{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Linear Algebra II\n", "\n", "In this set of notes, we'll consider singular value and eigenvalue problems. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd # for pagerank example\n", "from matplotlib.image import imread # for image compression\n", "from matplotlib import pyplot as plt # for image compression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SVD\n", "\n", "There are lots of circumstances in which we should compute the singular value decomposition (SVD) or eigenvalue decomposition of a matrix. SVD is somewhat more general. \n", "\n", "

Everybody knows that the #SVD is the #bestmatrixdecomposition !!!

#UDVt #minimumreconstructionerror #maximalvariance #nonconvexbutstillsolvable #nothanksQR#seeyoulaterEigenDecomp#blessed https://t.co/je7Xetgfhr

— Dr. Daniela Witten (@daniela_witten) July 5, 2020
\n", "\n", "As you may remember, a *[singular value decomposition](https://en.wikipedia.org/wiki/Singular_value_decomposition)* of a real matrix $\\mathbf{A} \\in \\mathbb{R}^{m \\times n}$ is \n", "\n", "$$\\mathbf{A} = \\mathbf{U}\\mathbf{D}\\mathbf{V}^T\\;, $$\n", "\n", "where $\\mathbf{D} \\in \\mathbb{R}^{m \\times n}$ has nonzero entries (the *singular values* $\\sigma_i$) only along its diagonal, and where $\\mathbf{U} \\in \\mathbb{R}^{m \\times m}$ and $\\mathbf{V} \\in \\mathbb{R}^{n \\times n}$ are orthogonal matrices. The singular values $\\sigma_i$ collectively give some measure of how \"large\" the matrix $\\mathbf{A}$ is. \n", "\n", "Numpy makes it easy to compute the SVD of a matrix: " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4, 2, 1, 2, 2],\n", " [3, 4, 1, 2, 2],\n", " [2, 3, 3, 4, 4],\n", " [3, 2, 3, 1, 3],\n", " [2, 2, 1, 1, 4],\n", " [1, 1, 1, 1, 4],\n", " [3, 2, 2, 2, 1]])" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = np.random.randint(1, 5, size = (7, 5))\n", "A" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "U, sigma, V = np.linalg.svd(A)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([13.81539265, 3.72603666, 2.44819628, 2.09949877, 1.36015318])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sigma # singular values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the components of the SVD to reconstruct the original matrix $\\mathbf{A}$. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[13.81539265, 0. , 0. , 0. , 0. ],\n", " [ 0. , 3.72603666, 0. , 0. , 0. ],\n", " [ 0. , 0. , 2.44819628, 0. , 0. ],\n", " [ 0. , 0. , 0. , 2.09949877, 0. ],\n", " [ 0. , 0. , 0. , 0. , 1.36015318],\n", " [ 0. , 0. , 0. , 0. , 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ]])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "D = np.zeros_like(A,dtype=float) # matrix of zeros of same shape as A\n", "D[:5,:5] = np.diag(sigma)\n", "D" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[4., 2., 1., 2., 2.],\n", " [3., 4., 1., 2., 2.],\n", " [2., 3., 3., 4., 4.],\n", " [3., 2., 3., 1., 3.],\n", " [2., 2., 1., 1., 4.],\n", " [1., 1., 1., 1., 4.],\n", " [3., 2., 2., 2., 1.]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U @ D @ V # == A up to numerical precision" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[13.81539265, 0. , 0. , 0. , 0. ],\n", " [ 0. , 3.72603666, 0. , 0. , 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ],\n", " [ 0. , 0. , 0. , 0. , 0. ]])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# low-rank approximation of A\n", "D = np.zeros_like(A,dtype=float) # matrix of zeros of same shape as A\n", "D[:2,:2] = np.diag(sigma[:2])\n", "D" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[3.2096557 , 2.65898671, 1.68173466, 2.08466542, 1.67933816],\n", " [3.42226876, 2.85044822, 1.82194842, 2.24275516, 1.88861276],\n", " [3.0260681 , 2.95788871, 2.43342142, 2.55390929, 4.46809998],\n", " [2.57181111, 2.39956408, 1.85323727, 2.02138112, 3.06622612],\n", " [1.58786939, 1.76571022, 1.67849578, 1.61885415, 3.71096771],\n", " [0.68832846, 1.11390247, 1.38277045, 1.15648122, 3.83777171],\n", " [2.98553926, 2.40609154, 1.43791263, 1.85137671, 1.13203631]])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U @ D @ V # close to A, using only two singular vectors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Application: Image Compression\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To illustrate the power of SVD, let's use it to *compress images*. In general, storing an image with $m \\times n$ greyscale pixels requires storing $m \\times n$ numbers, which can be quite expensive when $m$ or $n$ are large! SVD can be used to compress images by treating them as matrices and discarding the small singular values. Let's see an example! \n", "\n", "We will use an image of Maru. Maru is a Cat On The Internet who is famous for doing stuff like this: \n", "\n", "![](https://media2.giphy.com/media/9NAXEP3RiJjm8/giphy.webp?cid=ecf05e47dbjp1upvg5ovlw54yn1j9zrhaa73vg4x5m4er4ow&rid=giphy.webp&ct=g)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-0.5, 639.5, 412.5, -0.5)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "maru = imread(\"https://i.pinimg.com/originals/0e/d0/23/0ed023847cad0d652d6371c3e53d1482.png\")\n", "plt.imshow(maru)\n", "plt.gca().axis(\"off\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Basic SVD for images only works on greyscale images -- there are ways to use SVD for color images, but this is beyond scope for today. The following simple function will convert the base image to greyscale: " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def to_greyscale(im):\n", " return 1 - np.dot(im[...,:3], [0.2989, 0.5870, 0.1140])" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-0.5, 639.5, 412.5, -0.5)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "grey_maru = to_greyscale(maru)\n", "plt.imshow(grey_maru, cmap = \"Greys\")\n", "plt.gca().axis(\"off\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can write a function that encapsulates the steps we did in the previous section to compress the matrix, keeping only the top $k$ singular values in order to reconstruct the target matrix. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def reconstruct(gs, k):\n", " U, sigma, V = np.linalg.svd(gs)\n", " D = np.zeros_like(gs,dtype=float) # matrix of zeros of same shape as A\n", " D[:k,:k] = np.diag(sigma[:k])\n", " return U @ D @ V" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axarr = plt.subplots(2, 3, figsize = (15, 7))\n", "\n", "for i in range(6):\n", " row = i // 3\n", " col = i % 3\n", " \n", " n_components = (i+1)*5\n", " \n", " axarr[row, col].imshow(reconstruct(grey_maru, n_components), cmap = \"Greys\") \n", " axarr[row, col].set(title = f\"{n_components} components, % storage = {np.round(n_components / np.min(grey_maru.shape),2)}\")\n", " axarr[row, col].axis(\"off\")\n", "\n", "# plt.imshow(reconstruct(gs,20), cmap = \"Greys\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can make a relatively clear picture with just 7% of the storage requirement! " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Eigenvalue-Eigenvector Decomposition\n", "\n", "As you may remember, the eigenvalue-eigenvector decomposition for a matrix is related to the SVD. Eigenvalue-eigenvector decompositions are especially relevant in the case of symmetric matrices. \n", "\n", "> **Spectral Theorem for Symmetric Matrices**: if $\\mathbf{A} \\in \\mathbb{R}^{n \\times n}$ is a real symmetric matrix, then there exists a real diagonal matrix $\\Lambda \\in \\mathbb{R}^{n \\times n} $ and orthogonal matrix $\\mathbf{U} \\in \\mathbb{R}^{n \\times n}$ such that $\\mathbf{A} = \\mathbf{U} \\Lambda\\mathbf{U}^T$. \n", "\n", "This theorem ensures that a real symmetric matrix $\\mathbf{A}$ possesses a full complement of *eigenvalue-eigenvector pairs* $(\\lambda, \\mathbf{u})$ which satisfy the equation \n", "\n", "$$\\mathbf{A}\\mathbf{u} = \\lambda \\mathbf{u}\\;.$$\n", "\n", "Numpy gives us a convenient function with which to calculate the eigenvalues and eigenvectors: " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "A = np.random.randint(1, 5, size = (5, 5))\n", "A = (A + A.T)/2 # symmetric version\n", "Lam, U = np.linalg.eig(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first array gives the eigenvalues of $\\mathbf{A}$, while the second array gives the eigenvectors (as columns). We can check the eigenvalue-eigenvector condition above: " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k = 0\n", "np.allclose(A @ U[:,k], Lam[k] * U[:,k])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In many cases, it's useful to get the eigenvectors corresponding to the largest or smallest eigenvalues of a matrix. This can be done via sorting: " ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([13.68905209, -1.78600902, -0.30640512, 1.83340778, 1.56995427]),\n", " array([[-0.43856823, -0.17597506, 0.02785015, 0.88085129, 0.00400728],\n", " [-0.48057741, 0.04276079, 0.44893646, -0.24168668, -0.7122222 ],\n", " [-0.45277844, -0.52913012, 0.27873659, -0.34252959, 0.5656787 ],\n", " [-0.38084075, 0.82801568, 0.12008095, -0.02977984, 0.3924845 ],\n", " [-0.47608326, -0.04019507, -0.8399803 , -0.21788803, -0.13670041]]))" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Lam, U" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-0.30640511777428914,\n", " array([ 0.02785015, 0.44893646, 0.27873659, 0.12008095, -0.8399803 ]))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# eigenvector with second-smallest eigenvalue\n", "# spoiler, you're going to need this one soon!\n", "\n", "ix = Lam.argsort()\n", "\n", "Lam, U = Lam[ix], U[:,ix]\n", "\n", "# 2nd smallest eigenvalue and corresponding eigenvector\n", "Lam[1], U[:,1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Application: PageRank\n", "\n", "The *PageRank score* provides a way to estimate the importance of entities in a network. Historically, PageRank was the algorithm used by Google to rank webpages: pages with higher PageRanks would appear higher in search results. \n", "\n", "Let's continue with the webpage example for a bit. PageRank works by allowing a \"random surfer\" to move around webpages by following links. Each time the surfer lands on a page, it then looks for all the links on that page. It then picks one at random and follows it, thereby arriving at the next page, where the process repeats. Because the surfer moves between linked pages, PageRank expresses an intuitive idea: **important pages are linked to other important pages.** [This diagram](https://en.wikipedia.org/wiki/PageRank#/media/File:PageRanks-Example.jpg) from Wikipedia gives a nice illustration. Note that more important webpages (higher PageRank) tend to be connected to other important webpages. \n", "\n", "
\n", " \"A\n", "
A schematic for PageRank.
\n", "
\n", "\n", "PageRank can be estimated via random walks, and you may even have done this in PIC16A. However, the most efficient way to compute PageRank for small-to-medium-sized data is by computing eigenvectors of matrices. (The spectral theorem above does not apply because the relevant matrix is not symmetric, but this turns out not to be a problem). Let's take a look. \n", "\n", "Our data for this example comes from the hit Broadway musical \"Hamilton.\"\n", "\n", "
\n", " \"The\n", "
The Hamilton data set
\n", "
\n", "\n", "The good folks at [The Hamilton Project](http://hamilton.newtfire.org/) analyzed the script for us, obtaining data on **who talks about whom** in each of the show's songs. When character A mentions character B, we'll think of this as a *link* from A to B, suggesting that B might be important. First we'll grab data: " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
sourcetarget
0burrhamilton
1burrweeks
2burrmadison
3burrjay
4burrtheodosiaDaughter
\n", "
" ], "text/plain": [ " source target\n", "0 burr hamilton\n", "1 burr weeks\n", "2 burr madison\n", "3 burr jay\n", "4 burr theodosiaDaughter" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "url = \"https://philchodrow.github.io/PIC16A/homework/HW3-hamilton-data.csv\"\n", "df = pd.read_csv(url, names = [\"source\", \"target\"])\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we construct the matrix of directed links: " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "# construct matrix of directed links \n", "# A[i,j] is the number of times that i mentions j\n", "\n", "N = np.unique(np.concatenate((df.source, df.target))) # get all unique nodes\n", "\n", "n = len(N)\n", "\n", "name_to_ix = {N[i] : i for i in range(n)}\n", "\n", "A = np.zeros((n, n))\n", "\n", "for row in df.iterrows():\n", " ix_i = name_to_ix[row[1].source]\n", " ix_j = name_to_ix[row[1].target]\n", " A[ix_i, ix_j] += 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From this we construct the so-called PageRank matrix. " ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ ":5: RuntimeWarning: divide by zero encountered in true_divide\n", " D_inv = np.diag(1/A.sum(axis = 1))\n" ] } ], "source": [ "# form the PageRank matrix\n", "\n", "# normalized adjacency matrix, corresponding to the transition\n", "# of a random walk\n", "D_inv = np.diag(1/A.sum(axis = 1))\n", "D_inv[np.isinf(D_inv)] = 0\n", "M = np.dot(A, D_inv)\n", "\n", "# teleportation parameter\n", "a = 0.15\n", "\n", "# \n", "P = (1-a)*M + a*np.ones((n, n))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The leading eigenvector of the PageRank matrix is guaranteed to be real and positive with eigenvalue 1.0 (from the theory of Markov chains). We single this one out -- it's the one we want! " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "eigs = np.linalg.eig(M)\n", "s = np.real(eigs[1][:,eigs[0] == 1.0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's make a nice display: " ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
characterPageRank
14hamilton0.815778
3burr0.381702
17jefferson0.238992
4company0.206834
43washington0.160793
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" ], "text/plain": [ " character PageRank\n", "14 hamilton 0.815778\n", "3 burr 0.381702\n", "17 jefferson 0.238992\n", "4 company 0.206834\n", "43 washington 0.160793" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# display as a sorted data frame\n", "ranks = pd.DataFrame({\n", " \"character\" : [N[i] for i in range(len(N))],\n", " \"PageRank\" : [s[i][0] for i in range(len(N))]\n", "})\n", "ranks.sort_values(\"PageRank\", ascending = False).head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Through Power of Linear Algebra, we have discovered that Alexander Hamilton is the main character of the musical *Hamilton*. " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }