{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Lecture 6: Matrix rank, singular value decomposition" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Syllabus\n", "**Week 1:** Matrices, vectors, matrix/vector norms, scalar products & unitary matrices \n", "**Week 2:** TAs-week (Strassen, FFT, a bit of SVD) \n", "**Week 3:** Matrix ranks, singular value decomposition, linear systems \n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Recap of the previous lecture (a week ago)\n", "- Concept of block matrices (Lecture 3.1)\n", "- Matrix norms, scalar products, unitary matrices (Lecture 3.2)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Today lecture\n", "Today we will talk about:\n", "- Rank of the matrix, idea of linear dependence\n", "- Singular value decomposition (SVD) and low-rank approximation" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Matrix and linear spaces\n", "A matrix can be considered as a sequence of vectors, its columns:\n", "$$\n", " A = [a_1, \\ldots, a_m], \n", "$$\n", "where $a_m \\in \\mathbb{C}^n$. \n", "A matrix-by-vector product is equivalent to taking a linear combination of those columns \n", "$$\n", " y = Ax, \\quad \\Longleftrightarrow y = a_1 x_1 + a_2 x_2 + \\ldots +a_m x_m.\n", "$$\n", "\n", "This is a special case of **block matrix notation** that we have already seen." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Linear dependence\n", "The vectors are called linearly dependent, if there exist non-zero coefficients $x_i$ such that \n", "$$\\sum_i a_i x_i = 0,$$\n", "or in the matrix form,\n", "$$\n", " Ax = 0, \\quad \\Vert x \\Vert \\ne 0.\n", "$$\n", "In this case, we say that the matrix $A$ has a non-trivial **nullspace**." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Dimension of a linear space\n", "A **linear space** is defined as all possible vectors of the form \n", "$$\n", " \\sum_{i=1}^m a_i x_i, \n", "$$\n", "where $x_i$ are some coefficients and $a_i, i = 1, \\ldots, m$ are given vectors. In the matrix form, the linear space is a collection of the vectors of the form \n", "$$A x.$$\n", "This set is also called the **range** of the matrix.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Matrix rank\n", "What is a matrix rank? \n", "\n", "A matrix rank is defined as the maximal number of linearly independent columns in a matrix, or the **dimension of its column space**. \n", "\n", "You can also use linear combination of rows to define the rank. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "** Theorem** \n", "The dimension of the column space of the matrix is equal to the dimension of the row space of the matrix." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Are there any \"small-dimensional subspaces\"?\n", "\n", "- Of course, not! (I.e. a random matrix is a full-rank matrices). \n", "\n", "Why do we care? " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## In practice, everything is \"small-dimensional\"\n", "\n", "**Johnson–Lindenstrauss lemma** \n", "\n", "Given $0 < \\epsilon < 1$, a set of points in $\\mathbb{R}^N$ and $n > \\frac{8 \\log m}{\\epsilon^2}$\n", "\n", "and linear map $f$ from $\\mathbb{R}^N \\rightarrow \\mathbb{R}^M$\n", "\n", "$$(1 - \\epsilon) \\Vert u - v \\Vert^2 \\leq \\Vert f(u) - f(v) \\Vert^2 \\leq (1 + \\epsilon) \\Vert u - v \\Vert^2.$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Skeleton decomposition\n", "A very useful representation for computation of the matrix rank is the **skeleton decomposition**, which can be graphically represented as follows: \n", "\n", "or in the matrix form\n", "$$\n", " A = U \\widehat{A}^{-1} V^{\\top},\n", "$$\n", "where $U$ are some $r$ columns of $A$, $V^{\\top}$ are some rows of $A$, $\\widehat{A}$ is the submatrix on the intersection, which should be **nonsingular**." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "**Remark.** \n", "An inverse of the matrix $P$ the matrix $Q = P^{-1}$ such that \n", "$ P Q = QP = I$. \n", "If the matrix is square and has full rank (i.e. equal to $n$) then the inverse exists." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Proof for the skeleton decomposition\n", "Let $U$ be the $r$ columns based on the submatrix $\\widehat{A}$. Then they are linearly independent. Take any other column $u$ of $A$. Then it is a linear combination of the columns of $U$, i.e. \n", "$u = U x$. \n", "These are $n$ equations. We take $r$ of those corresponding to the rows that contain $\\widehat{A}$ and get the equation \n", "$$\\widehat{u} = \\widehat{A} x,$$ therefore \n", "$$x = \\widehat{A}^{-1} \\widehat{u},$$ and that gives us the result." