{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Szinguláris érték felbontás\n", "\n", "## (SVD, Singular Value Decomposition)\n", "\n", "Az [SVD](https://en.wikipedia.org/wiki/Singular_value_decomposition) a sajátérték-sajátvektor felbontás általánosítása téglalap alakú mátrixokra. Az SVD az $\\mathbf{X}$ (*n*⁢ x *m*)-es transzformáló mátrix hatását három jól érthető részre bontja:\n", "\n", "* forgatás ($\\mathbf{V}^T$)\n", "\n", "* skálázás ($\\mathbf{\\Lambda}^{1/2}$)\n", "\n", "* forgatás ($\\mathbf{U}^T$)\n", "\n", "A mátrix SVD felbontása:\n", "\n", " $$\\mathbf{X}= \\mathbf{U}\\mathbf{\\Lambda}^{1/2}\\mathbf{V}^T$$\n", "\n", "ábrán személtetve:\n", "\n", "\n", "\n", "## Az SVD felbontás kapcsolata a sajátérték felbontással\n", "\n", "Egy szimmetrikus $\\mathbf{A}$ mátrix felbontható ortogonális $\\mathbf{U}$ mátrixszal ($\\mathbf{U}^T\\mathbf{U}=\\mathbf{E}$, $\\mathbf{E}$ egységmátrix) és a sajátértékekből álló átlós $\\mathbf{\\Lambda}$ mátrixszal az alábbi módon:\n", "\n", " $$\\mathbf{A}= \\mathbf{U}\\mathbf{\\Lambda}\\mathbf{U}^T$$\n", "\n", "Egy *tetszőleges* (*n*⁢ x *m*)-es $\\mathbf{X}$ mátrixból kétféleképpen is szimmetrikus mátrixot készíthetünk (egyik (*m*⁢ x *m*)-es, a másik (*n*⁢ x *n*)-es lesz): $\\mathbf{X}^T \\mathbf{X}$ vagy $\\mathbf{X} \\mathbf{X}^T$. Ezek a *szimmetrikus* mátrixok felbonthatók *azonos* sajátértékek szerint:\n", "\n", " $$\\mathbf{X}^T \\mathbf{X}=\\mathbf{V}\\mathbf{\\Lambda}\\mathbf{V}^T=(\\mathbf{V}\\mathbf{\\Lambda}^{1/2}\\mathbf{U}^T)(\\mathbf{U}\\mathbf{\\Lambda}^{1/2}\\mathbf{V}^T)$$\n", "\n", "és\n", "\n", " $$\\mathbf{X} \\mathbf{X}^T=\\mathbf{U}\\mathbf{\\Lambda}\\mathbf{U}^T=(\\mathbf{U}\\mathbf{\\Lambda}^{1/2}\\mathbf{V}^T)(\\mathbf{V}\\mathbf{\\Lambda}^{1/2}\\mathbf{U}^T)$$\n", "\n", "tehát bármely *r* rangú $\\mathbf{X}$ mátrix felbontható ortogonális $\\mathbf{U}$ és $\\mathbf{V}$ mátrixszokkal és a szinguláris értékekből álló átlós $\\mathbf{\\Lambda}^{1/2}$ mátrixszal:\n", "\n", " $$\\mathbf{X}= \\mathbf{U}\\mathbf{\\Lambda}^{1/2}\\mathbf{V}^T$$ \n", "\n", "ahol\n", "\n", " $$\\mathbf{\\Lambda}^{1/2}=\\begin{bmatrix}\\sqrt{\\lambda_1} & \\cdots & 0\\\\ \\vdots & \\ddots & \\vdots \\\\ 0 & \\cdots & \\sqrt{\\lambda_r}\\end{bmatrix}$$\n", "\n", "és *r* az $\\mathbf{X}$ mátrix *rangja*.\n" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Példa\n", "\n", "Legyen\n", "\n", "$$\\mathbf{X} = \\begin{bmatrix} 1 & 2\\\\ 2 & 1\\\\ 1 & 3 \\end{bmatrix}$$ \n", "\n", "Keressük meg az $\\mathbf{X} \\mathbf{X}^T$ mátrix sajátértékeit, ezután számítsuk ki $\\mathbf{\\Lambda}^{1/2}$-t, az $\\mathbf{X}$ mátrix SVD felbontását és a $\\mathbf{V}_1$, $\\mathbf{V}_2$ sajátvektorokat. Ezután számítsuk ki $\\mathbf{U}$-t a megfelelő képletből és az $\\mathbf{X}$ mátrix $\\mathbf{X}_1$ legjobb 1-rangú közelítését (erről a témáról majd az SVD tulajdonságainál lesz szó).\n", "\n", "Megoldás (Python, NumPy [`eig`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html) )" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "array([[ 1., 2.],\n", " [ 2., 1.],\n", " [ 1., 3.]])" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "from numpy import linalg as LA\n", "X = np.array([[1,2],[2,1],[1,3]])\n", "# X'.X sajátérték felbontása\n", "e,V = LA.eig(np.dot(X.T,X))\n", "Lam = np.sqrt(np.diag(e))\n", "# szinguláris értékek\n", "np.diag(Lam)\n", "U = np.dot(X,V)/np.sqrt(e)\n", "# ez az eredeti X mátrix:\n", "np.dot(U,np.dot(Lam,V.T))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.12017367, -0.06973949],\n", " [-1.06201737, 0.61631261],\n", " [ 0.55429524, -0.32167002]])" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# X legjobb 1-rangú közelítése\n", "X1 = np.sqrt(e[1])*np.outer(U[:,1],V[:,1].T)\n", "# eltérések:\n", "X1 - X" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "SVD felbontás a beépített [numpy.linalg.svd](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.svd.html) függvény használatával." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "array([ 4.2499715 , 1.39202811])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# X SVD felbontása beépített függvénnyel\n", "U,S,V = LA.svd(X)\n", "# szinguláris értékek nagyság szerint rendezve\n", "S" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Az SVD felbontás két változata\n", "\n", "\n", "\n", "## Az SVD tulajdonságai\n", "\n", "A kétfajta sajátvektor rendszer egymásból számítható:\n", "\n", "$$\\mathbf{U}_m=\\frac{1}{\\sqrt{\\lambda_m}}\\mathbf{X}\\mathbf{V}_m \\;\\;\\;\\;\\;m=1,...,r.$$\n", "\n", "Az SVD-vel felírható $\\mathbf{X}$ legjobb *k*-ad rangú közelítése:\n", "\n", "$$\\mathbf{X}_k=\\sum_{m=1}^{k}\\sqrt{\\lambda_m}\\mathbf{U}_m\\mathbf{V}_m^T \\;\\;\\;\\;\\;k\\le r,$$\n", "\n", "a közelítés hibája:\n", "\n", "$$\\varepsilon_k^2=\\sum_{m,n}\\left | x(m,n)-x_k(m,n)\\right |^2$$ a figyelembe nem vett sajátértékek összege: $$\\varepsilon_k^2=\\sum_{m=k+1}^r \\lambda_m$$\n", "\n", "## A mátrix sorfejtése, spektruma\n", "\n", "Az $\\mathbf{X}$ mátrix *k* tagból álló sorfejtése\n", "\n", "$$\\mathbf{X}_k=\\sum_{m=1}^{k}\\sqrt{\\lambda_m}\\mathbf{U}_m\\mathbf{V}_m^T \\;\\;\\;\\;\\;k\\le r,$$\n", "\n", "a mátrix *spektrum*át a $\\sqrt{\\lambda_m}$ szinguláris értékek adják (*m*=1, … , *r* ).\n", "\n", "## Pszeudoinverz\n", "\n", "Bármely téglalap alakú $\\mathbf{X}$ mátrixra létezik az $\\mathbf{X}^+$ pszeudoinverz:\n", "\n", " $$\\mathbf{X}^+= \\mathbf{V}\\mathbf{\\Lambda}^{1/2+}\\mathbf{U}^T$$ \n", "\n", "ahol\n", "\n", " $${\\mathbf{\\Lambda}^{1/2+}\\atop{(m,m)}} = \\begin{bmatrix}\\lambda_1^{-1/2} & \\cdots & 0 & \\cdots & 0\\\\ \\vdots & \\ddots & \\vdots & & \\vdots\\\\ 0 & \\cdots & \\lambda_r^{-1/2} & \\cdots & 0\\\\ \\vdots & & \\vdots & \\ddots & \\vdots \\\\ 0 & \\cdots & 0 & \\cdots & 0\\end{bmatrix}$$ .\n", "\n", "A $\\mathbf{\\Lambda}^{1/2+}$ mátrix főátlójában az *r*-nél nagyobb indexű elemek zérusok." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## A legkisebb négyzetek problémájának megoldása SVD-vel\n", "\n", "A feladat a következő hiba norma minimalizációja:\n", "\n", "$$\\left \\| \\mathbf{A}\\mathbf{x}-\\mathbf{y} \\right \\|$$ \n", "\n", "A legkisebb négyzetes (LKN) megoldás $\\mathbf{x}$-re az $\\mathbf{A}$ mátrix SVD felbontásával számított pszeudoinverzzel kapható meg:\n", "\n", "$$\\mathbf{x}= \\mathbf{V}\\mathbf{\\Lambda}^{1/2+}\\mathbf{U}^T \\mathbf{y}$$ .\n", "\n", "## A súlyozott legkisebb négyzetek problémájának megoldása SVD-vel\n", "\n", "Most minimalizáljuk a következő hiba normát:\n", "\n", "$$ (\\mathbf{A}\\mathbf{x}-\\mathbf{y})^T \\mathbf{P} (\\mathbf{A}\\mathbf{x}-\\mathbf{y})$$ \n", "\n", "A legkisebb négyzetes (LKN) megoldás $\\mathbf{x}$-re a $\\mathbf{P}_0\\mathbf{A}$ mátrix SVD felbontásával ($\\mathbf{P}_0\\mathbf{A}= \\mathbf{U}\\mathbf{\\Lambda}^{1/2}\\mathbf{V}^T$) számított pszeudoinverzzel kapható meg, ahol $\\mathbf{P}_0$ a $\\mathbf{P}$ mátrix négyzetgyöke, $\\mathbf{P}=\\mathbf{P}_0^T\\mathbf{P}_0$:\n", "\n", "$$\\mathbf{x}= \\mathbf{V}\\mathbf{\\Lambda}^{1/2+}\\mathbf{U}^T \\mathbf{P}_0\\mathbf{y}$$ ." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Mátrix approximáció SVD-vel\n", "\n", "Példa: magyarországi geoidfelület közelítése SVD-vel\n", "\n", "Beolvassuk a geoid adatokat:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "geoid = np.loadtxt(\"geoid.txt\")" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "geoidmagasságok rácsa 35 sor, 70 oszlop" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/tg/.local/lib/python2.7/site-packages/subprocess32.py:472: RuntimeWarning: The _posixsubprocess module is not being used. Child process reliability may suffer if your program uses threads.\n", " \"program uses threads.\", RuntimeWarning)\n" ] }, { "data": { "image/png": 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/VoMbPS027x+ITfpL4/3HisjNIvJQ/O8xJgNfYaFkonNTu6VJmhJ0WCnSZZst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\nE/w8v7zPNVlMBb2MLqPztvE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = np.flipud(np.reshape(geoid[:,2],(35,70)))\n", "import matplotlib.pyplot as plt\n", "cmap = plt.get_cmap('PiYG')\n", "levels=np.linspace(37,47)\n", "plt.contourf(N,levels=levels,cmap=cmap)\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "SVD felbontást számítunk" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 2.13748970e+03 3.01654946e+01 1.27873105e+01 4.23156000e+00\n", " 3.37888239e+00 2.95186350e+00 1.90147820e+00 1.25895030e+00\n", " 9.66044712e-01 8.79068869e-01]\n", "(35, 35) (70, 70)\n" ] } ], "source": [ "U,S,V = LA.svd(N)\n", "# csökkenő sajátértékek szerint van rendezve\n", "print S[0:10]\n", "print U.shape, V.shape" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "A mátrix spektruma" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# a mátrix rangja\n", "r = LA.matrix_rank(N)\n", "plt.semilogy(range(r),S[:r])\n", "plt.xlabel(\"index\")\n", "plt.ylabel(\"singular value\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Legjobb *n*-edfokú SVD közelítés, `step`-enként kirajzoltatva" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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HfVZwnV3apZiWffbR5uM3hZPCSBpLuh64B/gM8I/AfWYWzcK4E3hkRt3zo331fnjf7E9z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\nYlZLkXdeRdDrLGNbR9ibzITxkcIYx0XQmxoMLUt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D+HYAh1CViP99Vz9mvkTXXdu5/xTz2Z7c3p3NRb62+dgmYpe3LSH4Y7OjUZ87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\nhhup6vbNwUfe5nUTpUqcxRYmh0jcNiTEXWJRMoe4XShNqnq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AGKrT0huhizAarkeP3YDeyTyXsF12SipChJ6KFKKfD51LDyuMzdUUy0DosQ0m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\njNRXaAcL8SPaslgWgdwwvLaxZ21vdqLOssMXqtjqNayFULP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def svdapprox(U,S,V,k,n,step):\n", " dm = np.zeros((len(U),len(V)))\n", " for i in range(k,n):\n", " dm = dm + S[i]*np.outer(U.T[i],V[i])\n", " if np.mod(i,step) == 0:\n", " cmin = np.amin(dm)\n", " cmax = np.amax(dm)\n", " # print cmin, cmax\n", " levels=np.arange(cmin,cmax,step=0.1)\n", " plt.contourf(dm,levels=levels,cmap=cmap)\n", " plt.title(\"SVD approx. rank=%d\" % (i+1))\n", " plt.colorbar()\n", " plt.show()\n", " # raw_input()\n", " return dm\n", "\n", "Na = svdapprox(U,S,V,0,11,5) " ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "az utolsó közelítés hibája" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "min: -0.127 max: 0.123\n" ] }, { "data": { "image/png": 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sEMLJ+riR0Ej2IYRAtNRVSfZmqcb332CtuvqNVDNQI9l3IXorbYNf0agJOaLP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dN = N - Na\n", "cmin = np.amin(dN)\n", "cmax = np.amax(dN)\n", "print \"min: %.3f max: %.3f\" % (cmin, cmax)\n", "levels=np.arange(cmin,cmax,step=0.01)\n", "plt.contourf(dN,levels=levels,cmap=cmap)\n", "plt.title(\"Error of SVD approximation (m)\")\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Feladat\n", "Számítsa ki a közelítés hibáját a figyelembe nem vett szinguláris értékek segítségével!" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "np.sqrt(np.sum(S[11:]**2)/(35*70-1))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }