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@cjauvin
Last active February 5, 2016 03:23
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{
"metadata": {
"name": "",
"signature": "sha256:c89206808f997f4ff73a893d57c57dd32025231d4b01752b472f563ef34e173d"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ma compr\u00e9hension de la PCA"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Supposons que je d\u00e9finisse un dataset $X$ dans $R^2$, o\u00f9 les deux dimensions sont fortement corr\u00e9l\u00e9es (avec un peu de bruit ajout\u00e9 pour faire bonne mesure!)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"n = 100\n",
"x = random.random(n)\n",
"noise = random.normal(scale=0.1, size=n)\n",
"y = x * 3 + noise\n",
"X = vstack((x, y))\n",
"scatter(x, y);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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16tUjKChIiUYWUbIhIiI5wqBBg3jhhRcwmV4BCgL3U6DAThYtWkDZsmXdHV6upmkUERHJ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\n",
"text": [
"<matplotlib.figure.Figure at 0x10e5c2410>"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"La forte corr\u00e9lation entre les deux dimensions est aussi exprim\u00e9e par le fait que les \u00e9l\u00e9ments non-diagonaux de la matrice de covariance $S$ sont $>> 0$."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"X_centered = X.T - mean(X, axis=1)\n",
"S = np.dot(X_centered.T, X_centered) / (n - 1)\n",
"assert(array_equal(S, cov(X))) # juste pour v\u00e9rifier que je fais la m\u00eame chose que Numpy\n",
"S"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 2,
"text": [
"array([[ 0.09367849, 0.28069923],\n",
" [ 0.28069923, 0.8508528 ]])"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Le but de la PCA est de trouver une matrice $P$ qui constitue une nouvelle base orthonormale vers laquelle les donn\u00e9es $X$ seront projet\u00e9es (\u00e0 partir donc de la base orthogonale implicite $I$ dans laquelle $X$ avait \u00e9t\u00e9 pr\u00e9alablement d\u00e9finie), donc $P \\cdot X = Y$. Toutefois, on ajoute la contrainte que la matrice de covariance de $Y$ devrait \u00eatre diagonale, ce qui devrait d\u00e9couler du fait que les dimensions de $Y$ ont \u00e9t\u00e9 maximalement d\u00e9corr\u00e9l\u00e9es. La fa\u00e7on d'y parvenir est de d\u00e9finir $P$ en tant que les eigen-vecteurs de $S$ (ici s'arr\u00eate pas mal ma compr\u00e9hension en fait, parce que je n'ai pas pouss\u00e9 mon \u00e9tude jusqu'\u00e0 comprendre pourquoi exactement)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"P = linalg.eig(S)[1]\n",
"Y = np.dot(P.T, X)\n",
"cov(Y)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
"array([[ 9.69249313e-04, 2.24287480e-17],\n",
" [ 2.24287480e-17, 9.43562042e-01]])"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Si on repr\u00e9sente graphiquement $Y$, on voit que la projection vers $P$ a deux effets : (1) r\u00e9aligner sur le plan les deux dimensions o\u00f9 la variance est maximale, et (2) d\u00e9corr\u00e9ler les deux dimensions :"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"scatter(Y.T[:, 0], Y.T[:, 1]);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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MiRMnePHFl7hypT5wDLf7EjCTRYuWMXToUKvjidyVSoiIpGsDBgzko48+4cKF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\n",
"text": [
"<matplotlib.figure.Figure at 0x10ea35210>"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Si on modifie l'exp\u00e9rience de mani\u00e8re \u00e0 r\u00e9duire le bruit \u00e0 presque rien :"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = random.random(n)\n",
"noise = random.normal(scale=0.0001, size=n)\n",
"y = x * 3 + noise\n",
"X = vstack((x, y))\n",
"scatter(x, y);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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EQ/KJiNyOVatWsW7dalyuz4ARwD/xrs/ozsiRo3G5XOYGFMkBsrVsJCQkMHHi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\nRERExFAqNkRERMRQ/w/3vkbHvHoG9wAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x10eaa6f10>"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On constate que la d\u00e9corr\u00e9lation est beaucoup plus \"difficile\" :"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"P = linalg.eig(cov(X))[1]\n",
"Y = np.dot(P.T, X)\n",
"scatter(Y.T[:, 0], Y.T[:, 1]);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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f5164ZfNXhISE4O/vf8XbPidPuh6dvNLtogsmT55MgwYN/nIOEbk+c+fO5dCh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\nX3fVqlUEBwezePFi/R8dd3d3vvzyS4YNG0ZAQAAAw4cPJyQ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"text": [
"<matplotlib.figure.Figure at 0x10ec6d350>"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}
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