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## A closer look\n", "Any rank-$r$ matrix can be written in the form\n", "$$A = U \\widehat{A}^{-1} V^{\\top},$$\n", "where $U$ is $n \\times r$, $V$ is $m \\times r$ and $\\widehat{A}$ is $r \\times r$, or \n", "$$\n", " A = U' V'^{\\top}.\n", "$$\n", "So, every rank-$r$ matrix can be written as a product of a \"tall\" matrix $U'$ by a long matrix $V'$. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "In the index form, it is \n", "$$\n", " a_{ij} = \\sum_{\\alpha=1}^r u_{i \\alpha} v_{j \\alpha}.\n", "$$\n", "For rank 1 we have\n", "$$\n", " a_{ij} = u_i v_j,\n", "$$\n", "i.e. it is a separation of indices and rank-$r$ is a sum of rank-$1$ matrices!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Storage\n", "It is interesting to note, that for the rank-$r$ matrix \n", "$$A = U V^{\\top}$$\n", "only $U$ and $V$ can be stored, which gives us $(n+m) r$ parameters, so it can be used for compression. We can also compute matrix-by-vector product much faster." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The slowest run took 6.03 times longer than the fastest. This could mean that an intermediate result is being cached \n", "1000 loops, best of 3: 562 µs per loop\n", "The slowest run took 6.92 times longer than the fastest. This could mean that an intermediate result is being cached \n", "100000 loops, best of 3: 12.8 µs per loop\n" ] } ], "source": [ "import numpy as np\n", "n = 1000\n", "r = 10\n", "u = np.random.randn(n, r)\n", "v = np.random.randn(n, r)\n", "a = u.dot(v.T)\n", "x = np.random.randn(n)\n", "%timeit a.dot(x)\n", "%timeit u.dot(v.T.dot(x))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "We can also try to compute the matrix rank using the built-in ```np.linalg.matrix_rank``` function" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Rank of the matrix: 1\n", "Rank of the matrix: 50\n" ] } ], "source": [ "#Computing matrix rank\n", "import numpy as np\n", "n = 50 \n", "a = np.ones((n, n))\n", "print 'Rank of the matrix:', np.linalg.matrix_rank(a)\n", "b = a + 1e-6 * np.random.randn(n, n)\n", "print 'Rank of the matrix:', np.linalg.matrix_rank(b, tol=1e-8)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Instability of the matrix rank\n", "For any rank-$r$ matrix $A$ with $r < \\min(m, n)$ there is a matrix $B$ such that its rank rank is equal to $\\min(m, n)$ and\n", "$$\n", " \\Vert A - B \\Vert = \\varepsilon.\n", "$$\n", "So, does this mean that numerically matrix rank has no meaning? (I.e., small perturbations lead to full rank)! \n", "The solution is to compute the best **rank-r** approximation to a matrix." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Singular value decomposition\n", "To compute low-rank approximation, we need to compute **singular value decomposition**. \n", "Any matrix $A$ can be written as a product of three matrices: \n", "$$\n", " A = U \\Sigma V^*,\n", "$$\n", "where $U$ is an $n \\times K$ unitary matrix, $V$ is an $m \\times K$ unitary matrix, $K = \\min(m, n)$ $\\Sigma$ is a diagonal matrix with non-negative elements $\\sigma_1 \\geq \\ldots, \\geq \\sigma_K$ on the diagonal. \n", "\n", "Computation of the best rank-$r$ approximation is equivalent to setting $\\sigma_{r+1}= 0, \\ldots, \\sigma_K = 0$. The error is then determined by the omitted singular value! \n", "$$\n", " \\min_{A_r} \\Vert A - A_r \\Vert = \\sigma_{r+1},\n", "$$\n", "that is why it is important to look at the decay of the singular vectors." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Low-rank approximation via SVD\n", "$\\Vert A - A_r \\Vert = \\Vert U \\Sigma V^* - A_r \\Vert = \\Vert \\Sigma - U^* A_r V \\Vert$, \n", "where we used that for spectral norm (and for the Frobenius as well) we have \n", "\n", "$$\\Vert X Q \\Vert = \\Vert X \\Vert$$\n", "for any unitary $Q$ and any matrix $X$. This is called **unitary equivalence** of the spectral norm (and Frobenius as well). \n", "What is left is to note that the best rank-$r$ approximation of the diagonal matrix is its subdiagonal. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Computing the SVD is tricky; we will talk about the algorithms hidden in this computation later. But we already can do this in Python!" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Rank of the matrix: 1\n", "Rank of the matrix: 50\n" ] } ], "source": [ "#Computing matrix rank\n", "import numpy as np\n", "n = 50 \n", "a = np.ones((n, n))\n", "print 'Rank of the matrix:', np.linalg.matrix_rank(a)\n", "b = a + 1e-5 * np.random.randn(n, n)\n", "print 'Rank of the matrix:', np.linalg.matrix_rank(b)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.62173054286e-06\n", "2.62173054287e-06\n" ] } ], "source": [ "u, s, v = np.linalg.svd(b)\n", "print s[1]/s[0]\n", "r = 1\n", "u1 = u[:, :r]\n", "s1 = s[:r]\n", "v1 = v[:r, :]\n", "a1 = u1.dot(np.diag(s1).dot(v1))\n", "print np.linalg.norm(b - a1, 2)/s[0]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "We can use SVD to compute approximations of **function-related** matrices, i.e. the matrices of the form \n", "$$a_{ij} = f(x_i, y_j),$$\n", "where $f$ is a certain function, and $x_i, \\quad i = 1, \\ldots, n$ and $y_j, \\quad j = 1, \\ldots, m$ are some **one-dimensional grids**." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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EdYb/GNKREKeDmR9vYebHmzl7Tl1CvsIjBcBam2utffGC40XGmFrAA8BsT1xT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\nEqRUAEREgpQKgIhIkPr/nZE60nwuyzsAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "n = 1000\n", "a = [[1.0/(i+j+1) for i in xrange(n)] for j in xrange(n)] #Hilbert matrix \n", "a = np.array(a)\n", "u, s, v = np.linalg.svd(a)\n", "fig, ax = plt.subplots(1, 1)\n", "ax.semilogy(s[:30])\n", "#We have very good low-rank approximation of it!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Now we can do something more interesting, like function approximation" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.61306034376e-10\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "n = 128\n", "t = np.linspace(0, 5, n)\n", "x, y = np.meshgrid(t, t)\n", "f = 1.0 / (x + y + 0.5)\n", "u, s, v = np.linalg.svd(f, full_matrices=False)\n", "r = 10\n", "u = u[:, :r]\n", "s = s[:r]\n", "v = v[:r, :] #Mind the transpose here!\n", "fappr = u.dot(np.diag(s).dot(v))\n", "er = np.linalg.norm(fappr - f, 'fro') / np.linalg.norm(f, 'fro')\n", "print er\n", "plt.semilogy(s/s[0])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "And do some 3D plotting" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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jnj5J4p8ASn+d+uODmlUO56ITa12toDFi82Fu/FgLwZwZCIGcRai6RMHtlpFl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7Z3phjVWNMzd+5MWqkJTWWQ9wk6CxYDgSCHHOJk48b42C0O/Qbat1mvDSwIApLUrTbwvkctW1PD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\nCInEphQKxzEQWbbbH8BsrhAO/6rJFrYaspzD6XwGq/Ur8vk8i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7FaH8TpDBKL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\nPMarryYwebJ1456NhWOtVssLL0xg6FClhGNhM7WlFisUCjp06ES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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "fig = plt.figure(figsize=(10, 5))\n", "ax = fig.add_subplot(121, projection='3d')\n", "ax.plot_surface(x, y, f)\n", "ax.set_title('Original function')\n", "ax = fig.add_subplot(122, projection='3d')\n", "ax.plot_surface(x, y, fappr - f)\n", "ax.set_title('Approximation error with rank=%d, err=%3.1e' % (r, er))\n", "fig.subplots_adjust()\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Linear factor analysis & low-rank\n", "Consider a linear factor model, \n", "\n", "$$y = Ax, $$ where $y$ is a vector of length $n$, and $x$ is a vector of length $r$. \n", "The data is organizes as samples: we observe vectors \n", "$$y_1, \\ldots, y_T,$$\n", "then the factor model can be written as \n", "$$\n", " Y = AX,\n", "$$\n", "where $Y$ is $n \\times T$, $A$ is $n \\times r$ and $X$ is $r \\times T$. This is exactly a rank-$r$ model: it tells us that the vector lie in a small subspace! \n", "We also can use SVD to recover this subspace (but not the independent components). Principal component analysis can be done by SVD!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Take home message\n", "- Matrix rank definition\n", "- Skeleton approximation and dyadic representation of a rank-$r$ matrix\n", "- Singular value decomposition" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Next lecture\n", "- Linear systems\n", "- Inverse matrix\n", "- Condition number\n", "- Linear least squares\n", "- Pseudoinverse" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "##### Questions?" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open(\"./styles/custom.css\", \"r\").read()\n", " return HTML(styles)\n", "css_styling()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Slideshow", "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": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }