import GridSearchCV\n", "from sklearn.linear_model import Ridge" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 41 }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, We name each stage and then we refer to a hyperparameter in a specific stage with the conventional name\n", "`stage-name`__`hyperparameter-name`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.metrics import mean_squared_error, make_scorer" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 42 }, { "cell_type": "code", "collapsed": false, "input": [ "pipeline = Pipeline([(\"pre1\", PolynomialFeatures()),\n", " (\"regressor\", Ridge())])\n", "parameters = {\n", " 'pre1__degree': range(1, 15),\n", " 'pre1__interaction_only': [False, True],\n", " 'regressor__alpha': (1e-5, 1e-4, 1e-3, 1e-2, 1e-1, 1, 1e1, 1e2),\n", " 'regressor__fit_intercept': [False, True],\n", "}\n", "scorer = make_scorer(mean_squared_error, greater_is_better=False)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 43 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- **scoring**: The criteria that decide which model is better evaluated on the cross-validation dataset. In classification it will be `accuracy` or `f1_score`\n", "\n", "\n", "- **n_jobs=8**: Runs the grid search in parallel on `8` workers.\n", "\n", "\n", "- **cv=3**: divides the training dataset into `3` equal parts. For each combination of hyperparameters, we run three iterations. Each iteration trains a model on two parts and evaluates on the remaning part. The performance will be the average of the three runs." ] }, { "cell_type": "code", "collapsed": false, "input": [ "model = GridSearchCV(pipeline, parameters, scoring=scorer, n_jobs=1, cv=3, verbose=1)\n", "model = model.fit(X4[:, np.newaxis], y4)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "[Parallel(n_jobs=1)]: Done 1 jobs | elapsed: 0.0s\n", "[Parallel(n_jobs=1)]: Done 50 jobs | elapsed: 0.1s\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ "[Parallel(n_jobs=1)]: Done 200 jobs | elapsed: 0.3s\n", "[Parallel(n_jobs=1)]: Done 450 jobs | elapsed: 0.9s\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ "[Parallel(n_jobs=1)]: Done 800 jobs | elapsed: 1.9s\n", "[Parallel(n_jobs=1)]: Done 1250 jobs | elapsed: 3.1s\n" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "Fitting 3 folds for each of 448 candidates, totalling 1344 fits\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ "[Parallel(n_jobs=1)]: Done 1344 out of 1344 | elapsed: 3.4s finished\n" ] } ], "prompt_number": 44 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have 448 candidates because we have:\n", "\n", "- 14 choices of `degree`\n", "- 2 choices of `interaction_only`\n", "- 8 choices of `alpha`\n", "- 2 choices of `fit_intercept`\n", "\n", "448 = 14 \\* 2 \\* 8 \\* 2\n", "\n", "We calculate the performance of each candidate, by having three cross validation iterations.\n", "\n", "1344 = 448 \\* 3" ] }, { "cell_type": "code", "collapsed": false, "input": [ "train_predictions = model.predict(X4[:, np.newaxis])\n", "Y_train = true_fun(X4)\n", "train_err = mean_squared_error(Y_train, train_predictions)\n", "X_test = np.linspace(0, 1, 100)\n", "test_predictions = model.predict(X_test[:, np.newaxis]) \n", "Y_test = true_fun(X_test)\n", "test_err = mean_squared_error(Y_test, test_predictions)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 45 }, { "cell_type": "code", "collapsed": false, "input": [ "print(\"\\n\\nReport of the grid search\")\n", "print(\"===========================\")\n", "print(\"Training error = {:.4f}\\t Testing error = {:.4f}\".format(train_err, test_err))\n", "print(\"Thes best hyperparameter combination as chosen by the grid search\\n\", model.best_params_) " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", "Report of the grid search\n", "===========================\n", "Training error = 0.0033\t Testing error = 0.0060\n", "Thes best hyperparameter combination as chosen by the grid search\n", " {'regressor__fit_intercept': False, 'pre1__interaction_only': False, 'regressor__alpha': 0.0001, 'pre1__degree': 3}\n" ] } ], "prompt_number": 46 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The best degree is 3, which confirms our pervious manual search!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Are all hyperparameters important?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pandas as pd\n", "from pandas import DataFrame" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 47 }, { "cell_type": "code", "collapsed": false, "input": [ "def gs2df(model):\n", " \"\"\" Convert grid search data to a dataframe.