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Diffstat (limited to 'PVCM/cama/en/ma30 ACP.ipynb')
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diff --git a/PVCM/cama/en/ma30 ACP.ipynb b/PVCM/cama/en/ma30 ACP.ipynb new file mode 100644 index 0000000..04f1e16 --- /dev/null +++ b/PVCM/cama/en/ma30 ACP.ipynb @@ -0,0 +1,460 @@ +{ + "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" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "# Principal component analysis (PCA)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import numpy.linalg as lin\n", + "\n", + "%matplotlib inline\n", + "%config InlineBackend.figure_format = 'retina'\n", + "\n", + "np.set_printoptions(precision=3, linewidth=150, suppress=True)\n", + "plt.style.use(['seaborn-whitegrid','data/cours.mplstyle'])" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib\n", + "\n", + "def arrow2D(a,b, color='k', **kargs):\n", + " astyle = matplotlib.patches.ArrowStyle(\"simple\", head_length=.8, head_width=.8, tail_width=.1)\n", + " plt.plot([a[0],b[0]], [a[1],b[1]] ,visible = False) # to define the visible windows\n", + " plt.annotate(\"\", xytext=a, xy=b, \n", + " arrowprops=dict(arrowstyle=astyle, shrinkA=0, shrinkB=0, aa=True, color=color, **kargs))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "## A cloud of dots\n", + "\n", + "When we have a cloud of points we can study its shape by a **principal component analysis** (PCA). This comes back\n", + "to seek the eigenvectors of the covariance matrix (or correlation which is the covariance matrix normalized by the standard deviations). These eigenvectors describe the point cloud to us.\n", + "\n", + "To check it, let's make\n", + "a scatter plot with a strong correlation between $x$ and $y$:\n", + "\n", + "$$ y = 0.2 \\, x + 1.45 + U(-1,1) \\quad \\textrm{avec U la loi uniforme qui simule du bruit.}$$\n", + "\n", + "This linear relation between $x$ and $y$ allows us to know that we have:\n", + "\n", + "*a slope of 0.2* a vertical offset of 1.45 in x=0\n", + "\n", + "The goal is to\n", + "see if, with only the scatter plot, we can find the correlation between $x$ and $y$ despite the noise.\n", + "\n", + "$$ y = α x + β$$" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "N = 50\n", + "x = 10 * np.random.rand(N) - 5\n", + "nuage = np.array([x, 0.2 * x + 1.45 + (2 * np.random.rand(N) - 1)])" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 720x360 with 1 Axes>" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 589 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(nuage[0], nuage[1], 'x')\n", + "plt.title('Un nuage de points')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Graphically, we are looking for the line that minimizes the distance between the points and their projection on the line.\n", + "\n", + "\n", + "We can also construct the **covariance matrix** (see below) and see that the slope of the first eigenvector is\n", + "equal to this coefficient 0.2 which connects x to y.\n", + "\n", + "Then the average of the point cloud in a point of the line that we are looking for, which means that with the direction vector that is the first eigenvector, we have our line." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[9.107, 1.925],\n", + " [1.925, 0.764]])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cov = np.cov(nuage.copy())\n", + "cov" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Let us take this opportunity to recall that if a matrix is symmetric then\n", + "\n", + "* its eigenvalues are real\n", + "* its eigenvectors are orthogonal" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Valeurs propres de la matrice de covariance : [9.53 0.341] \n", + "\n", + "Vecteurs propres de la matrice de covariance :\n", + " [[ 0.977 -0.215]\n", + " [ 0.215 0.977]]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_26870/3419464211.py:2: ComplexWarning: Casting complex values to real discards the imaginary part\n", + " val = val.astype('float') # on convertit puisqu'on sait que ce sont des réels\n" + ] + } + ], + "source": [ + "val, vec = lin.eig(cov)\n", + "val = val.astype('float') # on convertit puisqu'on sait que ce sont des réels\n", + "print(\"Valeurs propres de la matrice de covariance :\", val,\"\\n\")\n", + "print(\"Vecteurs propres de la matrice de covariance :\\n\", vec)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 720x360 with 1 Axes>" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 595 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(nuage[0], nuage[1], 'x')\n", + "arrow2D((0,0), val[0] * vec[:,0], 'r') # vecteur propre multiplié par sa valeur propre\n", + "arrow2D((0,0), val[1] * vec[:,1], 'g')\n", + "plt.title('Un nuage de points et les vecteurs propres de sa matrice de covariance')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Let's check that the slope of the first eigenvector is close to 0.2:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "La pente est de 0.21963615318288862 \n", + "\n", + "Le points moyen du nuage est [-0.152 1.327]\n" + ] + } + ], + "source": [ + "pente = vec[1,0] / vec[0,0] \n", + "print(\"La pente est de\", pente, '\\n')\n", + "moyenne = nuage.mean(axis=1)\n", + "print(\"Le points moyen du nuage est\", moyenne)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Le décalage verticale est de 1.360408912029785\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 720x360 with 1 Axes>" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 