{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "

Introduction to Python for Data Sciences

Franck Iutzeler
\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "\n", "
Chap. 4 - Scikit Learn
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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3- Unsupervised Learning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Clustering\n", "\n", "\n", "Clustering is the task of assigning data points to a known number of classes. The *K Means* algorithm is one of the most well known, it clusters data by minimizing the squared distance of cluster points to their mean." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "#import seaborn as sns\n", "#sns.set() " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_blobs\n", "X, y_true = make_blobs(n_samples=300, centers=4, cluster_std=0.60, random_state=0)\n", "plt.scatter(X[:, 0], X[:, 1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As before, we proceed by selecting a KMeans model and fitting it to the data." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "KMeans(n_clusters=4)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.cluster import KMeans\n", "\n", "kmeans = KMeans(n_clusters=4)\n", "kmeans.fit(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the model, one can get the *data points labels* with the attribute labels_ and the cluster centers with cluster\\_centers_." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2 1 0 1 2 2 3 0 1 1 3 1 0 1 2 0 0 2 3 3 2 2 0 3 3 0 2 0 3 0 1 1 0 1 1 1 1\n", " 1 3 2 0 3 0 0 3 3 1 3 1 2 3 2 1 2 2 3 1 3 1 2 1 0 1 3 3 3 1 2 1 3 0 3 1 3\n", " 3 1 3 0 2 1 2 0 2 2 1 0 2 0 1 1 0 2 1 3 3 0 2 2 0 3 1 2 1 2 0 2 2 0 1 0 3\n", " 3 2 1 2 0 1 2 2 0 3 2 3 2 2 2 2 3 2 3 1 3 3 2 1 3 3 1 0 1 1 3 0 3 0 3 1 0\n", " 1 1 1 0 1 0 2 3 1 3 2 0 1 0 0 2 0 3 3 0 2 0 0 1 2 0 3 1 2 2 0 3 2 0 3 3 0\n", " 0 0 0 2 1 0 3 0 0 3 3 3 0 3 1 0 3 2 3 0 1 3 1 0 1 0 3 0 0 1 3 3 2 2 0 1 2\n", " 2 3 2 3 0 1 1 0 0 1 0 2 3 0 2 3 1 3 2 0 2 1 1 1 1 3 3 1 0 3 2 0 3 3 3 2 2\n", " 1 0 0 3 2 1 3 0 1 0 2 2 3 3 0 2 2 2 0 1 1 2 2 0 2 2 2 1 3 1 0 2 2 1 1 1 2\n", " 2 0 1 3]\n", "[[ 0.94973532 4.41906906]\n", " [-1.37324398 7.75368871]\n", " [ 1.98258281 0.86771314]\n", " [-1.58438467 2.83081263]]\n" ] } ], "source": [ "print(kmeans.labels_)\n", "print(kmeans.cluster_centers_)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(X[:, 0], X[:, 1], c=kmeans.labels_)\n", "plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], c='r' , s = 100 , marker=\"*\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The different clusters have visibly been recovered. It is to be noted that from the cluster center, one can define Voronoi regions (regions that are closer to one center than any other one) that are exactly the predicted regions from the K Means algorithm." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.spatial import Voronoi, voronoi_plot_2d\n", "\n", "vor = Voronoi(kmeans.cluster_centers_)\n", "voronoi_plot_2d(vor)\n", "plt.scatter(X[:, 0], X[:, 1], c=kmeans.labels_)\n", "plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], c='r' , s = 100 , marker=\"*\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dimension reduction\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to reduce the dimension of our features either for direct learning or for visualization, dimension reduction is important and is implemented extensively in Scikit Learn [Decompositions](http://scikit-learn.org/stable/modules/decomposition.html#decompositions).\n", "\n", "One of the most standard methods is the *Principal Components Analysis* (PCA) that consists in projecting the feature matrix onto its top $n$ singular values (This was used in image compression in the NumPy notebook). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A first example \n", "\n", "Let us look at the PCA on a 2D synthetic data." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import seaborn as sns\n", "sns.set() " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rng = np.random.RandomState(1)\n", "X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n", "plt.scatter(X[:, 0], X[:, 1])\n", "plt.axis('equal');" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "PCA(n_components=2)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.decomposition import PCA\n", "\n", "pca = PCA(2)\n", "pca.fit(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PCA model outputs components_ that are the singular vectors and explained\\_variance_ for the magnitude of the associated singular values." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.94446029 -0.32862557]\n", " [-0.32862557 0.94446029]]\n", "[0.7625315 0.0184779]\n" ] } ], "source": [ "print(pca.components_)\n", "print(pca.explained_variance_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This illustration is provided in the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas. The greater axis is more informative and thus the second one would be dropped in the case of 1D dimensional reduction." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def draw_vector(v0, v1, ax=None):\n", " ax = ax or plt.gca()\n", " arrowprops=dict(arrowstyle='->',\n", " linewidth=2,\n", " shrinkA=0, shrinkB=0)\n", " ax.annotate('', v1, v0, arrowprops=arrowprops)\n", "\n", "# plot data\n", "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n", "for length, vector in zip(pca.explained_variance_, pca.components_):\n", " v = vector * 3 * np.sqrt(length)\n", " draw_vector(pca.mean_, pca.mean_ + v)\n", "plt.axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dimension reduction and visualization on the iris dataset\n", "\n", "The features are 4D and thus hard to represent; instead of taking just 2, let us apply PCA to find 2 interesting meta features. \n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "from sklearn.preprocessing import LabelEncoder\n", "\n", "\n", "\n", "iris = pd.read_csv('data/iris.csv')\n", "classes = pd.DataFrame(iris[\"species\"])\n", "features = iris.drop([\"species\",],axis=1)\n", "\n", "lenc = LabelEncoder()\n", "num_classes = np.array(classes.apply(lenc.fit_transform))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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sepal_lengthsepal_widthpetal_lengthpetal_width
05.13.51.40.2
14.93.01.40.2
24.73.21.30.2
34.63.11.50.2
45.03.61.40.2
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" ], "text/plain": [ " sepal_length sepal_width petal_length petal_width\n", "0 5.1 3.5 1.4 0.2\n", "1 4.9 3.0 1.4 0.2\n", "2 4.7 3.2 1.3 0.2\n", "3 4.6 3.1 1.5 0.2\n", "4 5.0 3.6 1.4 0.2" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "features.head()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "PCA(n_components=2)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pca = PCA(2)\n", "pca.fit(features)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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sepal_lengthsepal_widthpetal_lengthpetal_width---- Variance ----
vec. 10.361387-0.0845230.8566710.3582894.228242
vec. 20.6565890.730161-0.173373-0.0754810.242671
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" ], "text/plain": [ " sepal_length sepal_width petal_length petal_width \\\n", "vec. 1 0.361387 -0.084523 0.856671 0.358289 \n", "vec. 2 0.656589 0.730161 -0.173373 -0.075481 \n", "\n", " ---- Variance ---- \n", "vec. 1 4.228242 \n", "vec. 2 0.242671 " ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "reduction = pd.DataFrame(pca.components_)\n", "reduction.columns = [\"sepal_length\",\"sepal_width\",\"petal_length\",\"petal_width\"]\n", "reduction[\"---- Variance ----\"] = pca.explained_variance_\n", "reduction.index = [\"vec. 1\", \"vec. 2\"]\n", "reduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We notice an important first vector that combines the 4 features (sepal_width seems less important).\n", "\n", "We can now project the data onto these two vectors and plot the result to see if the classes are recognizable in this reduced space." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'vec. 2')" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "projected = pca.transform(features)\n", "\n", "plt.scatter(projected[:, 0], projected[:, 1], c=num_classes)\n", "plt.xlabel('vec. 1')\n", "plt.ylabel('vec. 2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the classes are way more separable this way than with just 2 features (see before). Furthermore, the vector 1 can almost be used alone to separate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Exercise:** *Clustering for color compression in images.* \n", ">\n", "> Take a black and white image with 256 gray levels, the (1D) vector of its pixel values can be obtained with the `flatten` method of NumPy. \n", "> \n", "> The goal of this exercise is to use clustering to convert the 255 greyscale values of the pixels to 8 values. To do so:\n", "> * cluster the pixels values into 8 clusters and replace the pixels values with their cluster centroids.\n", "> * Compare with a *uniform* quantizer." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(480, 640)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib.image as mpimg\n", "import matplotlib.cm as cm\n", "\n", "#### IMAGE\n", "img = mpimg.imread('img/flower.png')\n", "img_gray = 0.2989 * img[:,:,0] + 0.5870 * img[:,:,1] + 0.1140 * img[:,:,2] # Apparently these are \"good\" coefficients to convert to grayscale\n", "####\n", "\n", "print(img_gray.shape)\n", "\n", "plt.figure()\n", "plt.xticks([]),plt.yticks([])\n", "plt.title(\"Original\")\n", "plt.imshow(img_gray, cmap = cm.Greys_r) \n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(307200, 1)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pixels = img_gray.flatten().reshape(-1, 1)\n", "pixels.shape" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true }, "outputs": [], "source": [] } ], "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": "3.8.10" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "position": { "height": "462px", "left": "1160px", "right": "47px", "top": "174px", "width": "553px" }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }