{ "nbformat": 4, "nbformat_minor": 2, "metadata": { "anaconda-cloud": {}, "kernelspec": { "name": "python3", "display_name": "Python 3.8.2 64-bit ('base': conda)" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.2" }, "colab": { "name": "05.09-Principal-Component-Analysis.ipynb", "provenance": [], "include_colab_link": true }, "interpreter": { "hash": "d361e8bd3ab8be8f3ea65790adb41c2b64f49b1477d0d1af835155fecf213182" } }, "cells": [ { "cell_type": "markdown", "source": [ "\"Open" ], "metadata": { "id": "view-in-github", "colab_type": "text" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "\n", "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", "\n", "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" ], "metadata": { "deletable": true, "editable": true, "id": "kM9vLKej7PCP" } }, { "cell_type": "markdown", "source": [ "# Principal Component Analysis" ], "metadata": { "id": "4GAVkeXi7PCT" } }, { "cell_type": "markdown", "source": [ "Up until now, we have been looking in depth at supervised learning estimators: those estimators that predict labels based on labeled training data.\n", "Here we begin looking at several unsupervised estimators, which can highlight interesting aspects of the data without reference to any known labels.\n", "\n", "In this section, we explore what is perhaps one of the most broadly used of unsupervised algorithms, principal component analysis (PCA).\n", "PCA is fundamentally a dimensionality reduction algorithm, but it can also be useful as a tool for visualization, for noise filtering, for feature extraction and engineering, and much more.\n", "After a brief conceptual discussion of the PCA algorithm, we will see a couple examples of these further applications.\n", "\n", "We begin with the standard imports:" ], "metadata": { "deletable": true, "editable": true, "id": "py57XRkB7PCU" } }, { "cell_type": "code", "execution_count": 1, "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set()" ], "outputs": [], "metadata": { "deletable": true, "editable": true, "id": "pW8zBoR77PCU" } }, { "cell_type": "markdown", "source": [ "## Introducing Principal Component Analysis\n", "\n", "Principal component analysis is a fast and flexible unsupervised method for dimensionality reduction in data, which we saw briefly in [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb).\n", "Its behavior is easiest to visualize by looking at a two-dimensional dataset.\n", "Consider the following 200 points:" ], "metadata": { "deletable": true, "editable": true, "id": "FKYKkX9K7PCV" } }, { "cell_type": "code", "execution_count": 2, "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');" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {} } ], "metadata": { "deletable": true, "editable": true, "id": "06V0mvy77PCW", "outputId": "db96766f-a63e-4e36-937e-169c2553b0f6" } }, { "cell_type": "markdown", "source": [ "By eye, it is clear that there is a nearly linear relationship between the x and y variables. Rather than attempting to *predict* the y values from the x values, the unsupervised learning problem attempts to learn about the *relationship* between the x and y values.\n", "\n", "In principal component analysis, this relationship is quantified by finding a list of the *principal axes* in the data, and using those axes to describe the dataset.\n", "Using Scikit-Learn's ``PCA`` estimator, we can compute this as follows:" ], "metadata": { "deletable": true, "editable": true, "id": "LbiZoIBE7PCX" } }, { "cell_type": "code", "execution_count": 3, "source": [ "from sklearn.decomposition import PCA\n", "pca = PCA(n_components=2)\n", "pca.fit(X)" ], "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "PCA(n_components=2)" ] }, "metadata": {}, "execution_count": 3 } ], "metadata": { "deletable": true, "editable": true, "id": "-fq83CdE7PCY", "outputId": "b5d6ef65-642d-45fe-b238-c23cb453eb55" } }, { "cell_type": "markdown", "source": [ "The fit learns some quantities from the data, most importantly the \"components\" and \"explained variance\":" ], "metadata": { "deletable": true, "editable": true, "id": "1gVDFhNb7PCY" } }, { "cell_type": "code", "execution_count": 4, "source": [ "print(pca.components_)" ], "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "[[-0.94446029 -0.32862557]\n", " [-0.32862557 0.94446029]]\n" ] } ], "metadata": { "deletable": true, "editable": true, "id": "QK-15FLA7PCZ", "outputId": "c4dafa74-b477-499c-d149-1c0aa0682206" } }, { "cell_type": "code", "execution_count": 5, "source": [ "print(pca.explained_variance_)" ], "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "[0.7625315 0.0184779]\n" ] } ], "metadata": { "deletable": true, "editable": true, "id": "YQPg9vOB7PCZ", "outputId": "574bb9f0-7141-4485-c729-e6bae30dd7df" } }, { "cell_type": "markdown", "source": [ "To see what these numbers mean, let's visualize them as vectors over the input data, using the \"components\" to define the direction of the vector, and the \"explained variance\" to define the squared-length of the vector:" ], "metadata": { "deletable": true, "editable": true, "id": "jiHqUhzN7PCZ" } }, { "cell_type": "code", "execution_count": 6, "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');" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {} } ], "metadata": { "deletable": true, "editable": true, "id": "PPfu58PG7PCa", "outputId": "a1fe4cf7-0033-48a9-ec4b-e768552c8e44" } }, { "cell_type": "markdown", "source": [ "These vectors represent the *principal axes* of the data, and the length of the vector is an indication of how \"important\" that axis is in describing the distribution of the data—more precisely, it is a measure of the variance of the data when projected onto that axis.\n", "The projection of each data point onto the principal axes are the \"principal components\" of the data.\n", "\n", "If we plot these principal components beside the original data, we see the plots shown here:" ], "metadata": { "deletable": true, "editable": true, "id": "7aTO8vNE7PCa" } }, { "cell_type": "code", "execution_count": 8, "source": [ "from sklearn.decomposition import PCA\n", " \n", "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", "rng = np.random.RandomState(1)\n", "X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n", "pca = PCA(n_components=2, whiten=True)\n", "pca.fit(X)\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n", "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n", "\n", "# plot data\n", "ax[0].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, ax=ax[0])\n", "ax[0].axis('equal');\n", "ax[0].set(xlabel='x', ylabel='y', title='input')\n", "\n", "# plot principal components\n", "X_pca = pca.transform(X)\n", "ax[1].scatter(X_pca[:, 0], X_pca[:, 1], alpha=0.2)\n", "draw_vector([0, 0], [0, 3], ax=ax[1])\n", "draw_vector([0, 0], [3, 0], ax=ax[1])\n", "ax[1].axis('equal')\n", "ax[1].set(xlabel='component 1', ylabel='component 2',\n", " title='principal components',\n", " xlim=(-5, 5), ylim=(-3, 3.1));" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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", 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" ] }, "metadata": {} } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "This transformation from data axes to principal axes is an *affine transformation*, which basically means it is composed of a translation, rotation, and uniform scaling.\n", "\n", "While this algorithm to find principal components may seem like just a mathematical curiosity, it turns out to have very far-reaching applications in the world of machine learning and data exploration." ], "metadata": { "deletable": true, "editable": true, "id": "8FtD1sRQ7PCb" } }, { "cell_type": "markdown", "source": [ "### PCA as dimensionality reduction\n", "\n", "Using PCA for dimensionality reduction involves zeroing out one or more of the smallest principal components, resulting in a lower-dimensional projection of the data that preserves the maximal data variance.\n", "\n", "Here is an example of using PCA as a dimensionality reduction transform:" ], "metadata": { "deletable": true, "editable": true, "id": "M5X4aRFp7PCb" } }, { "cell_type": "code", "execution_count": 9, "source": [ "pca = PCA(n_components=1)\n", "pca.fit(X)\n", "X_pca = pca.transform(X)\n", "print(\"original shape: \", X.shape)\n", "print(\"transformed shape:\", X_pca.shape)" ], "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "original shape: (200, 2)\n", "transformed shape: (200, 1)\n" ] } ], "metadata": { "deletable": true, "editable": true, "id": "2-NxpqHY7PCb", "outputId": "c2b538c4-8bcd-4e16-bbbc-2ed8ae940c0d" } }, { "cell_type": "markdown", "source": [ "The transformed data has been reduced to a single dimension.\n", "To understand the effect of this dimensionality reduction, we can perform the inverse transform of this reduced data and plot it along with the original data:" ], "metadata": { "deletable": true, "editable": true, "id": "yysD1oWJ7PCb" } }, { "cell_type": "code", "execution_count": 10, "source": [ "X_new = pca.inverse_transform(X_pca)\n", "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n", "plt.scatter(X_new[:, 0], X_new[:, 1], alpha=0.8)\n", "plt.axis('equal');" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {} } ], "metadata": { "deletable": true, "editable": true, "id": "sSj44k8L7PCb", "outputId": "044f19c0-bec2-4bd5-d176-0bff90109b34" } }, { "cell_type": "markdown", "source": [ "The light points are the original data, while the dark points are the projected version.\n", "This makes clear what a PCA dimensionality reduction means: the information along the least important principal axis or axes is removed, leaving only the component(s) of the data with the highest variance.\n", "The fraction of variance that is cut out (proportional to the spread of points about the line formed in this figure) is roughly a measure of how much \"information\" is discarded in this reduction of dimensionality.\n", "\n", "This reduced-dimension dataset is in some senses \"good enough\" to encode the most important relationships between the points: despite reducing the dimension of the data by 50%, the overall relationship between the data points are mostly preserved." ], "metadata": { "deletable": true, "editable": true, "id": "PEYij20L7PCc" } }, { "cell_type": "markdown", "source": [ "### PCA for visualization: Hand-written digits\n", "\n", "The usefulness of the dimensionality reduction may not be entirely apparent in only two dimensions, but becomes much more clear when looking at high-dimensional data.\n", "To see this, let's take a quick look at the application of PCA. We start by loading the data:" ], "metadata": { "deletable": true, "editable": true, "id": "fVw5AdFj7PCc" } }, { "cell_type": "code", "execution_count": 11, "source": [ "from sklearn.datasets import load_digits\n", "digits = load_digits()\n", "digits.data.shape" ], "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "(1797, 64)" ] }, "metadata": {}, "execution_count": 11 } ], "metadata": { "deletable": true, "editable": true, "id": "5yRezN4I7PCc", "outputId": "278420ff-d1e6-4fe1-9476-31e9bc83bb9f" } }, { "cell_type": "markdown", "source": [ "The data consists of 8Ă—8 pixel images, meaning that they are 64-dimensional.\n", "To gain some intuition into the relationships between these points, we can use PCA to project them to a more manageable number of dimensions, say two:" ], "metadata": { "deletable": true, "editable": true, "id": "tUWHaaHF7PCc" } }, { "cell_type": "code", "execution_count": 14, "source": [ "pca = PCA(2) # project from 64 to 2 dimensions\n", "projected = pca.fit_transform(digits.data)\n", "print(digits.data.shape)\n", "print(projected.shape)" ], "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "(1797, 64)\n", "(1797, 2)\n" ] } ], "metadata": { "deletable": true, "editable": true, "id": "c38k4mHG7PCd", "outputId": "8a769a23-0560-45c5-91d5-57aa00ca8467" } }, { "cell_type": "markdown", "source": [ "We can now plot the first two principal components of each point to learn about the data:" ], "metadata": { "deletable": true, "editable": true, "id": "W6-39qpW7PCd" } }, { "cell_type": "code", "execution_count": 16, "source": [ "plt.scatter(projected[:, 0], projected[:, 1],\n", " c=digits.target, edgecolor='none', alpha=0.5,\n", " cmap=plt.cm.get_cmap('nipy_spectral', 10))\n", "plt.xlabel('component 1')\n", "plt.ylabel('component 2')\n", "plt.colorbar();" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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", 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" ] }, "metadata": {} } ], "metadata": { "deletable": true, "editable": true, "id": "9HJDS2uq7PCd", "outputId": "571928ae-4be9-4f34-c118-bf907dc63a6a" } }, { "cell_type": "markdown", "source": [ "Recall what these components mean: the full data is a 64-dimensional point cloud, and these points are the projection of each data point along the directions with the largest variance.\n", "Essentially, we have found the optimal stretch and rotation in 64-dimensional space that allows us to see the layout of the digits in two dimensions, and have done this in an unsupervised manner—that is, without reference to the labels." ], "metadata": { "deletable": true, "editable": true, "id": "KP_6BJeN7PCd" } }, { "cell_type": "markdown", "source": [ "### What do the components mean?\n", "\n", "We can go a bit further here, and begin to ask what the reduced dimensions *mean*.\n", "This meaning can be understood in terms of combinations of basis vectors.\n", "For example, each image in the training set is defined by a collection of 64 pixel values, which we will call the vector $x$:\n", "\n", "$$\n", "x = [x_1, x_2, x_3 \\cdots x_{64}]\n", "$$\n", "\n", "One way we can think about this is in terms of a pixel basis.\n", "That is, to construct the image, we multiply each element of the vector by the pixel it describes, and then add the results together to build the image:\n", "\n", "$$\n", "{\\rm image}(x) = x_1 \\cdot{\\rm (pixel~1)} + x_2 \\cdot{\\rm (pixel~2)} + x_3 \\cdot{\\rm (pixel~3)} \\cdots x_{64} \\cdot{\\rm (pixel~64)}\n", "$$\n", "\n", "One way we might imagine reducing the dimension of this data is to zero out all but a few of these basis vectors.\n", "For example, if we use only the first eight pixels, we get an eight-dimensional projection of the data, but it is not very reflective of the whole image: we've thrown out nearly 90% of the pixels!" ], "metadata": { "deletable": true, "editable": true, "id": "VJO8qkRE7PCd" } }, { "cell_type": "code", "execution_count": 17, "source": [ "def plot_pca_components(x, coefficients=None, mean=0, components=None,\n", " imshape=(8, 8), n_components=8, fontsize=12,\n", " show_mean=True):\n", " if coefficients is None:\n", " coefficients = x\n", " \n", " if components is None:\n", " components = np.eye(len(coefficients), len(x))\n", " \n", " mean = np.zeros_like(x) + mean\n", " \n", "\n", " fig = plt.figure(figsize=(1.2 * (5 + n_components), 1.2 * 2))\n", " g = plt.GridSpec(2, 4 + bool(show_mean) + n_components, hspace=0.3)\n", "\n", " def show(i, j, x, title=None):\n", " ax = fig.add_subplot(g[i, j], xticks=[], yticks=[])\n", " ax.imshow(x.reshape(imshape), interpolation='nearest')\n", " if title:\n", " ax.set_title(title, fontsize=fontsize)\n", "\n", " show(slice(2), slice(2), x, \"True\")\n", " \n", " approx = mean.copy()\n", " \n", " counter = 2\n", " if show_mean:\n", " show(0, 2, np.zeros_like(x) + mean, r'$\\mu$')\n", " show(1, 2, approx, r'$1 \\cdot \\mu$')\n", " counter += 1\n", "\n", " for i in range(n_components):\n", " approx = approx + coefficients[i] * components[i]\n", " show(0, i + counter, components[i], r'$c_{0}$'.format(i + 1))\n", " show(1, i + counter, approx,\n", " r\"${0:.2f} \\cdot c_{1}$\".format(coefficients[i], i + 1))\n", " if show_mean or i > 0:\n", " plt.gca().text(0, 1.05, '$+$', ha='right', va='bottom',\n", " transform=plt.gca().transAxes, fontsize=fontsize)\n", "\n", " show(slice(2), slice(-2, None), approx, \"Approx\")\n", " return fig" ], "outputs": [], "metadata": {} }, { "cell_type": "code", "execution_count": 18, "source": [ "from sklearn.datasets import load_digits\n", "\n", "digits = load_digits()\n", "sns.set_style('white')\n", "\n", "fig = plot_pca_components(digits.data[10],\n", " show_mean=False)" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {} } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "The upper row of panels shows the individual pixels, and the lower row shows the cumulative contribution of these pixels to the construction of the image.\n", "Using only eight of the pixel-basis components, we can only construct a small portion of the 64-pixel image.\n", "Were we to continue this sequence and use all 64 pixels, we would recover the original image." ], "metadata": { "deletable": true, "editable": true, "id": "JOsJcKDr7PCe" } }, { "cell_type": "markdown", "source": [ "But the pixel-wise representation is not the only choice of basis. We can also use other basis functions, which each contain some pre-defined contribution from each pixel, and write something like\n", "\n", "$$\n", "image(x) = {\\rm mean} + x_1 \\cdot{\\rm (basis~1)} + x_2 \\cdot{\\rm (basis~2)} + x_3 \\cdot{\\rm (basis~3)} \\cdots\n", "$$\n", "\n", "PCA can be thought of as a process of choosing optimal basis functions, such that adding together just the first few of them is enough to suitably reconstruct the bulk of the elements in the dataset.\n", "The principal components, which act as the low-dimensional representation of our data, are simply the coefficients that multiply each of the elements in this series.\n", "This figure shows a similar depiction of reconstructing this digit using the mean plus the first eight PCA basis functions:" ], "metadata": { "deletable": true, "editable": true, "id": "-CTxffPb7PCe" } }, { "cell_type": "code", "execution_count": 19, "source": [ "pca = PCA(n_components=8)\n", "Xproj = pca.fit_transform(digits.data)\n", "sns.set_style('white')\n", "fig = plot_pca_components(digits.data[10], Xproj[10],\n", " pca.mean_, pca.components_)" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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85MKs6FeJkJdtYFI/1OFPPurpUUgxOGZjq/zljEZ1FdF4Ra4MBkpnqx8tdw5HlNzn3AZ9+2z+5CNFs6CB0YDOJPfNBJu8X4fccsdKg/HAy0OVZ1eMvM/RJuGc878/+5UPk9mwvzk1eR1FbrnvNjTLuSr10j/qRsnnAEu03J5T5tCdS1PMZjQw2AfFqQvFkN8rqyb36wJFHgH1gM6ojR4mgwGdhz99oz4sSDPYt1iTnO/6yfIXHE5Fn/Z2LtXdci6MrgU8UhXvDeBbPnidXnsZXaeLR563OzDVrV6M4mtrH3yanhbwsimvBjevnHPB20Etf8Win4NaPlAWs4b0xnE+f3NIRERERDXPc612Kt+sHFiquFS3eL1IsyUGvCwAzGsZeF3GuEz57qcvfpwh37H3xT/MRQEvm1OWF/iGTTqikxyG1+nigM7bHZjqFmjn9PD2TbJy2dR6QW3bofi2xxfhyPfZeOueiIiI6PzluVbT3VrA18y66havFyY9uGvFhpbAl6+ToP6JhTc5iicYfGEJYowRzPjGs6TRdTqnLSAiIiIiIopQrHJJ1eKq5EvEWK/ZqkIP8jPnrg3Lldu8st9JMZa4QvH7mhByaxrcBr8v+Eo7IS5TapeLl3zURf6ty7SN6ju5K/O3i7EudTuLMVsN3CAud8unnm5XHhRj+39KEmMHzOrvp9qVy4+WKGqiwGzwOxizFrok2To0FmP6QTkX+gm5vw+8WP1Ix+ydcr/6XVEPSRN+o6IhdPlIbVUsxqIGPirGDt70oBibVKx+hH/UZrlIiC1OLrTgEr5pDfIBk0piGsq/dbIfln/b1bS+vM5VherfKm+eJPe7Fy+R3x+T8PspUwiPF7fijkI9i1y8ZMOuhmLsJfMR5TbvLGgqxgZ3OiDGdJfBOckVws7hhcto+/+T8kf5M9G2Vp2PjbvlXFpi5POsW+6uIWFLljew5UG58MlhJIqxu7vnKLf55Efyo3u/yT/bw1XC7wnNQTwCSbUb79ARERERERFFKA7oiIiIiIiIIhQHdERERERERBGKAzoiIiIiIqIIxQEdERERERFRhOKAjoiIiIiIKEJx2gKqFvXNsWJMPyGXVD/Wb6QYM1nUpa9j0uW4S1FWXTeIBVpk26TrMOlVl26oyZNgbr+onRizZsjlxT9du1PZlmZx8rLNHXJ557wamFi+WZN8MVbnL/3E2P4HNoux+fhNuc23LHId9+TkUjFWeKLqe2cKYeVx1wG57HXZb3IZ9tiuaWIs/pZLldvM3y6X8LZFyztnjjI+Msyu0JWlj740UYw5NywTY5327RdjboNj8mw3xctTqXR0y31VmrbApYWug1ibybXPLb0zxVjMz9vklf7jlHKbywrkKU+e/P1iMRYXb9xfQ1mJvaw0Soyt1+qIsbe0vWKsiVmeDgUAEhT9u/h3+TLKHFV1x0Ndld6WJq/QWleeYiJ3pTwdR+7xROU2r2iYK8aikuS+f+pQ1Zjh1A4B+ubHdDH2imJqinmJ8nto7Xe9cpv9v5WPzz5ueWoZcQoYXQc4cwEFgHfoiIiIiIiIIhQHdERERERERBGKAzoiIiIiIqIIxQEdERERERFRhDpvi6LsGtosqOVtY2cEvOyP7Z4MatuXv9c/qOVnfpYc8LIPH/1XUNsmIiIiogufK4gqPWtusga1bWsPuRiVNzlTtga17Yyn5QI6vkif4Qp42X04FtS2JbxDR0REREREFKHO2zt0FNmcirq7+oGDYiyxV4oYM7Vppdxm6YL/iLF6ZrmctW5Q0txLlXO/3eeUS0Q3m9hejE0fs0+MHS07odzmI4kdxVhCeZkYO46q0xaEOB2o01zRPxRt+5dN/lbsSOEJ5TYbt5JPd5Y68h4aTVsQSvv/JZdhLyhNEGPtO8s5LPz4V+U2D52Upw6BfKjAZFCGHQA0LXR1tl25cql1fPGVGOpYt4UYK3Spy/TnmeVS63VT5WWLiqOV6w0FLVbehqVjHzGmt7tZjA1c+oBym8f2yeeOnxVvT8dY43L2bj103x27XPJ7leKS++Gt0c3F2IOXHVBu01JXntYk7yf5+DUqTe8WprqoDot/birGHj8iP80zrtGNyvWOSJGn8ig9KE97o1XzLYRLouVpAoa5GomxvIISMZY4X/3U07t3ytcsWh15+qaD7wnHCmquf9CFhXfoiIiIiIiIIhQHdERERERERBGKAzoiIiIiIqIIxQEdERERERFRhOKAjoiIiIiIKEJxQEdERERERBShOG0BVQuHYrLK8vW/ibHoznJpaa1OXeU2be0biLF6O5zKZavbJTcWibGoXveIsZFrRoix/t/LuQKAA4XyPuchuAlBg2WyyaWtHcv/Lcbez5envDjltCu3mTBULsXuzjksL7hdLmkdCuV2+TSclijXiDdddYMYi97+uXKb16S2EWOtygOfMDUUSn6Vp5CIu0Se0uIlU5wYm2uWzw0AsFGXy9JffyBejJmECuPS3wPxy3z5OD4+Z7QYa9VQnpoi6Qr1R/8D5fLx8M3vcvn3mmAymArA46YM+fzQ9y+DxJil4wTlNt0njoixemOfE2Mnd1d/CXqn/NGCrzU5eEmi/D4+dIV6GoeCvTYx5nbJ9wnqJJcr1xusS+6TrxGa7Zb79Px/NxRjv29WT1szYN7zYszx2WuKJY2nLSAKFO/QERERERERRSgO6IiIiIiIiCIUB3REREREREQRigM6IiIiIiKiCMUBHRERERERUYSq1iqXf6jXLOBlbWNnBLXtonuGB7xs52O/BrXtPU/Klel80bt+EAsfDWrTRERERFQLZCZeFvCyca/8PahtL/3D3wJe9t6TwV2nH3KoKx970whypVdv3JAr9XqjKZblHToiIiIiIqIIxXnoqFoccRSKsZP75G827PnyHHVWxfx1AGBJk+eLqaclKpetbkXZ8nxE0Tu/E2NR17UXY00uVsydBmDb6/JcgL9Gye1Jr4Ep+079Lm8kvntjMaZpOfI6Heo5jkwZ3eX1tjwmx+YuMWhH4N+wnSs5WZ4DLe2JDmJMqy/PI7VpgzyvEgDcEh0lxrr/WZ7rreS/QlsC+GrQrZ/+71xHc+R539JwUoylNpVjf9wVq2zLVKv8Hvwb8iMTV+vGT2PIR55M1zW4UfW43OOS59cbnP8fMXaHrbMYe6Oeeq7BujfL59KW78jzMrp14/OKLvw9ECdK5c+PtVuSxNjgeZ+Ksc/vFjr2/6i6d6/ZfxRjJZNWGqwrdOcOb9pqdcTYmxnyMZEwZ65yvUe6PCrGjhfLfeeSxKrnaMWUtSINgGbQpVw5x8Vl1q2Sj+MOmnz8H/VyJ6boPnkeWdUcgYB6fjsif/EOHRERERERUYTigI6IiIiIiChCcUBHREREREQUoTigIyIiIiIiilAc0BEREREREUUoDuiIiIiIiIgiFKctoGpx8FSeGItrkCrGYvvLZdrhcCi36T6SK8ZiFGWzo8xVDwOzKXRltgFg1RG5jPzeoV+IsXvi8sVYdIx6foE3zGYx1sGULMbSIS8XKvk5cin2hOREMXZfotw/kuqqv58yp7cRY/b/LBNjRiXXdYPy8oFKaG4XY1F/fECMOX9eK8ZSrKeU23xwhFXe5p//T4zZdz5ivIwdgDzzg1/MJrmse3xbeboFUz25RLtjl/r9Ou40nn4AAHZFJ4ix9nbjj9AyUyATFxhrHS3XPs9s0E6M1dfk91jzcqyUbZSnB4mNkfNssRhPh2B2uwD16dtnZsWUIf8yyVNXdN8SLcZuy/uPcpt/bXSDGOtzpTwdiiVmeZW/mZ1uQFnO3j+lefL7nO6U3+fYXvKE0rpTPicBQN168vmlaW/5/XHkVD0ubHb/86ED0A02U7RZbneORT53FJjl2N3tDyjbsmaDPM1OgVnO/zXWAsO/O+EG5OYQiXiHjoiIiIiIKEJxQEdERERERBShOKAjIiIiIiKKUBzQERERERERRSgO6IiIiIiIiCIUB3REREREREQRqlqnLThadqI6V6/09LaUIJb+NahtH8+VyzrXFifL5bLGWzbLJfxveM+4LDoA6OUlym3m9HlSjK0zrqYNALCYqpbpV1QbDohTUTX95SPfirF1Ka3F2JBCOY8A0MwivwfJbnlqglMGUzaUaaGdxqG4VC61/f5kuYb1n+vI0zg0fUkuHw4Aji/niLGcN/eLMafLVuVvrhDnQ+L44m0xpufJU4O0/kcn5Xqjrr9djKmmQzDFGvcbzSyXKhfXpRl/oxgVJR+slpu7ySs0mH7E42/vfa5sy9bje8XYwIYXiTE7jKcOcQTwXamm6TAZlORPSikVl1nUSl7fqX3ycuVb1O/X/m2JYiw2Rp5/wBpn/N5FuVxAmXKTPmuQIk9N8JejiWJMiy0XYwvr36jcZr/JF4sx15fviTHdYPYKo78FI7qOPH3Nlcfl6ThO/Usux699/aBymwntqp4TPSy9e8rr/e9/q/wtqsQO/HpcuT1fuV3yeXnwPPnccWLC+2Js/uYmym1Os28XY8PrtBVjLpfxOcKl1ex9lo7u2ICX1U/Jx6IvfooO/HO0OdKC2nbx6n1BLX+RW90vVHSjOTd8X1gM8Q4dERERERFRhOKAjoiIiIiIKEJxQEdERERERBShOKAjIiIiIiKKUBzQERERERERRahqrXJJFy6X63Q1M4vZuEqR2aBSokeeSa42lnP4qBjT7XLVNgA4osvVvlRVJs0Ghfs8f/Pspzee1xVpdsN4qaIqosUix5yavE+FkPMIAGVCWwCgGIr2GLT15P/W5W8+8jTjingORT4KNXm/jkKusGfO91Jxq0SuknpUl9dbbFB1zLNfvuTD85pjwmuj5LcJthNym/UiuWygViBXtwMAi+I4cx4vFGP2cuP+eMx+et/8yYfUN2IU77FVtV+KKpduTd0u1TFYrOiPeSbjfBT4cbx4XpMrnL8sbnkdJxWngDKXXE7RaldXWcsV3hsAsCnen1KX8T7kuvzvH7nCfjsVVd6Om+SDyaw4xgsU7zEAHCpQVFgulj+XTjqr5uOYH7k4+3W5Pr7+bLmKz4BYu/zZoslFkAEA5jI5l5Z8uUqxu6Rqe46W+n+sHBeqy9rc8j7Z8+TzWpHQbwGgyEvfgEk+zlTnjmPCcZQH3z9biM7GAR0FJDc3FwCQ3jjO72XHIlsODhoeaJPUFJV5G8TKJfRzc3Nx0UVy2fKzXwcA8+N+8btpTWJjxNgxHBJjbyli3vwQ4HL+5mNctFwaO+Re+rB61qvo4r7kw5OLRwsKjF+gqtj92iovjQvUkmpZqz/5eD5WnipC9I8AlgGAeHW4Wbw81cwnkMuSfyJXbwfgXz6edhwzfoFiwI9t6u2L5Nk/TosJsIy8l/X6k4/HSwNoQ0KA58T4g8rwtFflPhAof8+lj56UpykR1RH6FADIM3UEZ/2igBbzp2/8FUeMX6D6znesPG2NUkyuMhwtf3xjmeLcsczLZn3tH0QeHNBRQNq2bYuFCxciJSUFZqNbXBHO5XIhNzcXbdvK88icjfmojPk440LPBcB8nIv5qIz5OIPn0srYNyrzt38QeXBARwGx2WzIyMgIdzOqlT/fjp2djwULFuDTTz/Frl278Kc//QmTJ0+ueJ0qdja73Y5x48bhv//9L06cOIGLLroIjz/+OK6//nqf4tWhOvIBACtXrsTMmTNx+PBh1K9fH5MnTxb71p49ezB+/Hj89NNPSE5OxjPPPIOePXue1/nw5VhR5ejEiRMYM2YMvvvuOyQlJeGJJ55A3759xXWpXt++fftKry0rK8OQIUPwt7/9zad9UQlVPqT3+Fze9mXYsGHYunUrLJbTH3OpqalYtaq67nhWFcr+cTZ/90t1fB08eBDjx4/H1q1bYbVakZmZidGjR1esO5SqKx/+7IO3c5G/x1qgAj2X+uKpp57CunXrUFpaipSUFNx3330YNGhQQK+tqWOouvqGP+c7Vd+o6c8X3pmjQHBAR2Hn6yAnUqSmpuKhhx7C2rVrUV5e7nPsbE6nEw0bNsT8+fPRqFEjfP311/h//+//Yfny5UhPT/caP5+o9vm7777D1KlT8corr+CKK66oeKTGiNPpxEMPPYQ77rgDc+fOxYYNGzBy5EgsWbIEaWlpEZMPI6ocTZgwAVFRUfjuu++QnZ2NESNGoHXr1mjZsqXhulSv37JlS8XrSktLcc0116BXr17Vum/+UL3HzZs3r/RaX/bl//7v/8SL2Ujm6355O77Gjx+PevXq4dtvv0VRURHuueceLFq0CHfddVd1NT3k/NkHb+dff4+189GIESMwadIkWK1W7NmzB3fddRfatGljeMfHl9dG8jHkz/lO1Tci6fOWai9WuaSw85xIBw4cGO6mhMTNN9+MHj16IDEx0a/Y2WJjY/HII48gPT0dJpMJN954I9LT0/HTTz/5FPfVihUrkJWVhY4dO6JHjx5Yv369X8v7QrXPM2bMwEMPPYR27drBZDIhLS0NaWlphuvZu3cvjh07hrvvvhtmsxldu3ZFhw4dsHTp0ojKhxEpR6WlpVi9ejUee+wxxMXFISMjA927d8fSpUsN1+PP61etWoXk5GS/77RXZ45U77FKoPviTbj6Q6h4O74OHjyI3r17Izo6GikpKejWrRt+/fVXv7YR7hz5sw+qc5G/x5ok3Plo2bIlrNbTvwvXNA2apmH/fuPfnvrz2kCFOx8e3s4Rqr4R6Z8vVDvwDh2F3c033wwA2L59O44elavvSWbNmoUjR45g/PjxAIDCwkJcffXV2Lx5M6Kjo0PaVuD0RRIAPPLIIyFft+T48ePYt28fLrnkkoDiRubMmYNPPvkEU6ZMQZs2bbB7927Exflf5CbQfLhcLuzYsQPdu3dHz549UV5ejh49euCZZ56BzVa12oRuUN1O13Xs3r27yt8jMR9G9u3bB5PJVOnuVOvWrbFx48agX79kyRL0798fmqLi6Ln8zZG/ufDnPT6btC8vv/wypk6diubNm+Pxxx9H586dfWoHELr+cLZQ9Q1f9suX4+uuu+7CypUr0alTJxQVFWHt2rV47LHHfG5HsDkKRT6C3QcPf481I+dDPgBg3LhxWLJkCcrKynDZZZcpHw309tpwHkOhPJcGcr6ThPPzhUjCO3QU8Xbt2oU2bdpU/Ds7OxvNmzevlsFcODgcDjz11FMYMGAALr74Yr/jd999d8UHo0d+fj5mzpyJl19+GZdffjlMJhNatWqFunXr4tZbb0X79u2xa9euatsn4PSHosPhwJdffomFCxfis88+w88//4xZs2YZvr5FixZITk7G22+/DYfDgW+//RYbN25EWVnl8v2hzEd6ejq2bNmC22+/HUOHDsUTTzwBh0Mu2R1qpaWliI+vXKIxPj4eJcIUDL6+/tChQ9i4cSP69+9vuB5/c3T8+HHccccdGDp0KO666y4cO6aorqfg63vsy7489dRT+Oc//4m1a9fi9ttvx4MPPmh498HffQVOf9PepUuXgPYxWL7uly/HV6dOnfDrr7+iY8eOuO6669C2bVv06NGjyrr8yREAdOnSBcOGDcOwYcOQn++tpGZwfN0Hb/w51vztM+vXr8ef//xnDBs2DF999ZXfbfPXuHHjsHnzZixcuBA9e/asuAvn72ur4xg6cuRIRd/IzMzEpEmTQrfjAm/nO3+E8vOlUaNGGDVqFIYMGYLBgwdjz549QbePai8O6CgiGJ0kPc4d0O3cubPiwiLSud1uPPPMM4iKijL8Ibe3OABkZWVVufj8/vvvcemll6J169aV/m6z2TB79mxkZmaGbicEnrsEw4YNQ2pqKpKTkzF8+HB8/fXXhq+PiorCa6+9hq+//hrdunXD3Llz0atXr0qPkIU6HwDQqFEjvPvuu1iwYAGaNGmCNWvW+LyPw4YNQ6tWrQz/Gzx4sNflY2NjUVxcee614uJi8ZtdX1//2WefoWPHjmjSpInhevzNUVJSEhYtWoQFCxagf//++Pjjj73umxFf3uNzSfty5ZVXok6dOrBarRgwYAA6dOhg2Lf83Ve3241Vq1ahYcOGAe2jxNe+4ut+eTu+3G437r33XvTs2RNbt27FunXrUFhYiL///e9V1uVvjjp16oT58+dj/vz5SE5OrrZ8+LMP3vhzrPmTj/LycsydOxdvvfUW5s+fb1jgxxf+nkvMZjMyMjJw5MgRLF68WLlu6bXVcQxlZGRU9I327dsHNPj2Nxfezne+CvXnS3Z2Nux2OxYtWoQnn3wS8+bNC6p9VLtV6yOXveu28f4iIh9kZWUZXkDZ7Xbs378fl156acXfdu7cWWmAF6l0XceYMWNw/PhxvPXWW4iKivIr7tGvX78qfyssLERCQkKVv0dFRQV8AeavunXrokGDBn49AtO6dWssWLCg4t933HFHxbeu1ZEPAJUGE2azGSaT79+DzZ8/3+fXGmnWrBlcLhf27duHZs2aATjdv6VHfXx9/dKlS3H//feL2/U3R2eXEC8pKQmqiITqPTbibV88NE0zfKTT331dvnw5MjMzMWdOgPNaCQLtK9J+eTu+Tpw4gcOHD2Po0KGwWq2wWq0YOHAgpk2bhmeeeabSa/3N0ebNmzFkyBBkZGTg8ccfD+gxN1/y4c8+eOPPseZPPjyP/o8cORI2mw3jxo1DSkqKX20DAu8fLpfL59/FeXttqI4h4PSdrm3btgV0h87fXPh6jlCpjs+XBg0awGQyQdd1FBYWIikpKag2BiJBnhfdK9ePvn+5aaSuO/DHXy+21g9q20d/C2LHAZQH/+RuyPEOHUWEfv364aqrrqry9z179iAtLQ0xMadn99R1HRs2bDD81jgYI0aMQEZGBjIyMjB79mzMnj274t8jRoyo9Fqn04ny8nK43W64XC6Ul5fD6XR6jZ1r7Nix2LNnD9544w3D35R5i6u0adMGP/zwA3bu3Ald17Fv3z6/HvcIVT6ysrIwf/585OXlobCwEO+++y5uuOEGcbs7d+5EeXk5Tp06hXfeeQfHjh1DVlZWjeTjwIED+Oabbwzb508+jEg5io2NRc+ePTF9+nSUlpbihx9+wJo1a3DLLbcYrseX12/evBlHjx71u7qltxxlZ2dj0KBBePnll/Hss88GnAvVe3wuaV88v6Xy5HHZsmXYtGkTunXrFtS+ulwufPHFF+jTp49P6wGC7xvB7Jfq+EpOTkZ6ejoWL14Mp9OJoqIiLFmyxOenG6QcpaamYvXq1Vi4cCHy8vKwevXqasuHv/ugOhf5e6z5mo+8vDzs378fs2bNwm233VblSZNQ5iMvLw8rV65ESUkJXC4X1q5di5UrVxo+HuzttdV1DHl8//336Nq1a5UvyEKZD8D38523z+bq+HxJSkqC1WpFr169MHHiRAwZMsTv/SPyYFEUCjun0wmXy1XpRGo2m32aC+mXX36p+MBMTU3FrFmzkJOTg8aNG4e0jW+++WbF/3v7ofasWbMwc+bMin8vW7YMDz/8MB555BFlDADuu+8+ZGRkoG/fvvjggw9gtVorfYCOHz8e/fr1Q05OjjLuTYcOHTBy5EiMGDECRUVFaNy4MV566SUfsxG6fDz00EMoKChAZmYmoqOj0bt3b4wcObLitZ58PPjggwBOf9P68ccfw+l0omPHjpg7dy6sVmu156O4uBijRo3ClClTDH+P4k8+/M3R2LFjMXr0aFx99dVITEzEuHHjKt0BOzdH3l7/2WefoWfPnqhTp47P7QO856hNmzb46KOP8Pnnn2PdunWYMGFCQLmQ3mOjfZX2xel0Ytq0adi7dy/MZjNatGiB1157DS1atAhqX5ctW4bevXv7dZc22L5xNm/7dW5+vB1fM2fOxKRJk/DWW2/BZDKhc+fOGD16tE9tkXLkuVMGnC54tXXr1kqPcIcyH9724dx8eDv/ejt2AslHfHw8OnToAKvViq5du2L27NmVlgtlPjRNw+LFizF27Fi43W40btwYo0ePrnis8ex8eHttdR1DHl9++aXhFzWh7h/SOcKfvlFdny/ffvstdF3HqlWrsH37dkyePBnTpk0LeF+pdtN0o/vnOF0K+KabbsK+/cVwOg1f4tWfG3UNuGFvbpoS8LIAMCLDv8ctzvbuof8Gte31qZ2CWj4YnY9tCHhZi0VDs6Z1sGbNmhqdW2XGjBmVTqQAKn3IqkyZMgUHDx7EL7/8gtLSUjzwwAN499130bFjR78GKP62F6jZKpc1bdSoUbjnnnsqPcoqudDz4Zkbbfjw4eja1fs57ULPhxG73V5xEb927Vp8++23+Otf/3rB5eLvf/87srOzoWkatm7digEDBuC5557zefkLLR9GiouLKy6eX375ZVx88cXiI7O1IR8FBQV4/PHHMXfuXGzbtg3vv/8+XnzxRcPX1oZ8AKcftxwwYACWLVum/HLkQs/H119/jXXr1uHZZ5/FwYMHMXbsWLzzzjs+L++5Ti89boEe4OOLE2LbBbQcAAx+o733Fym8+dAW7y8SrNWKgtr2WFNwj1x+5U4MeNlXTm4NeFnNpCO2vtPwOp136CjsHnnkkYBP2Lt27cKgQYMwffr0ir8NGzYsVE2rle6//35kZ2fjt99+w+233y4+7lZbrFixAj/++CNef/11vP766xg8eLBfj9zVBj/99BOmTp0Kk8mE6OjoGqlcFw5PP/10xf9nZWX5NZirLTZs2ICZM2fCZrMhPT09oCkELiRJSUno2bMnhg4dCpPJdMEeG/74/vvv0aVLF7/udF+IrrnmGixZsgRDhw6F3W7HqFGjwt0kimC8Q2eAd+hq9g5dMK677jrMmTPHr/lgiIiIiCIZ79AF7kK8Q1e7vx6hiFZYWIj8/HxcdNFF4W4KEREREVFY8JFLilh169bFjh07wt0MIiIiIqKw4YCOAlJWVoYdO3YgJSWl0hxUFwqXy4Xc3Fy0bdvWpxLFzEdlzMcZF3ouAObjXMxHZczHGTyXVsa+UZm//YPIgwM6CsiOHTtw5513hrsZ1W7hwoXIyMjw+jrmozLm44zakguA+TgX81EZ83EGz6WVsW9U5mv/IPLggI4CkpKSAgA4mFMCp6tq0RyrOUpcdlp8RzHWfflIMebN1r7Txdho/ZAY21d0tMrfzGYNjRvFVOynN97yYdLkn6teW1+eBP21P8vb15o1V7bp3Qm/iLFFp3aLsUPF+VX+FnA+DpXCZZAPoRYTAKBVolyQ58Ob4sSYFhetbNODn5eLsQ358qTqLt1V5W9ms4b0RrE+5cPzmtyjdriqrgoOt8Ef/yfJJs8V92m6vO3k/uqiRovm2sXYh47fxNjh0hOGfzeZgXopZr/yYTlZB5ru38+4L4tOE2MTrisVY+Ymqcr1rp8j941PouXYPnuB4d/dmgtldQr9yoerMBpwV82HS5d/vN86tqEYm35XPTGmeSl6tXr8XjH2scV4nwHgsL3Q8O+65oaeUBKSfKi0i5XnH530J7lohKlpI+V6P50h7/MSvernh0e+o9hgY24g4ZTf59Lokwkw6VXvSrkhn0vbRzcQY2P+6BBjpoubKdv01dRjYuxjywkxlu8sqfK3QI6VU/lmwyIgqmMlzZYoxua1lPtZXKbxJPUeP844Lsb+YZYLd+SU5RkHTDqikxw+9w8iDw7oKCCexx2cLt2wCqrqYYhkXb7wbtxAfeGlclCvOuGzh6a4MFBVcfX1sQ5v+TBp8jaidHnw2yhefuRCS45XtilekWfVhVIo8+ES8qEa0BldtHg0ssmnLC1WziMAWBQf9kaDTg+nO7h8nMkFDAd0Rl8AeKgqlzUwybmor+g3AJCgy+vV3PI+KcaeAPzLh6ablNsyEq04xhvZ5AtUs5d8JCsKnkUH2FcB//IBt8n4uFQUmbYGeu5IUk8qn6Q4d6jOV+J51nR6N0KSDwVl/4hTDOjqxirXW1dXfFmgKy6jFO3391xq0s1Cf5M7SIwqH7GB5yPQ/qE6XvzpG7pbMzw36orzmmrbDS1yrE5CjLJNOW45xxbFOVo6t3v+eqE+UkrVh1UuiYiIiIiIIhQHdERERERERBGKAzoiIiIiIqIIxQEdERERERFRhKrWoihfFGZX5+qVGkBd8U4lNS4xqG23GiBXkPPFoKWKX8FHiKuSLxFjvWZfJS9okd8314blym1e2e+kGEtcIVdHrAkJ0fKPzGcmycUcrMPHiLHyfzyj3GYzh5zLOubwzm8TbZF/SL68idy2qLvvEmMH7lug3ObVZrnq3+YoeZtF5VULImiQf3zvL5ei0sjyOPk4SnnqD2Js39jNym1e45LzvywqQYwd0qpWQAUAU+jSgShNLgbwWmbVKnkelqvbibF1z8pVGwGgWby83rqO8J47TJqc3IVD5X5r6tRNjO0f8aFym5ldT4mxL36Qj6P9MK7cp6squ/hJlY83b1MUMMr8oxgre1197rjjZrnQxz//KRenytOqfibpmhbCbAAmxblo6m2KQkHXXC3GTr23UrnNPgPkz7OVK+UiIrmQP6NDQVXlcs1N8jnP2kO+JsmZslW5zYyn5Yqx6TPkc/s+yJVC/aVpGqA4LlR+jnIGvuEGzQJfFoBD2xLwsldBXRTOm2Z9jD/LfLX38+Cu86sD79ARERERERFFKA7oiIiIiIiIIhQHdERERERERBGKAzoiIiIiIqIIxQEdERERERFRhOKAjoiIiIiIKEJV67QFVHvVN8tljfUTxqWtAeBYv5FizGRRF3uOSZfjLkWhaKOS2qGeOKJJXH0xlvaIXH6+bPwjYmzBZ8nKbTZWlMOPU0xbUBP56JDcQoylzBstxo4OfVGM9T6uLkM8Jlp+D66s20yMrT32s3K9wcpIaSnGLnt/kBjLHiyXns8s3KPc5pbWjcVY22Mp8nL6b8aBEHaQa21yGfDoUU+KsfnXThdjI/K/U25zV2pbMdbcLpc7Xy+USXdDLp/ur2vimosx66MviLEZnZ4XY88c3qbcZuFAuaT9lZvkc8c6qWy87g7ZRB/Xxsr5iH7mJTH2fdtnxdijKFdu8/uHGomxjoo926YbHBhGfwtCF5t8LEc9PEqM/dB5ohj7q1mepgEAVt4rT21yhS4vW71nUiAz8TIxFvfK38XY0j/8TYzde/JX5TYPORqIsUaQjxW3cNIM7aQWVJvwDh0REREREVGE4oCOiIiIiIgoQnFAR0REREREFKE4oCMiIiIiIopQHNARERERERFFKA7oiIiIiIiIIhSnLaBq4VSU7dYPHBRjib3kkummNq2U2yxd8B8xVs9cR26PQRnpEFeWxmXRaWJMa9FajJV9vEmM3ZzkVG6zuChajDXQw5uPrhY5H+ZUuSz5N0flEtFXxspTZQBAJ0uBGNvgqitvs5qncegbJZfpt7TqKsa+xpdi7KakNsptJvaJEWMt3zGLMacwFYZZAwB5OX9cVyavxxRfT4zttsjTdNyYJk9LAAApneVYqxWKKU+EA0PXQtdDMh3ye6WZ5Y/wf+nyNB6dU9TnUlNTuRR+V/sBMTZLOlHoeoh6B9DdIZ/XIE2bAGCxTZ5eIMquvhTSHfK5tku5/F6/bdQe3R2yXADAdeXyNAGmWPm8tsUiny8TTXb1RssdYqiLXT4OFxueS0N3rHR0K6ZLOnVSjP0ULfeN5pA/qwCgePU+MXaRu4ncHsWxQhQI3qEjIiIiIiKKUNV6h+5YyYmAl7W/I0+K6osxI+XJYL158jt5AmJf2H8vDmr5r46oJ7IkIiIiIgrGv8vlJ6a8cX/+SVDbHtLocMDLmqKCu5PpyAlu+S+LjwS8bLlLvsPtjQmAdB+ad+iIiIiIiIgiFAd0REREREREEYoDOiIiIiIiogjFAR0REREREVGE4rQFVC0civLR5et/E2PRneWS9VoduQQzANjayyXt6+1Ql/ivbk1gk4OOcjEUd1snORYnTz0AAI7V34kx2xr1stWtmUtRGn/bGjEWrSjpfKc9XrnNFmNSxVjLF44rl61OzRW/j3ZuWiHGik1yLvrb45TbtPS7TYylvPmhctnqlqTLCXFu/UqMtVD0qRaQ33sAsHSW47blh8SYWyi5HspS7K1NcpEt3SmXlx/oThZjxV7q5mvNLhFjtij5/I0aOM22RIkYcx38WYzZNEX/iJJzBQB6SZkYc6rO7TXgEpOcD3e+3HdV3+bX1dRF5XS76o0OvCBdsBLkyw64fpQ/V+q65WkLLraqi+Qd/U1xrSOvlijkeIeOiIiIiIgoQnFAR0REREREFKE4oCMiIiIiIopQHNARERERERFFKA7oiIiIiIiIIhQHdERERERERBGKAzoiIiIiIqIIxXnoqFoccRSKsZP75Hl77PnyHEdWxfx1AGBJixFj9bRE5bLVbad+Uoy5t/4gxvQyeY46TVNPcmPPkZd16rHKZavbenOpGBueK8+ddMQifwdVoJiXDQB6JySIsTblR8SYhqp5NvqbN5qmwegtWxslzyV2y9q1Ymy/YlsNTOq5sfQTuWKs3CTvm9TnvHRF42WgwWSQx7U2eR6rTmv/LcYKTPLHWRMv86PpR46JsRyLvF6T03jH3QH0D8laTZ5f8fLc38VYXZc8P5bby3e57uztYmyXUz3fY6iYNM2wY/1gkufQvMImH+NtHfL7eLVbPW+juUWiGPvGdkJeUJ4iLmS2Qs7HH8zyPscoTpedXerPB3MzeZsbrPK8iW571Y1KczmqaELf+DlKcaA3aCaGHNoWMXYV1P29WZ98Mbb3c/ncThRqvENHREREREQUoc7bO3SXTN4Q1PI7rq0f8LIxt10b1LazRm8OankiIiIiIm90XYfu/41OAMChU/IdRm+ufyO4JxHWZEYHvKy5ab2gtj3uveDavq9wd8DLRlvkp1C8MbuBRBjnjXfoiIiIiIiIIhQHdERERERERBGKAzoiIiIiIqIIxQEdERERERFRhDpvi6JQZDt4Kk+MxTVIFWOx/TvIK3U4lNt0H5FLscfo8g9gowxKO5sVpdsDsbbgFzG2c6ZZjLV5trG8Ui+14o/9Kk8dofr9dE3k48sTP4uxUwuPi7Fb6keJMWsdl3qjpQ3F0F6rfCo0m6p+72UKpE6/YFmRnIvb3rlMjGVB7jcdr1BNagC4vvpCjK22yOXudeGX94H+IN/IV87DYuyOD+Qfkw+QZy1BQmqZcpuFX8jv5yqzXArf4TDuc7ou59Bfi10HxNjwaS+Lse7XyefL8qPqN6z0Szn+UVSiGHPahWNQdyt6q38+xFExdteSOWKsfzv5mIjp1ly5TccPu8TYwhL5s87prpoPDXrIcgEAS00FYmzwMjkfmS0OirG4y9XTnjh+kI/Rt8uKxJjb6ERhCt2x8u9yeZ/cn38ixoY0kvfHFKU+Vhw5cvzLYnk6nHKX8fFpAhDeSYUoUvEOHRERERERUYTigI6IiIiIiChCcUBHREREREQUoTigIyIiIiIiilAc0BEREREREUUoDuiIiIiIiIgiFKctoGpxsvyUGNuyWS4ff8N7j4gxvbxEuc2cPk+KsXWKivYWU9Ui0uYQf9WhyscLirLNC9xyTLuklXKb2SVyOetd+m/KZatbXqlc2vqGDYli7L931xdj1sdfVG7zWL+RYmyu0y7GjEptB9I9dF03LO+ff+qkuMxg9w4x9vMNiuk/HhyobMvK4evF2KqSTWLMqAw7AOgBTOOgQ4fbYAKNQmepuMyLZUlibOZweUoDnCpXtmX8+9FibFNJthgza1JPCF2Z/mPl8vQj9/yzqRibP+ZyMWYtlI8/AHjhNXmah28LtyiXNWIy65AzbMyt64bzYRwok6cJGDk7XozNeqSlvDGz+t26/19xYmxfoTztSL3YqlNemOB/LlRyHCfE2KjpdcTY5PubyCs1mKrlbA+8IfefXQXy8dKwTnKVv2km3e8y/dK59NCpfHGZ69+Qz1FrMuV3xNy0nrIt496T17uvcLcYi7YYn6/MbiAxpD2EagveoSMiIiIiIopQHNARERERERFFKPGRS5fr9KM1FrP/j9KEgmYyuJ/uh8MOxTN2XthOqB/t88ahOYJa3mIJT84977XnvSciIiKi84/nWi2Y62XN6NlVH7m14K4VD5U5A17WXKJ+jN6bUgR3nR3MdbqXJ7x9WtboOl0c0OXm5gIA0hvLz45XL/m3Q74Y+NvxwBee+UVQ20ZMcIs3ayo/914TcnNzcdFFF4W1DURERERkzHOdHpMcni/hSyD/ntUX/f3/Oe4ZWw4Hte1gf6Z4Pl6niwO6tm3bYuHChUhJSYE5mOEkRQyXy4Xc3Fy0bds23E0hIiIiIgGv02sf1XW6OKCz2WzIyMio1obR+cfXO3PeHsk1m+Tb0Xkm+VZ5zuGjYky3y9XvAOCILt++dyrujhudB1W3tY14y4dJUQXQrnhE91CRXB0T+epKdQWanGfVoxJmg30w+/k4rud1RusCDIvXnYmZ5G0cKpGrUUYp+g4A5Lnl/qHKh9GjFf7k40wujOOqCpEms5yow3Z5f2x5gfcNg6KvFcxu4XgPIB+65vb7V9xlmvz+HypWdKoyeTkAKFU9PaOoQis+tfO/ZfzJh7gdXd6+8txRKJ8v9ZNyFUsAKFH2D/8f0fI8EhaSfCiUq/qHap9VnR6AXbFe1aNXRrnyFEb191wayONtpyC/j8rjxUvVWlWeVfkwejQwkL4hPWKoenxQlT/Vo3/eHu1TPbqnyoX0eeDPtQev02sn6Tqd0xZQQIJ5JHcs5LLGGDQ80CapKeoiN4iVy537+vhpMPnYDXkKgT8uUE0vsE694qoVs32SnmATY37no5G/BakBB+TBSN+vFAOVr+73e1sV5GrnaBIvP0PtSz48uUhJU5TVF8kXKAP3Kh4rf36BerWKvpGcIF+EJEPuG4B/+XDGFytfZ2SLqm8s93t1Zygev7EG8WiOP/kw1zW+cFQNNXZhrxj74ztyzCvFPiekBL7aUORDZSvkMvF/et/v1Z2h6PaBPnrl77m0PF79JY2RtZCnrln7qd+rO0PRP9T5kAdO/vSNQB4xVD0eqHz0z9ujfQHnQo0/fSF/aboexC8iqdYqKyvDjh07Lthb/Wff1rbZ1BexAPNxLubjjAs9FwDzcS7mozLm4wyeSytj36jM3/5B5MEBHRERERERUYTiPHREREREREQRigM6IiIiIiKiCMUBHRERERERUYTigI6IiIiIiChC/X+ZxdVW2Gm1fQAAAABJRU5ErkJggg==", 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" ] }, "metadata": {} } ], "metadata": {} }, { "cell_type": "markdown", "source": [ "Unlike the pixel basis, the PCA basis allows us to recover the salient features of the input image with just a mean plus eight components!\n", "The amount of each pixel in each component is the corollary of the orientation of the vector in our two-dimensional example.\n", "This is the sense in which PCA provides a low-dimensional representation of the data: it discovers a set of basis functions that are more efficient than the native pixel-basis of the input data." ], "metadata": { "deletable": true, "editable": true, "id": "uH8Hi7hE7PCe" } }, { "cell_type": "markdown", "source": [ "### Choosing the number of components\n", "\n", "A vital part of using PCA in practice is the ability to estimate how many components are needed to describe the data.\n", "This can be determined by looking at the cumulative *explained variance ratio* as a function of the number of components:" ], "metadata": { "deletable": true, "editable": true, "id": "QAjsQ7jm7PCe" } }, { "cell_type": "code", "execution_count": 20, "source": [ "pca = PCA().fit(digits.data)\n", "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n", "plt.xlabel('number of components')\n", "plt.ylabel('cumulative explained variance');" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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", 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" ] }, "metadata": {} } ], "metadata": { "deletable": true, "editable": true, "id": "t78SPHAM7PCf", "outputId": "75d6f4e7-f604-45a6-e955-2306c92cd2d5" } }, { "cell_type": "markdown", "source": [ "This curve quantifies how much of the total, 64-dimensional variance is contained within the first $N$ components.\n", "For example, we see that with the digits the first 10 components contain approximately 75% of the variance, while you need around 50 components to describe close to 100% of the variance.\n", "\n", "Here we see that our two-dimensional projection loses a lot of information (as measured by the explained variance) and that we'd need about 20 components to retain 90% of the variance. Looking at this plot for a high-dimensional dataset can help you understand the level of redundancy present in multiple observations." ], "metadata": { "deletable": true, "editable": true, "id": "5FttCFzh7PCf" } }, { "cell_type": "markdown", "source": [ "## PCA as Noise Filtering\n", "\n", "PCA can also be used as a filtering approach for noisy data.\n", "The idea is this: any components with variance much larger than the effect of the noise should be relatively unaffected by the noise.\n", "So if you reconstruct the data using just the largest subset of principal components, you should be preferentially keeping the signal and throwing out the noise.\n", "\n", "Let's see how this looks with the digits data.\n", "First we will plot several of the input noise-free data:" ], "metadata": { "deletable": true, "editable": true, "id": "RsdcBWrb7PCf" } }, { "cell_type": "code", "execution_count": 21, "source": [ "def plot_digits(data):\n", " fig, axes = plt.subplots(4, 10, figsize=(10, 4),\n", " subplot_kw={'xticks':[], 'yticks':[]},\n", " gridspec_kw=dict(hspace=0.1, wspace=0.1))\n", " for i, ax in enumerate(axes.flat):\n", " ax.imshow(data[i].reshape(8, 8),\n", " cmap='binary', interpolation='nearest',\n", " clim=(0, 16))\n", "plot_digits(digits.data)" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {} } ], "metadata": { "deletable": true, "editable": true, "id": "BZlNFUiL7PCf", "outputId": "bce4b343-f67d-4c21-fbea-450a0f36101c" } }, { "cell_type": "markdown", "source": [ "Now lets add some random noise to create a noisy dataset, and re-plot it:" ], "metadata": { "deletable": true, "editable": true, "id": "Bb9QKgWz7PCh" } }, { "cell_type": "code", "execution_count": 22, "source": [ "np.random.seed(42)\n", "noisy = np.random.normal(digits.data, 4)\n", "plot_digits(noisy)" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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", 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" ] }, "metadata": {} } ], "metadata": { "deletable": true, "editable": true, "id": "PXi1OzNh7PCh", "outputId": "d99244ac-b6b9-45cc-dbcf-752769882b67" } }, { "cell_type": "markdown", "source": [ "It's clear by eye that the images are noisy, and contain spurious pixels.\n", "Let's train a PCA on the noisy data, requesting that the projection preserve 50% of the variance:" ], "metadata": { "deletable": true, "editable": true, "id": "ScydKTGO7PCh" } }, { "cell_type": "code", "execution_count": 23, "source": [ "pca = PCA(0.50).fit(noisy)\n", "pca.n_components_" ], "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "12" ] }, "metadata": {}, "execution_count": 23 } ], "metadata": { "deletable": true, "editable": true, "id": "XktLcP9h7PCi", "outputId": "26a26399-6ffe-4851-d872-cf2d77b89724" } }, { "cell_type": "markdown", "source": [ "Here 50% of the variance amounts to 12 principal components.\n", "Now we compute these components, and then use the inverse of the transform to reconstruct the filtered digits:" ], "metadata": { "deletable": true, "editable": true, "id": "tkxs4lud7PCi" } }, { "cell_type": "code", "execution_count": 24, "source": [ "components = pca.transform(noisy)\n", "filtered = pca.inverse_transform(components)\n", "plot_digits(filtered)" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {} } ], "metadata": { "deletable": true, "editable": true, "id": "ehWep0IR7PCi", "outputId": "d8cf066a-5932-497e-97dc-0c08cfcb74e4" } }, { "cell_type": "markdown", "source": [ "This signal preserving/noise filtering property makes PCA a very useful feature selection routine—for example, rather than training a classifier on very high-dimensional data, you might instead train the classifier on the lower-dimensional representation, which will automatically serve to filter out random noise in the inputs." ], "metadata": { "deletable": true, "editable": true, "id": "6BklBbnl7PCi" } }, { "cell_type": "markdown", "source": [ "## Example: Eigenfaces\n", "\n", "Labeled Faces in the Wild dataset made available through Scikit-Learn:" ], "metadata": { "deletable": true, "editable": true, "id": "zT6PdQ247PCi" } }, { "cell_type": "code", "execution_count": 25, "source": [ "from sklearn.datasets import fetch_lfw_people\n", "faces = fetch_lfw_people(min_faces_per_person=60)\n", "print(faces.target_names)\n", "print(faces.images.shape)" ], "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "['Ariel Sharon' 'Colin Powell' 'Donald Rumsfeld' 'George W Bush'\n", " 'Gerhard Schroeder' 'Hugo Chavez' 'Junichiro Koizumi' 'Tony Blair']\n", "(1348, 62, 47)\n" ] } ], "metadata": { "deletable": true, "editable": true, "id": "1UpwEJSw7PCi", "outputId": "6b6fca63-7b47-4824-a4ce-981fe703e863" } }, { "cell_type": "markdown", "source": [ "Let's take a look at the principal axes that span this dataset.\n", "Because this is a large dataset, we will use ``RandomizedPCA``—it contains a randomized method to approximate the first $N$ principal components much more quickly than the standard ``PCA`` estimator, and thus is very useful for high-dimensional data (here, a dimensionality of nearly 3,000).\n", "We will take a look at the first 150 components:" ], "metadata": { "deletable": true, "editable": true, "id": "J9Ci-7CR7PCi" } }, { "cell_type": "code", "execution_count": 27, "source": [ "from sklearn.decomposition import PCA as RandomizedPCA\n", "\n", "pca = RandomizedPCA(150)\n", "pca.fit(faces.data)" ], "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "PCA(n_components=150)" ] }, "metadata": {}, "execution_count": 27 } ], "metadata": { "deletable": true, "editable": true, "id": "lFuZONie7PCj", "outputId": "f1efdd9a-6bfe-45cf-ac0c-e6a24bcddc83" } }, { "cell_type": "markdown", "source": [ "In this case, it can be interesting to visualize the images associated with the first several principal components (these components are technically known as \"eigenvectors,\"\n", "so these types of images are often called \"eigenfaces\").\n", "As you can see in this figure, they are as creepy as they sound:" ], "metadata": { "deletable": true, "editable": true, "id": "yq_F5rP97PCj" } }, { "cell_type": "code", "execution_count": 28, "source": [ "fig, axes = plt.subplots(3, 8, figsize=(9, 4),\n", " subplot_kw={'xticks':[], 'yticks':[]},\n", " gridspec_kw=dict(hspace=0.1, wspace=0.1))\n", "for i, ax in enumerate(axes.flat):\n", " ax.imshow(pca.components_[i].reshape(62, 47), cmap='bone')" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {} } ], "metadata": { "deletable": true, "editable": true, "id": "Pzub1D6D7PCj", "outputId": "01e34abb-8269-4a07-8d7a-e68516ffebb4" } }, { "cell_type": "markdown", "source": [ "The results are very interesting, and give us insight into how the images vary: for example, the first few eigenfaces (from the top left) seem to be associated with the angle of lighting on the face, and later principal vectors seem to be picking out certain features, such as eyes, noses, and lips.\n", "Let's take a look at the cumulative variance of these components to see how much of the data information the projection is preserving:" ], "metadata": { "deletable": true, "editable": true, "id": "ilq33QDL7PCj" } }, { "cell_type": "code", "execution_count": 29, "source": [ "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n", "plt.xlabel('number of components')\n", "plt.ylabel('cumulative explained variance');" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {} } ], "metadata": { "deletable": true, "editable": true, "id": "QShFPr6R7PCj", "outputId": "56496651-9205-4f36-d1eb-7574b02358ce" } }, { "cell_type": "markdown", "source": [ "We see that these 150 components account for just over 90% of the variance.\n", "That would lead us to believe that using these 150 components, we would recover most of the essential characteristics of the data.\n", "To make this more concrete, we can compare the input images with the images reconstructed from these 150 components:" ], "metadata": { "deletable": true, "editable": true, "id": "x6ycaPLR7PCj" } }, { "cell_type": "code", "execution_count": 30, "source": [ "# Compute the components and projected faces\n", "pca = RandomizedPCA(150).fit(faces.data)\n", "components = pca.transform(faces.data)\n", "projected = pca.inverse_transform(components)" ], "outputs": [], "metadata": { "deletable": true, "editable": true, "id": "5fe8SKvF7PCj" } }, { "cell_type": "code", "execution_count": 31, "source": [ "# Plot the results\n", "fig, ax = plt.subplots(2, 10, figsize=(10, 2.5),\n", " subplot_kw={'xticks':[], 'yticks':[]},\n", " gridspec_kw=dict(hspace=0.1, wspace=0.1))\n", "for i in range(10):\n", " ax[0, i].imshow(faces.data[i].reshape(62, 47), cmap='binary_r')\n", " ax[1, i].imshow(projected[i].reshape(62, 47), cmap='binary_r')\n", " \n", "ax[0, 0].set_ylabel('full-dim\\ninput')\n", "ax[1, 0].set_ylabel('150-dim\\nreconstruction');" ], "outputs": [ { "output_type": "display_data", "data": { "image/png": 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", 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" ] }, "metadata": {} } ], "metadata": { "deletable": true, "editable": true, "id": "6T6Ohqou7PCk", "outputId": "f905f09d-fb5b-46ad-c04d-ed1786fbee01" } }, { "cell_type": "markdown", "source": [ "The top row here shows the input images, while the bottom row shows the reconstruction of the images from just 150 of the ~3,000 initial features.\n", "Although it reduces the dimensionality of the data by nearly a factor of 20, the projected images contain enough information that we might, by eye, recognize the individuals in the image.\n", "What this means is that our classification algorithm needs to be trained on 150-dimensional data rather than 3,000-dimensional data, which depending on the particular algorithm we choose, can lead to a much more efficient classification." ], "metadata": { "deletable": true, "editable": true, "id": "QgSgQZF67PCk" } }, { "cell_type": "markdown", "source": [ "## Principal Component Analysis Summary\n", "\n", "In this section we have discussed the use of principal component analysis for dimensionality reduction, for visualization of high-dimensional data, for noise filtering, and for feature selection within high-dimensional data.\n", "Because of the versatility and interpretability of PCA, it has been shown to be effective in a wide variety of contexts and disciplines.\n", "Given any high-dimensional dataset, I tend to start with PCA in order to visualize the relationship between points (as we did with the digits), to understand the main variance in the data (as we did with the eigenfaces), and to understand the intrinsic dimensionality (by plotting the explained variance ratio).\n", "Certainly PCA is not useful for every high-dimensional dataset, but it offers a straightforward and efficient path to gaining insight into high-dimensional data.\n", "\n", "PCA's main weakness is that it tends to be highly affected by outliers in the data.\n", "For this reason, many robust variants of PCA have been developed, many of which act to iteratively discard data points that are poorly described by the initial components.\n", "Scikit-Learn contains a couple interesting variants on PCA, including ``RandomizedPCA`` and ``SparsePCA``, both also in the ``sklearn.decomposition`` submodule.\n", "``RandomizedPCA``, which we saw earlier, uses a non-deterministic method to quickly approximate the first few principal components in very high-dimensional data, while ``SparsePCA`` introduces a regularization term that serves to enforce sparsity of the components." ], "metadata": { "deletable": true, "editable": true, "id": "lWlcwC1s7PCk" } } ] }