\"\"\"\n", " records = []\n", " for l in model.grid_scores_:\n", " d = dict(l.parameters)\n", " d[\"mean\"] = l.mean_validation_score\n", " d[\"scores\"] = l.cv_validation_scores\n", " records.append(d)\n", " return DataFrame.from_records(records)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 48 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_gsdf(df):\n", " \"\"\"Plot the average performance of each hyperparameter.\"\"\"\n", " for col in df.columns:\n", " if col == 'scores' or col == 'mean': continue\n", " temp = df.groupby(by=[col])[[\"mean\"]].mean()\n", " kind = 'bar' if isinstance(temp.index.values[0], str) else 'line'\n", " y_lim = temp.values.min() *0.975, temp.values.max() * 1.025\n", " temp.plot(kind=kind, ylim=y_lim, marker='o')" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 49 }, { "cell_type": "code", "collapsed": false, "input": [ "# scores of a grid search\n", "df = gs2df(model)\n", "\n", "# This is counter-intuitive and should not happen for classification\n", "# For more details why the scores are negative, look at\n", "# https://github.com/scikit-learn/scikit-learn/issues/2439\n", "df['mean'] *= -1\n", "\n", "df.head()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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meanpre1__degreepre1__interaction_onlyregressor__alpharegressor__fit_interceptscores
0 1.586537 1 False 0.00001 False [-2.15183132755, -0.322964405228, -2.28481454776]
1 1.586568 1 False 0.00001 True [-2.15189910988, -0.322964874614, -2.28483865444]
2 1.585520 1 False 0.00010 False [-2.15055228729, -0.32295515049, -2.28305280992]
3 1.585828 1 False 0.00010 True [-2.15122941479, -0.322959842746, -2.28329353293]
4 1.575430 1 False 0.00100 False [-2.13786380195, -0.322862831695, -2.26556273882]
\n", "

5 rows \u00d7 6 columns

\n", "
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 50, "text": [ " mean pre1__degree pre1__interaction_only regressor__alpha \\\n", "0 1.586537 1 False 0.00001 \n", "1 1.586568 1 False 0.00001 \n", "2 1.585520 1 False 0.00010 \n", "3 1.585828 1 False 0.00010 \n", "4 1.575430 1 False 0.00100 \n", "\n", " regressor__fit_intercept scores \n", "0 False [-2.15183132755, -0.322964405228, -2.28481454776] \n", "1 True [-2.15189910988, -0.322964874614, -2.28483865444] \n", "2 False [-2.15055228729, -0.32295515049, -2.28305280992] \n", "3 True [-2.15122941479, -0.322959842746, -2.28329353293] \n", "4 False [-2.13786380195, -0.322862831695, -2.26556273882] \n", "\n", "[5 rows x 6 columns]" ] } ], "prompt_number": 50 }, { "cell_type": "code", "collapsed": false, "input": [ "plot_gsdf(df)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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SwirSUxfiR99kXmbdjzMv/iGqhxR00S5IT91CWu7LaTk7NC9/dkkFK/amowDz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\ndnodBHXqgMOFE6R89SWeYx8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Qu3dvjBw5EkFBQTX2e+ihh3DgwIFmDYTq19FNjQ8e74z9F2/i0zPp+DXhFs6m5mNuXx88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\n09Ph7OyM559/vkXGVNdPBMe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4aztu7DgUllnx8WcHcamyFn0Gx6GozIqvvjyCWns9/G+LR/nZHOQfPQjvoiIYAkKRo43t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\nT0d6ejqGDh0KHx8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"text": [ "" ] } ], "prompt_number": 51 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Conclusion**: In this example, varying the hyperparameters of the regressor is not as important as varying the hyperparameters of the feature generator." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Learning Curve\n", "\n", "A learning curve is a plot of the training and cross-validation error as a function of the number of training points.\n", "Note that when we train on a small subset of the training data, the training error is computed using this subset, not the full training set.\n", "These plots can give a quantitative view into how beneficial it will be to add training samples." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.datasets import load_digits\n", "from sklearn import cross_validation\n", "from sklearn.learning_curve import learning_curve" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 52 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_learning_curve(estimator, title, X, y, ylim=None, cv=None,\n", " n_jobs=1, train_sizes=np.linspace(.1, 1.0, 5)):\n", " plt.figure()\n", " plt.title(title)\n", " if ylim is not None:\n", " plt.ylim(*ylim)\n", " plt.xlabel(\"Training examples\")\n", " plt.ylabel(\"Accuracy\")\n", " train_sizes, train_scores, test_scores = learning_curve(\n", " estimator, X, y, cv=cv, n_jobs=n_jobs, train_sizes=train_sizes)\n", " train_scores_mean = np.mean(train_scores, axis=1)\n", " train_scores_std = np.std(train_scores, axis=1)\n", " test_scores_mean = np.mean(test_scores, axis=1)\n", " test_scores_std = np.std(test_scores, axis=1)\n", " plt.grid()\n", "\n", " plt.fill_between(train_sizes, train_scores_mean - train_scores_std,\n", " train_scores_mean + train_scores_std, alpha=0.1,\n", " color=\"r\")\n", " plt.fill_between(train_sizes, test_scores_mean - test_scores_std,\n", " test_scores_mean + test_scores_std, alpha=0.1, color=\"g\")\n", " plt.plot(train_sizes, train_scores_mean, 'o-', color=\"r\",\n", " label=\"Training accuracy\")\n", " plt.plot(train_sizes, test_scores_mean, 'o-', color=\"g\",\n", " label=\"Cross-validation accuracy\")\n", "\n", " plt.legend(loc=\"best\")\n", " return plt" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 53 }, { "cell_type": "code", "collapsed": false, "input": [ "digits = load_digits()\n", "X5, y5 = digits.data, digits.target\n", "title = \"Learning Curves (Naive Bayes)\"\n", "# Cross validation with 100 iterations to get smoother mean test and train\n", "# score curves, each time with 20% data randomly selected as a validation set.\n", "cv = cross_validation.ShuffleSplit(digits.data.shape[0], n_iter=100,\n", " test_size=0.2, random_state=0)\n", "estimator = GaussianNB()\n", "__ = plot_learning_curve(estimator, title, X5, y5, ylim=(0.7, 1.01), cv=cv, n_jobs=4)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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DlJ2NHBcHfn4g3igrHcu3LCemnWVdjJh2MQz/dDictnKQvUCBdfRi2sWwYusK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\ntcSAPtQrIYSYHrU6DyFhVgJ8sgyn4fXM9ETMtBhB8jDGoNF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wZ8XyQRQWFhq8trCwgLOz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\noIJCCCHEKKigEEIIMYr/B0T9SWdC0FuKAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 54 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Practical Advice" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## High Bias (Underfitting)\n", "\n", "If our algorithm shows high bias, the following actions might help:\n", "\n", "- **Add more features**. \n", "\n", "\n", "- **Use a more sophisticated model**. Adding complexity to the model can help improve on bias. Switching from a linear classifier to non-linear one could reduce the bias.\n", "\n", "\n", "- **Decrease regularization**. Regularization is a technique used to impose simplicity in some machine learning models, by adding a penalty term that depends on the characteristics of the parameters. If a model has high bias, decreasing the effect of regularization can lead to better results.\n", "\n", "\n", "## High Variance (Overfitting)\n", "\n", "If our algorithm shows high variance, the following actions might help:\n", "\n", "- **Use fewer features**. Using a feature selection technique may be useful, and decrease the over-fitting of the estimator.\n", "\n", "\n", "- **Use more training samples**. Adding training samples can reduce the effect of over-fitting, and lead to improvements in a high variance estimator.\n", "\n", "\n", "- **Increase Regularization**. Regularization is designed to prevent over-fitting. In a high-variance model, increasing regularization can lead to better results.\n", "\n", "\n", "These choices become very important in real-world situations. For example, due to limited telescope time, astronomers must seek a balance between observing a large number of objects, and observing a large number of features for each object. Determining which is more important for a particular learning task can inform the observing strategy that the astronomer employs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Classification Metrics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Binary Case" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Accuracy\n", "$\n", "\\text{accuracy}=\\frac{\\text{true positives}+\\text{true negatives}}{\\text{number of examples}}$\n", "\n", "Not good if the classes are imabalanced.\n", "\n", "In binary classification, If 90% of the labels belong to the negative class, we can build easily a classifier with 90% accuracy by assigning all labels to the most frequent one.\n", "\n", "You should use instead $F_1$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $F_1$\n", "\n", "$\\text{precision}=\\frac{\\text{true positives}}{\\text{true positives}+\\text{false positives}}$\n", "\n", "\n", "\n", "$\\text{Recall}=\\frac{\\text{true positives}}{\\text{true positives} + \\text{false negatives}}$\n", "\n", "\n", "\n", "$F_1 = 2 \\cdot \\frac{\\mathrm{precision} \\cdot \\mathrm{recall}}{\\mathrm{precision} + \\mathrm{recall}}$\n", "\n", "\n", "In binary classification, If 90% of the labels belong to the negative class, we can build easily a classifier with 90% accuracy, however, the precision is 100% and the recall is 0%.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multi-class Case\n", "\n", "### Micro-average F1 score\n", "\n", "Calculate $F_1$ for each class alone, then compute **weighted-average** them according to their frequency. (Similar to accuracy).\n", "\n", "### Macro-average F1 score\n", "\n", "Calculate $F_1$ for each class alone, then compute **average** regardless of their frequency." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Working with text" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dataset\n", "\n", "The dataset is called [Twenty Newsgroups](http://qwone.com/~jason/20Newsgroups/).\n", "In order to get faster execution times for this first example we will work on a partial dataset with only 4 categories out of the 20 available in the dataset:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.datasets import fetch_20newsgroups\n", "categories = ['alt.atheism', 'soc.religion.christian', 'comp.graphics', 'sci.med']\n", "twenty_train = fetch_20newsgroups(subset='train', categories=categories, shuffle=True, random_state=42)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 55 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The returned dataset is a scikit-learn \u201cbunch\u201d: a simple holder object with fields that can be both accessed as python dict keys or object attributes for convenience, for instance the target_names holds the list of the requested category names" ] }, { "cell_type": "code", "collapsed": false, "input": [ "twenty_train.target_names" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 56, "text": [ "['alt.atheism', 'comp.graphics', 'sci.med', 'soc.religion.christian']" ] } ], "prompt_number": 56 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The files themselves are loaded in memory in the data attribute. For reference the filenames are also available:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "len(twenty_train.data)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 57, "text": [ "2257" ] } ], "prompt_number": 57 }, { "cell_type": "code", "collapsed": false, "input": [ "len(twenty_train.filenames)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 58, "text": [ "2257" ] } ], "prompt_number": 58 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let\u2019s print the first lines of the first loaded file" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print(\"\\n\".join(twenty_train.data[0].split(\"\\n\")[:3]))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "From: sd345@city.ac.uk (Michael Collier)\n", "Subject: Converting images to HP LaserJet III?\n", "Nntp-Posting-Host: hampton\n" ] } ], "prompt_number": 59 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Supervised learning algorithms will require a category label for each document in the training set. In this case the category is the name of the newsgroup which also happens to be the name of the folder holding the individual documents.\n", "\n", "\n", "For speed and space efficiency reasons scikit-learn loads the target attribute as an array of integers that corresponds to the index of the category name in the target_names list. The category integer id of each sample is stored in the target attribute:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "twenty_train.target[:10]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 60, "text": [ "array([1, 1, 3, 3, 3, 3, 3, 2, 2, 2])" ] } ], "prompt_number": 60 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bag of words" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The most intuitive way to do so is the bags of words representation:\n", "\n", "1. assign a fixed integer id to each word occurring in any document of the training set (for instance by building a dictionary from words to integer indices).\n", "\n", "1. for each document $i$, count the number of occurrences of each word w and store it in $X[i, j]$ as the value of feature $j$ where $j$ is the index of word $w$ in the dictionary\n", "\n", "The bags of words representation implies that `n_features` is the number of distinct words in the corpus: this number is typically larger that 100,000.\n", "\n", "If `n_samples == 10000`, storing X as a numpy array of type `float32` would require $10000 \\times 100000 \\times 4$ bytes = 4GB in RAM which is barely manageable on today\u2019s computers.\n", "Fortunately, most values in X will be zeros since for a given document less than a couple thousands of distinct words will be used. For this reason we say that bags of words are typically high-dimensional sparse datasets. We can save a lot of memory by only storing the non-zero parts of the feature vectors in memory.\n", "scipy.sparse matrices are data structures that do exactly this, and scikit-learn has built-in support for these structures." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Tokenizing\n", "\n", "Text preprocessing, tokenizing and filtering of stopwords are included in a high level component that is able to build a dictionary of features and transform documents to feature vectors:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.feature_extraction.text import CountVectorizer\n", "count_vect = CountVectorizer()\n", "X_train_counts = count_vect.fit_transform(twenty_train.data)\n", "X_train_counts.shape" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "/usr/local/lib/python2.7/dist-packages/numpy/core/fromnumeric.py:2499: VisibleDeprecationWarning: `rank` is deprecated; use the `ndim` attribute or function instead. To find the rank of a matrix see `numpy.linalg.matrix_rank`.\n", " VisibleDeprecationWarning)\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 61, "text": [ "(2257, 35788)" ] } ], "prompt_number": 61 }, { "cell_type": "markdown", "metadata": {}, "source": [ "CountVectorizer supports counts of N-grams of words or consequective characters. Once fitted, the vectorizer has built a dictionary of feature indices:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "count_vect.vocabulary_.get(u'algorithm')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 62, "text": [ "4690" ] } ], "prompt_number": 62 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The index value of a word in the vocabulary is linked to its frequency in the whole training corpus." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### From occurrences to frequencies" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Occurrence count is a good start but there is an issue: longer documents will have higher average count values than shorter documents, even though they might talk about the same topics.\n", "\n", "To avoid these potential discrepancies it suffices to divide the number of occurrences of each word in a document by the total number of words in the document: these new features are called tf for Term Frequencies.\n", " \n", "Another refinement on top of tf is to downscale weights for words that occur in many documents in the corpus and are therefore less informative than those that occur only in a smaller portion of the corpus.\n", "\n", "This downscaling is called tf\u2013idf for \u201cTerm Frequency times Inverse Document Frequency\u201d.\n", "\n", "Both tf and tf\u2013idf can be computed as follows:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.feature_extraction.text import TfidfTransformer\n", "tf_transformer = TfidfTransformer(use_idf=False).fit(X_train_counts)\n", "X_train_tf = tf_transformer.transform(X_train_counts)\n", "X_train_tf.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 63, "text": [ "(2257, 35788)" ] } ], "prompt_number": 63 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the above example-code, we firstly use the `fit(..)` method to fit our estimator to the data and secondly the `transform(..)` method to transform our count-matrix to a tf-idf representation. These two steps can be combined to achieve the same end result faster by skipping redundant processing. This is done through using the `fit_transform(..)` method as shown below, and as mentioned in the note in the previous section:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "tfidf_transformer = TfidfTransformer()\n", "X_train_tfidf = tfidf_transformer.fit_transform(X_train_counts)\n", "X_train_tfidf.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 64, "text": [ "(2257, 35788)" ] } ], "prompt_number": 64 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Training a classifier" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have our features, we can train a classifier to try to predict the category of a post. Let\u2019s start with a na\u00efve Bayes classifier, which provides a nice baseline for this task. scikit-learn includes several variants of this classifier; the one most suitable for word counts is the multinomial variant:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.naive_bayes import MultinomialNB\n", "clf = MultinomialNB().fit(X_train_tfidf, twenty_train.target)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 65 }, { "cell_type": "markdown", "metadata": {}, "source": [ "To try to predict the outcome on a new document we need to extract the features using almost the same feature extracting chain as before. The difference is that we call transform instead of `fit_transform` on the transformers, since they have already been fit to the training set:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "docs_new = ['God is love', 'OpenGL on the GPU is fast']\n", "X_new_counts = count_vect.transform(docs_new)\n", "X_new_tfidf = tfidf_transformer.transform(X_new_counts)\n", "predicted = clf.predict(X_new_tfidf)\n", "\n", "for doc, category in zip(docs_new, predicted):\n", " print('%r => %s' % (doc, twenty_train.target_names[category]))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "'God is love' => soc.religion.christian\n", "'OpenGL on the GPU is fast' => comp.graphics\n" ] } ], "prompt_number": 66 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Pipeline" ] }, { "cell_type": "code", "collapsed": false, "input": [ "twenty_test = fetch_20newsgroups(subset='test', categories=categories, shuffle=True, random_state=42)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 67 }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.linear_model import SGDClassifier\n", "text_clf = Pipeline([('vect', CountVectorizer()),\n", " ('tfidf', TfidfTransformer()),\n", " ('clf', SGDClassifier(loss='hinge', penalty='l2',\n", " alpha=1e-3, n_iter=5)),\n", "])\n", "_ = text_clf.fit(twenty_train.data, twenty_train.target)\n", "predicted = text_clf.predict(twenty_test.data)\n", "print(\"Accuracy of our SGD classifier is {:.2f}%\".format(np.mean(predicted == twenty_test.target)*100))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Accuracy of our SGD classifier is 91.28%\n" ] } ], "prompt_number": 68 }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn import metrics\n", "print(metrics.classification_report(twenty_test.target, predicted,\n", " target_names=twenty_test.target_names))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " precision recall f1-score support\n", "\n", " alt.atheism 0.94 0.82 0.87 319\n", " comp.graphics 0.88 0.98 0.92 389\n", " sci.med 0.95 0.89 0.92 396\n", "soc.religion.christian 0.90 0.95 0.92 398\n", "\n", " avg / total 0.92 0.91 0.91 1502\n", "\n" ] } ], "prompt_number": 69 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Clustering\n", "\n", "[Cluster analysis](http://en.wikipedia.org/wiki/Cluster_analysis) or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters). It is a main task of exploratory data mining, and a common technique for statistical data analysis, used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, and bioinformatics." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import time\n", "from sklearn import datasets\n", "from sklearn.metrics import euclidean_distances\n", "from sklearn.neighbors import kneighbors_graph\n", "from sklearn.preprocessing import StandardScaler\n", "from sklearn.cluster import (MeanShift, MiniBatchKMeans, AffinityPropagation, AgglomerativeClustering,\n", " DBSCAN, SpectralClustering)\n", "import sklearn.cluster" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 70 }, { "cell_type": "code", "collapsed": false, "input": [ "np.random.seed(0)\n", "\n", "# Generate datasets. We choose the size big enough to see the scalability\n", "# of the algorithms, but not too big to avoid too long running times\n", "n_samples = 150\n", "datasets_collection = {\n", "\"noisy_circles\": datasets.make_circles(n_samples=n_samples, factor=.5,\n", " noise=.05),\n", "\"noisy_moons\" :datasets.make_moons(n_samples=n_samples, noise=.05),\n", "\"blobs\": datasets.make_blobs(n_samples=n_samples, random_state=8),\n", "\"no_structure\": (np.random.rand(n_samples, 2), None),\n", "}" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 71 }, { "cell_type": "code", "collapsed": false, "input": [ "clustering_algos = {\n", " # create clustering estimators\n", " \"mean_shift\": MeanShift(bin_seeding=True),\n", " \"two_means\": MiniBatchKMeans(n_clusters=2),\n", " \"agglomerative\": AgglomerativeClustering(n_clusters=2,\n", " linkage='ward'),\n", " \"spectral\": SpectralClustering(n_clusters=2,\n", " eigen_solver='arpack',\n", " affinity=\"nearest_neighbors\"),\n", " \"dbscan\": DBSCAN(eps=.2),\n", " \"affinity_propagation\": AffinityPropagation(damping=.9, preference=-200),\n", " \"average_linkage\": AgglomerativeClustering(linkage=\"average\",\n", " affinity=\"cityblock\", n_clusters=2)\n", "}" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 72 }, { "cell_type": "code", "collapsed": false, "input": [ "colors = np.array([x for x in 'bgrcmykbgrcmykbgrcmykbgrcmyk'])\n", "colors = np.hstack([colors] * 20)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 73 }, { "cell_type": "code", "collapsed": false, "input": [ "def cluster(ds_name, algo_name):\n", " dataset = datasets_collection[ds_name]\n", " algorithm = clustering_algos[algo_name]\n", " X, y = dataset\n", " # normalize dataset for easier parameter selection\n", " X = StandardScaler().fit_transform(X)\n", "\n", " # estimate bandwidth for mean shift\n", " bandwidth = sklearn.cluster.estimate_bandwidth(X, quantile=0.3)\n", "\n", " # connectivity matrix for structured Ward\n", " connectivity = kneighbors_graph(X, n_neighbors=10)\n", " # make connectivity symmetric\n", " connectivity = 0.5 * (connectivity + connectivity.T)\n", "\n", " # Compute distances\n", " #distances = np.exp(-euclidean_distances(X))\n", " distances = euclidean_distances(X)\n", " # predict cluster memberships\n", " t0 = time.time()\n", " algorithm.fit(X)\n", " t1 = time.time()\n", " if hasattr(algorithm, 'labels_'):\n", " y_pred = algorithm.labels_.astype(np.int)\n", " else:\n", " y_pred = algorithm.predict(X)\n", "\n", " fig, axes = plt.subplots(1, 2)\n", " fig.set_size_inches((12,4))\n", " axes[0].scatter(X[:, 0], X[:, 1], c='black', s=10)\n", " axes[0].set_title('Data')\n", " axes[1].scatter(X[:, 0], X[:, 1], color=colors[y_pred].tolist(), s=10)\n", " axes[1].set_title('Clustered Data')\n", "\n", " if hasattr(algorithm, 'cluster_centers_'):\n", " centers = algorithm.cluster_centers_\n", " center_colors = colors[:len(centers)]\n", " plt.scatter(centers[:, 0], centers[:, 1], s=100, c=center_colors)\n", " plt.xlim(-2, 2)\n", " plt.ylim(-2, 2)\n", " plt.text(.99, .01, ('%.2fs' % (t1 - t0)).lstrip('0'),\n", " transform=plt.gca().transAxes, size=15,\n", " horizontalalignment='right')" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 74 }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.html.widgets import interact, RadioButtonsWidget, IntSliderWidget, TextWidget, DropdownWidget" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 75 }, { "cell_type": "code", "collapsed": false, "input": [ "_ = interact(cluster,\n", " algo_name=DropdownWidget(values=clustering_algos.keys()),\n", " ds_name=RadioButtonsWidget(values=datasets_collection.keys()))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "/usr/local/lib/python2.7/dist-packages/sklearn/manifold/spectral_embedding_.py:226: UserWarning: Graph is not fully connected, spectral embedding may not work as expected.\n", " warnings.warn(\"Graph is not fully connected, spectral embedding\"\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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JcmmGcmmGcpHGUJ+tGcqlGcqlGcplHJwZNBNCCCGEEMJVVJ5BCCE6ovIMQggxHSZfnkEI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\nZIFO5RmPHj1Cq1atlPc9PT3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JSExMhLe3NwYPHkztpcN9ai/Dt1dVVRXCwqpXW5g2bRpE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\nU8Nh4kQVpFJd3ZZKgcBAquHE8ain2QKh9uNQLn5M5WrdDy2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"text": [ "" ] } ], "prompt_number": 76 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "- [Scikit-learn tutorial](http://scikit-learn.org/stable/tutorial/)\n", "\n", "\n", "- [Scikit-learn examples](http://scikit-learn.org/stable/auto_examples/index.html)\n", "\n", "\n", "- [Machine learning for Astronomy](http://www.astroml.org/sklearn_tutorial/)" ] } ], "metadata": {} } ] }