589 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "eq_droite = lambda x: pente * (x - moyenne[0]) + moyenne[1]\n", + "\n", + "print(\"Le décalage verticale est de \", eq_droite(0))\n", + "\n", + "plt.plot(nuage[0], nuage[1], 'x')\n", + "plt.plot([nuage[0].min(), nuage[0].max()], [eq_droite(nuage[0].min()), eq_droite(nuage[0].max())]) \n", + "plt.title(\"Un nuage de points et sa droite d'approximation\")\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "On a donc α = 0.220 et β = 1.360 sachant que le nuage a été généré avec 0.2 et 1.45\n" + ] + } + ], + "source": [ + "print(f'On a donc α = {pente:.3f} et β = {eq_droite(0):.3f} sachant que le nuage a été généré avec 0.2 et 1.45')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "### Covariance matrix\n", + "\n", + "The covariance between two datasets __x__ and __y__ indicates how closely they are related (i.e. if the i-th value of __y__ can be deduced from the i-th value of __x__ or not). If their covariance is large\n", + "in absolute value then they are strongly related, if it is close to 0, they are either independent\n", + "is linked by a more complicated relationship than a simple linear relationship.\n", + "\n", + "Covariance measures the linear relationship between 2 variables (see [this video](https://www.youtube.com/watch?v=UM-AOmT2RWk)\n", + "for a quick and complete presentation of covariance and its properties).\n", + "\n", + "$$\n", + "\\textrm{cov}(\\textbf{x},\\textbf{y}) = \\frac{1}{N} \\sum_{i=1}^N (x_i - \\overline{\\textbf{x}}) (y_i - \\overline{\\textbf{y}})\n", + "$$\n", + "\n", + "with $N$ the number of points of the cloud, $\\overline{\\textbf{x}}$ and $\\overline{\\textbf{y}}$ the averages of $\\textbf{x}$ and $\\textbf{y}$.\n", + "\n", + "If we place the origin of the axes at the mean $(\\overline{\\textbf{x}},\\overline{\\textbf{y}})$ then the formula indicates that to have correlation there must be more points in 2 diagonally opposite quadrans.\n", + "\n", + "If, conversely, we draw random points, so no relationship between x and y, then we will have points distributed evenly around the mean, so a\n", + "zero covariance.\n", + "Finally if all the values of $\\textbf{y}$ have the same value, then they do not depend on x and $y_i - \\overline{\\textbf{y}} = 0 \\; \\forall i$ so the covariance is zero." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 720x360 with 1 Axes>" + ] + }, + "metadata": { + "image/png": { + "height": 318, + "width": 708 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(nuage[0], nuage[1], 'x')\n", + "plt.plot([moyenne[0], moyenne[0]], [nuage[1].min(), nuage[1].max()],'k')\n", + "plt.plot([nuage[0].min(), nuage[0].max()], [moyenne[1], moyenne[1]],'k')\n", + "plt.title('La covariance indique une direction privilégiée et donc plus de points dans les quadrans traversés')\n", + "plt.axis('equal');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "Here we can clearly see that the vast majority of points are in 2 opposite quadrans, of which our 2 variables are linked.\n", + "\n", + "The covariance matrix expresses all the possible covariances between the variables. In our case where\n", + "the cloud has 2 dimensions, we have:\n", + "\n", + "$$\n", + "\\textrm{Cov(nuage 2D)} = \n", + "\\begin{bmatrix}\n", + "\\textrm{cov}(\\textbf{x},\\textbf{x}) & \\textrm{cov}(\\textbf{x},\\textbf{y}) \\\\\n", + "\\textrm{cov}(\\textbf{y},\\textbf{x}) & \\textrm{cov}(\\textbf{y},\\textbf{y}) \\\\\n", + "\\end{bmatrix}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[8.925, 1.887],\n", + " [1.887, 0.749]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cov = lambda x,y : np.dot((x - x.mean()), (y - y.mean())) / len(x)\n", + "\n", + "Cov = lambda x,y : np.array([[cov(x,x), cov(x,y)], [cov(y,x), cov(y,y)]])\n", + "\n", + "Cov(nuage[0], nuage[1]) # par défaut Numpy divise par (N-1), avec bias=True il divise par N et donne ce résultat" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "This result shows that x is very linked with itself, which is obvious. On the other hand, it seems that there is\n", + "less connected with himself. In fact the variations of y are smaller (between 0 and 3 while x varies between -5 and 5) which explains this smaller value. The fact that cov(x,y) is greater than cov(y,y) is already a\n", + "indicator that x and y are related.\n", + "\n", + "The calculation of the eigenvalues and vectors of the covariance matrix is even more interesting with\n", + "a large dimension because it highlights which are the most important. Thus the example of the article\n", + "from Wikipedia on ['principal component analysis](https://fr.wikipedia.org/wiki/Analyse_en_principales_components)\n", + "on the pollution of the Doubs water shows that the first clean vector is that of known pollutants: nitrates (nit), phosphates (pho), ammonia (amm)\n", + "and the second is that of PH. Note the anti-correlation between oxygen content and pollutants.\n", + "\n", + "<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Cercle_des_cor%C3%A9lations_d%27une_ACP_norm%C3%A9e.svg/500px-Cercle_des_cor%C3%A9lations_d%27une_ACP_norm%C3%A9e.svg.png\"/>" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "lang": "en" + }, + "source": [ + "To fully understand this figure and see a use case, I invite you to watch this\n", + "[example of PCA with Excel](https://www.youtube.com/watch?v=GNBeWpkHFJw)." + ] + } + ] +}
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