{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "EE-311\n", "======\n", "\n", "Lab 5: Dimensionality Reduction\n", "----------------------------------------\n", "\n", "created by Zahra Farsijani and François Marelli on 25.03.2020" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Import libraries\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import sklearn\n", "from sklearn.datasets import load_iris, load_wine, make_circles\n", "from sklearn.linear_model import LogisticRegression\n", "from sklearn.model_selection import train_test_split\n", "import sklearn.decomposition\n", "import seaborn as sns\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from warnings import filterwarnings\n", "filterwarnings('ignore', category=sklearn.exceptions.ConvergenceWarning)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Dimensionality Reduction\n", "\n", "Many Machine Learning problems involve thousands or even millions of features for\n", "each training instance. Not only does this make training extremely slow, it can also\n", "make it much harder to find a good solution, and to visualize the data. This problem is often\n", "referred to as the curse of dimensionality. \n", "\n", "In this lab we will explore different types of methods to reduce the dimenionality of our data:\n", "\n", "1. Filter Methods\n", "2. Wrapper Methods\n", "3. Feature extraction\n", "\n", "There are two main approaches for feature selection:\n", "\n", "- wrapper methods, in which the features are selected using knowledge of the model\n", "- filter methods, in which the selection of features is independent of model used\n", "\n", "## 1.1 Filter Methods\n", "\n", "A simple approach for feature selection is the filter method, in which we the features of the dataset are ranked according to a scoring criterion.\n", "\n", "Selecting only the highest scoring features reduces the dimensionality of the dataset.\n", "\n", "We will test this method on the iris dataset with all features, for binary classification." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "data_X, data_y = load_iris(return_X_y=True)\n", "\n", "mask = (data_y == 0) | (data_y == 1)\n", "\n", "data_X = data_X[mask]\n", "data_y = data_y[mask]\n", "\n", "X_train, X_test, y_train, y_test = train_test_split(data_X, data_y, test_size=0.15, random_state=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since we have four features, we cannot effectively plot the data. \n", "\n", "Instead, we try to get more insights into the correlation between various features by plotting 2D graphs for each possible selection of 2 features in the dataset.\n", "\n", "What do you learn about the data? Can you see which features matter for classification and which ones don't?\n", "\n", "*Some 2D plots look more separated than others. Those features are likely the best we can use for binary classification. It looks like the two last features are the best.*" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "df = sns.load_dataset(\"iris\")\n", "df = df[df.species != 'virginica']\n", "sns.pairplot(df, hue=\"species\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Pearson's correlation coefficient filter\n", "\n", "A simple criterion to measure the information contained in the features is to compute the correlation between the features and the labels.\n", "\n", "Compute this criterion for all the features in the dataset, then select the two most informative features and show the resulting dataset in a scatterplot.\n", "\n", "According to the previous plot, which combination of features do you expect to be selected?\n", "\n", "*As expected, the two last features are selected.*" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correlation for each feature: [ 0.72829015 -0.69068434 0.96999023 0.96030697]\n", "Features, from most to least important: [2 3 0 1]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "# Your turn to code!\n", "\n", "correlation = (data_X - data_X.mean(0)).T.dot(data_y - data_y.mean()) / (data_X.std(0) * data_y.std() * data_X.shape[0])\n", "criterion = np.abs(correlation)\n", "print('Correlation for each feature: {}'.format(correlation))\n", "\n", "f_sorted = criterion.argsort()[::-1]\n", "\n", "print('Features, from most to least important: {}'.format(f_sorted))\n", "\n", "plt.scatter(data_X[:, f_sorted[0]], data_X[:, f_sorted[1]], c=data_y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.2 Wrapper Methods\n", "\n", "Wrapper methods select the best features by iteratively training the model and adding or removing features on the go.\n", "\n", "We will investigate the two basic versions of wrapper methods: Forward search and Backward search.\n", "\n", "### Forward search\n", "\n", "In this method, we start with having no feature in the model. In each iteration, we add the feature which best improves our model performance till the addition of a new feature does not bring any improvement anymore.\n", "\n", "Write a code that implements forward feature selection on a given model and dataset.\n", "\n", "*Comments in the code!*" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def forward_search(X_train, y_train, X_test, y_test, model):\n", " \"\"\"\n", " Implement forward search feature selection.\n", "\n", " Parameters\n", " ---------- \n", " X_train, X_test : numpy array of shape [n_samples, n_features], datasets\n", " \n", " y_train, y_test : numpy array of shape [n_train_samples, ], labels (binary)\n", " \n", " model : a sklearn model implementing the .fit() and .score() functions (e.g. LogisticRegression())\n", " \n", " Returns\n", " -------\n", " numpy array of shape [n_features_selected,]\n", " Vector with the indexes of selected features, sorted by first selected\n", " \"\"\"\n", " \n", " #######################################################\n", " # Your code here!\n", " \n", " # The list of features we keep, start with nothing\n", " features = []\n", " \n", " # Maximum iterations: we add each feature to the dataset => n_features\n", " for _ in range(X_train.shape[1]):\n", " # Set the initial score to an impossibly low value\n", " score = -1\n", " \n", " # We do not know what feature is the best to add yet\n", " best = None\n", " \n", " # If this is not the first iteration, compute the actual score of the current dataset\n", " if len(features) > 0:\n", " # Train and test only on the chosen features\n", " model.fit(X_train[:, features], y_train)\n", " score = model.score(X_test[:, features], y_test)\n", " \n", " # Ok we are ready to start iterating through all possible features\n", " for f in range(X_train.shape[1]):\n", " \n", " # If we are already using the feature, we cannot add it a second time: continue to the next one\n", " if f in features:\n", " continue\n", " \n", " # Create a copy of the feature list to temporarily append the new one\n", " f_train = features.copy() \n", " f_train.append(f)\n", " \n", " # Train and score the model with the added feature\n", " model.fit(X_train[:, f_train], y_train)\n", " f_score = model.score(X_test[:, f_train], y_test)\n", " \n", " # If it does better than our base (or the previous best), this becomes the new best\n", " if f_score > score:\n", " score = f_score\n", " best = f\n", " \n", " # After going through all features, if we have a best one to add (i.e. if we improved the model by adding a feature), add it to the set and reiterate\n", " if best is not None:\n", " features.append(best)\n", " \n", " # If no new feature improves the model, we are done\n", " else:\n", " break\n", " \n", " return np.array(features)\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run your forward search algorithm on the iris dataset and print which features have been selected for a basic logistic regression model.\n", "\n", "What dimensions are selected?\n", "\n", "Did you expect it?\n", "\n", "*Only the third feature is kept. Since the data are linearly separable along that dimension, the model will get 100% accuracy and will not be improved by the addition of another feature.*" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Selected features: [2]\n" ] } ], "source": [ "\n", "# Code here!\n", "\n", "model = LogisticRegression()\n", "\n", "features = forward_search(X_train, y_train, X_test, y_test, model)\n", "\n", "print('Selected features: {}'.format(features))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### The wine dataset\n", "\n", "The iris dataset is too simple to demonstrate the use of wrapper methods.\n", "\n", "We will use a bigger dataset called [the wine dataset](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_wine.html#sklearn.datasets.load_wine).\n", "\n", "How many features does this one have?" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of features: 13\n" ] } ], "source": [ "# Load and prepare data\n", "data_X_wine, data_y_wine = load_wine(return_X_y=True)\n", "\n", "mask = (data_y_wine == 0) | (data_y_wine == 1)\n", "\n", "data_X_wine = data_X_wine[mask]\n", "data_y_wine = data_y_wine[mask]\n", "\n", "X_train_wine, X_test_wine, y_train_wine, y_test_wine = train_test_split(data_X_wine, data_y_wine, test_size=0.35, random_state=3)\n", "\n", "print('Number of features:', data_X_wine.shape[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use your forward search function to reduce the wine dataset using a logistic regression model, and show what features have been selected.\n", "\n", "Further reduce the dimensionality by keeping only the 2 most relevant features.\n", "\n", "Then, compare the model accuracy for both selected features and ALL features for the wine dataset.\n", "\n", "*The model does not seem to suffer in performance when using the reduced dataset. This is not always true and depends on the data properties.*" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Selected features: [12 6]\n", "Accuracy with full dataset: 95.65%\n", "Accuracy with reduced dataset: 95.65%\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "model = LogisticRegression()\n", "\n", "features = forward_search(X_train_wine, y_train_wine, X_test_wine, y_test_wine, model)\n", "\n", "\n", "# Here you code!\n", "\n", "features = features[:2]\n", "\n", "acc_full = model.fit(X_train_wine, y_train_wine).score(X_test_wine, y_test_wine)\n", "acc_red = model.fit(X_train_wine[:, features], y_train_wine).score(X_test_wine[:, features], y_test_wine)\n", "\n", "print('Selected features: {}'.format(features))\n", "\n", "print('Accuracy with full dataset: {:.2f}%'.format(acc_full*100))\n", "print('Accuracy with reduced dataset: {:.2f}%'.format(acc_red*100))\n", "\n", "plt.scatter(data_X_wine[:, features[0]], data_X_wine[:, features[1]], c=data_y_wine)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Backward Search (bonus)\n", "\n", "In this method, as opposed to previous one, we start with using all features to train the model. \n", "\n", "In each iteration, we remove the feature which has the least effect on our model, untill removing of a new variable does not improve the performance of the model.\n", "\n", "Write a code that implements forward feature selection on a given model and dataset. It can be very similar to your forward search!" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def backward_search(X_train, y_train, X_test, y_test, model):\n", " \"\"\"\n", " Implement backward search feature selection.\n", "\n", " Parameters\n", " ---------- \n", " X_train, X_test : numpy array of shape [n_samples, n_features], datasets\n", " \n", " y_train, y_test : numpy array of shape [n_train_samples, ], labels (binary)\n", " \n", " model : a sklearn model implementing the .fit() and .score() functions (e.g. LogisticRegression())\n", " \n", " Returns\n", " -------\n", " numpy array of shape [n_features_selected,]\n", " Vector with the indexes of selected features, sorted by importance of feature\n", " \"\"\"\n", " \n", " \n", " #######################################################\n", " # Code here\n", " \n", " # Features we keep, start with all\n", " features = list(range(X_train.shape[1]))\n", " \n", " # Maximum iterations: we remove each feature to the dataset => n_features\n", " for _ in range(X_train.shape[1] - 1):\n", " # Train and test only on the chosen features to set the initial score\n", " model.fit(X_train[:, features], y_train)\n", " score = model.score(X_test[:, features], y_test)\n", " \n", " # We do not know what feature is the best to add yet\n", " best = None\n", " \n", " # Ok we are ready to start iterating through all remaining features\n", " for f in features: \n", " \n", " # Create a copy of the feature list to temporarily remove the new one\n", " f_train = features.copy() \n", " f_train.remove(f)\n", " \n", " # Train and score the model with less features\n", " model.fit(X_train[:, f_train], y_train)\n", " f_score = model.score(X_test[:, f_train], y_test)\n", " \n", " # If it does better than our base (or the previous best), this becomes the new best feature to be removed\n", " # If the score is the same, it is still an improvement because we have fewer features (=> non strict comparison)\n", " if f_score >= score:\n", " score = f_score\n", " best = f\n", " \n", " # After going through all features, if we have a best one to remove (i.e. if we improved the model by removing a feature), remove it from the set and reiterate\n", " if best is not None:\n", " features.remove(best)\n", " \n", " # If no new feature improves the model, we are done\n", " else:\n", " break\n", " \n", " return np.array(features)\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use your backward search function to reduce the wine dataset for a linear regression model.\n", "\n", "Can you reduce it further down to 2 features only? (*Spoiler: yes you can, but how?*)\n", "\n", "How does the ordering of features compare to the one obtained with the forward search?\n", "\n", "*Interestingly enough, this method does not converge to the same subset as the forward search, but we get the same accuracy. We could reduce the space further down by running more iterations even after the performance of the model starts degrading. However, we would get worse accuracy then.*" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Selected features: [ 1 2 3 4 9 11]\n", "Accuracy with full dataset: 95.65%\n", "Accuracy with reduced dataset: 97.83%\n" ] } ], "source": [ "\n", "# Here we code again!\n", "\n", "model = LogisticRegression()\n", "\n", "features = backward_search(X_train_wine, y_train_wine, X_test_wine, y_test_wine, model)\n", "\n", "acc_full = model.fit(X_train_wine, y_train_wine).score(X_test_wine, y_test_wine)\n", "acc_red = model.fit(X_train_wine[:, features], y_train_wine).score(X_test_wine[:, features], y_test_wine)\n", "\n", "print('Selected features: {}'.format(features))\n", "\n", "print('Accuracy with full dataset: {:.2f}%'.format(acc_full*100))\n", "print('Accuracy with reduced dataset: {:.2f}%'.format(acc_red*100))\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Feature extraction using PCA\n", "\n", "Where feature selection only tries to find the most important in the dataset, feature extraction actually combines multiple features to create new (better?) features.\n", "\n", "We will focus on a well-known feature extraction method: the Principal Component Analysis (PCA).\n", "\n", "PCA tries to define a new coordinate system such that the variance of the data is maximized along its main axes.\n", "\n", "This then allows to select only the first few axes to reduce the dimension of the space while still keeping most of the representative information contained in the data.\n", "\n", "**In this lab (and in the homework), we choose to not normalize 2D data for illustration purposes. We will later demonstrate the benefits of normalization on higher dimensionality datasets.**\n", "\n", "For demonstration purposes, we will create a toy dataset that illustrates the concepts of PCA.\n", "\n", "Wait... There are no labels!? Is this important?\n", "\n", "*The computation of PCA does not take labels into account. PCA tries to minimize the information lost when reducing dimensionality from a representation point of view: it keeps most of the information about the distribution of the data as a whole. However, the representation information may not always be what is needed to get good classification performance: the separability of different classes may be along a different axis than the main data variance.*" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data_X_toy = np.random.default_rng(0).multivariate_normal([1, 0.5], [[1, 0], [0, 25]], 500)\n", "\n", "# Rotate the gaussian\n", "theta = np.radians(60)\n", "c, s = np.cos(theta), np.sin(theta)\n", "R = np.array(((c, -s), (s, c)))\n", "data_X_toy = data_X_toy.dot(R)\n", "data_X_toy += (10, -5)\n", "\n", "plt.scatter(data_X_toy[:,0], data_X_toy[:,1])\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PCA is computed by extracting the eigenvectors of the covariance matrix of the data. \n", "\n", "Write the code to compute the PCA and plot the principal directions on the graph using `draw_vector`. \n", "\n", "How do you interpret it? Can you tell which is the principal axis and how?\n", "\n", "You can use:\n", "\n", "`np.cov` to compute covariance\n", "\n", "`np.linalg.eig` to perform eigen decomposition of a matrix\n", "\n", "*The principal components define a new system of coordinates in which the variance is maximized along the coordinate axes. The principal axis is the one with the obvious maximal variance (the one in orange).*" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def draw_vector(v0, v1, color='b', ax=None):\n", " \"\"\"\n", " Draw a vector on a matplotlib graph.\n", "\n", " Parameters:\n", " v0: np.array of size (2), the starting point of the vector\n", " v1: np.array of size (2), the end point of the vector\n", " color: str, color code for the plotting\n", " ax: which axes to plot to, leave empty to use current figure\n", " \"\"\"\n", " \n", " ax = ax or plt.gca()\n", " arrowprops=dict(ec=color,\n", " arrowstyle='->',\n", " linewidth=2,\n", " shrinkA=0, shrinkB=0)\n", " ax.annotate('', v1, v0, arrowprops=arrowprops, color='r')\n", "\n", "\n", "# Code here, you must.\n", "\n", "covar = np.cov(data_X_toy.T)\n", "eigenval, eigenvec = np.linalg.eig(covar)\n", "\n", "plt.figure(figsize=(10, 7))\n", "plt.scatter(data_X_toy[:,0], data_X_toy[:,1])\n", "plt.grid()\n", "\n", "for i, vec in enumerate(eigenvec.T):\n", " col = ['orange', 'red']\n", " draw_vector(data_X_toy.mean(0), data_X_toy.mean(0) + vec * 3 * np.sqrt(eigenval[i]), col[i])\n", "\n", "plt.axis('equal')\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A numerically more stable way to compute PCA is Singular Value Decomposition (SVD).\n", "\n", "Compute the principal components of the data using `np.linalg.svd` and check that the result is identical.\n", "\n", "Do not forget to center the data first (zero mean)! Why is it important? Try without that and see the result.\n", "\n", "*The singular value decomposition of a matrix $X$ gives the eigenvectors of $X^TX$. However, $X^TX$ is equivalent to the covariance matrix of $X$ only if the columns of $X$ have zero mean.\n", "Thus SVD is suitable for PCA only if we center the data first.*\n", "\n", "*Variance normalization is recommended but not necessary: PCA still works without normalization, but its result is different as the features with larger variances have much more weight in the computation.*" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# Program here\n", "data_X_centered = data_X_toy - data_X_toy.mean(0)\n", "U, s, Vt = np.linalg.svd(data_X_centered)\n", "\n", "plt.scatter(data_X_toy[:,0], data_X_toy[:,1])\n", "plt.grid()\n", "\n", "for i, vec in enumerate(Vt):\n", " col = ['orange', 'red']\n", " draw_vector(data_X_toy.mean(0), data_X_toy.mean(0) + vec * 0.15 * s[i], col[i])\n", "\n", "plt.axis('equal')\n", "plt.show()\n", "\n", "# Without centering\n", "U, s, Vt = np.linalg.svd(data_X_toy)\n", "\n", "plt.scatter(data_X_toy[:,0], data_X_toy[:,1])\n", "plt.grid()\n", "\n", "for i, vec in enumerate(Vt):\n", " col = ['orange', 'red']\n", " draw_vector(data_X_toy.mean(0), data_X_toy.mean(0) + vec * 0.05 * s[i], col[i])\n", "\n", "plt.title('Without centering')\n", "plt.axis('equal')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dimensionality reduction\n", "\n", "We can use PCA to reduce the dimension of a dataset by projecting it onto its N first principal components.\n", "\n", "Let us show it on the iris dataset. Use SVD to compute its principal components, and plot the percentage of information contained in each principal component (ratio of variance explained by each component).\n", "\n", "How many features seem relevant?\n", "\n", "You can use `plt.bar( . )` for the figure.\n", "\n", "*Since we want to compare the relative importance of components, it is crucial to normalize the dataset first, otherwise features with a large variance (features with a large scale) will look like they contain all the info.\n", "Think about this: if plotting size [cm] vs age [years], the size is likely goint to range between 100 and 200, while the age will range between 0 and 100 (roughly). Without normalization, it would mean that the size is twice as important as the age in all computations, just because of the units used. Without prior information, we should always consider that all features are equivalent in terms of importance, and therefore normalize everything to get rid of units and range differences. Check the difference on the plots: without normalization it looks like the first component contains all the information (but it does not!).*\n", "\n", "*The two first components contain more than 90% of the information. They are probably sufficient to efficiently represent our data.*" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# Your code here\n", "\n", "# Normalization !\n", "X_centered = (data_X - data_X.mean(0)) / data_X.std(0)\n", "\n", "_, s, Vt = np.linalg.svd(X_centered)\n", "\n", "eigenvalues = np.power(s, 2)\n", "info_ratio = eigenvalues / eigenvalues.sum()\n", "\n", "plt.title('Information percentage contained in each component')\n", "plt.bar(range(4), info_ratio*100)\n", "plt.show()\n", "\n", "# For the info, without normalization\n", "\n", "_, s2, Vt2 = np.linalg.svd(data_X)\n", "\n", "eigenvalues2 = np.power(s2, 2)\n", "info_ratio2 = eigenvalues2 / eigenvalues2.sum()\n", "\n", "plt.title('Information percentage contained in each component, no normalization')\n", "plt.bar(range(4), info_ratio2*100)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can choose to keep only the two first principal components to reduce the dimensionality of the dataset.\n", "\n", "Reminder: to project the data into the reduced space, compute the matrix multiplication of the dataset matrix $X$ by the matrix $W_{d}$, defined as the matrix containing the first $d$ principal vectors (i.e., the matrix composed of the first $d$ right eigenvectors).\n", "\n", "Reduce the iris dataset to a dimension of 2 using PCA and show the result as a scatterplot." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "# Time to shine\n", "\n", "W = Vt.T[:, :2]\n", "X_reduced = X_centered.dot(W)\n", "\n", "plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=data_y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fortunately enough, you do not have to write all this every time, as `sklearn.decomposition.PCA` is there for you!\n", "\n", "Use it to reduce the iris dataset to a dimension of 2, and show a scatter of the result.\n", "\n", "*The plot looks different from the last one, but it is totally equivalent to the one computed manually: if you check carefully, you will see that the vertical axis is just inversed. The sign of the principal components does not matter, only their direction.*" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Information contained in principal components: [0.76158591 0.20169267]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "# One more time\n", "\n", "pca = sklearn.decomposition.PCA(n_components=2).fit(X_centered)\n", "\n", "reduced = pca.transform(X_centered)\n", "\n", "print('Information contained in principal components: {}'.format(pca.explained_variance_ratio_))\n", "\n", "plt.scatter(reduced[:, 0], reduced[:, 1], c=data_y)\n", "plt.show()\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.3" } }, "nbformat": 4, "nbformat_minor": 4 }