{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 4. Randomized Projection & Randomized SVD" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true }, "source": [ "## Part 1: Random Projections (with word vectors)" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "The purpose of this section is to illustrate the idea of **random projections preserving structure** with the concrete example of **word vectors**!\n", "\n", "To use language in machine learning (for instance, how Skype translator translates between languages, or how Gmail Smart Reply automatically suggests possible responses for your emails), we need to represent words as vectors." ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "We can represent words as 100 dimensional vectors, using Google's Word2Vec or Stanford's GloVe. For example, here is the word \"python\" as a vector in GloVe:" ] }, { "cell_type": "code", "execution_count": 147, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "array([ 0.2493, 0.6832, -0.0447, -1.3842, -0.0073, 0.651 , -0.3396,\n", " -0.1979, -0.3392, 0.2669, -0.0331, 0.1592, 0.8955, 0.54 ,\n", " -0.5582, 0.4624, 0.3672, 0.1889, 0.8319, 0.8142, -0.1183,\n", " -0.5346, 0.2416, -0.0389, 1.1907, 0.7935, -0.1231, 0.6642,\n", " -0.7762, -0.4571, -1.054 , -0.2056, -0.133 , 0.1224, 0.8846,\n", " 1.024 , 0.3229, 0.821 , -0.0694, 0.0242, -0.5142, 0.8727,\n", " 0.2576, 0.9153, -0.6422, 0.0412, -0.6021, 0.5463, 0.6608,\n", " 0.198 , -1.1393, 0.7951, 0.4597, -0.1846, -0.6413, -0.2493,\n", " -0.4019, -0.5079, 0.8058, 0.5336, 0.5273, 0.3925, -0.2988,\n", " 0.0096, 0.9995, -0.0613, 0.7194, 0.329 , -0.0528, 0.6714,\n", " -0.8025, -0.2579, 0.4961, 0.4808, -0.684 , -0.0122, 0.0482,\n", " 0.2946, 0.2061, 0.3356, -0.6417, -0.6471, 0.1338, -0.1257,\n", " -0.4638, 1.3878, 0.9564, -0.0679, -0.0017, 0.5296, 0.4567,\n", " 0.6104, -0.1151, 0.4263, 0.1734, -0.7995, -0.245 , -0.6089,\n", " -0.3847, -0.4797], dtype=float32)" ] }, "execution_count": 147, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vecs[wordidx['python']]" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "**Goal**: Use randomness to reduce this from 100 dimensions to 20. Check that similar words are still grouped together." ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "**More info**: If you are interested in word embeddings and want more detail, I gave a longer workshop about them [available here](https://www.youtube.com/watch?v=25nC0n9ERq4) (with [code demo](https://github.com/fastai/word-embeddings-workshop))." ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "**Style note**: I use [collapsible headings](http://jupyter-contrib-nbextensions.readthedocs.io/en/latest/nbextensions/collapsible_headings/readme.html) and [jupyter themes](https://github.com/dunovank/jupyter-themes)" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "#### Loading the data" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "import pickle\n", "import numpy as np\n", "import re\n", "import json" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "np.set_printoptions(precision=4, suppress=True)" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "The dataset is available at http://files.fast.ai/models/glove/6B.100d.tgz\n", "To download and unzip the files from the command line, you can run:\n", "\n", " wget http://files.fast.ai/models/glove_50_glove_100.tgz \n", " tar xvzf glove_50_glove_100.tgz" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "You will need to update the path below to be accurate for where you are storing the data." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "path = \"../data/\"" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "vecs = np.load(path + \"glove_vectors_100d.npy\")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "with open(path + \"words.txt\") as f:\n", " content = f.readlines()\n", "words = [x.strip() for x in content] " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "wordidx = json.load(open(path + \"wordsidx.txt\"))" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "#### What our data looks like" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "We have a long list of words:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "400000" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(words)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "['the', ',', '.', 'of', 'to', 'and', 'in', 'a', '\"', \"'s\"]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "words[:10]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "['together',\n", " 'congress',\n", " 'index',\n", " 'australia',\n", " 'results',\n", " 'hard',\n", " 'hours',\n", " 'land',\n", " 'action',\n", " 'higher']" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "words[600:610]" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "wordidx allows us to look up a word in order to find out it's index:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "20019" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wordidx['python']" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "'python'" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "words[20019]" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "### Words as vectors" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "The word \"python\" is represented by the 100 dimensional vector:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "array([ 0.2493, 0.6832, -0.0447, -1.3842, -0.0073, 0.651 , -0.3396,\n", " -0.1979, -0.3392, 0.2669, -0.0331, 0.1592, 0.8955, 0.54 ,\n", " -0.5582, 0.4624, 0.3672, 0.1889, 0.8319, 0.8142, -0.1183,\n", " -0.5346, 0.2416, -0.0389, 1.1907, 0.7935, -0.1231, 0.6642,\n", " -0.7762, -0.4571, -1.054 , -0.2056, -0.133 , 0.1224, 0.8846,\n", " 1.024 , 0.3229, 0.821 , -0.0694, 0.0242, -0.5142, 0.8727,\n", " 0.2576, 0.9153, -0.6422, 0.0412, -0.6021, 0.5463, 0.6608,\n", " 0.198 , -1.1393, 0.7951, 0.4597, -0.1846, -0.6413, -0.2493,\n", " -0.4019, -0.5079, 0.8058, 0.5336, 0.5273, 0.3925, -0.2988,\n", " 0.0096, 0.9995, -0.0613, 0.7194, 0.329 , -0.0528, 0.6714,\n", " -0.8025, -0.2579, 0.4961, 0.4808, -0.684 , -0.0122, 0.0482,\n", " 0.2946, 0.2061, 0.3356, -0.6417, -0.6471, 0.1338, -0.1257,\n", " -0.4638, 1.3878, 0.9564, -0.0679, -0.0017, 0.5296, 0.4567,\n", " 0.6104, -0.1151, 0.4263, 0.1734, -0.7995, -0.245 , -0.6089,\n", " -0.3847, -0.4797], dtype=float32)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vecs[wordidx['python']]" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "This lets us do some useful calculations. For instance, we can see how far apart two words are using a distance metric:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "from scipy.spatial.distance import cosine as dist" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "Smaller numbers mean two words are closer together, larger numbers mean they are further apart." ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "The distance between similar words is low:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "0.27636240676695256" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dist(vecs[wordidx[\"puppy\"]], vecs[wordidx[\"dog\"]])" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "0.20527545040329642" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dist(vecs[wordidx[\"queen\"]], vecs[wordidx[\"princess\"]])" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "hidden": true }, "source": [ "And the distance between unrelated words is high:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "0.98835787578057777" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dist(vecs[wordidx[\"celebrity\"]], vecs[wordidx[\"dusty\"]])" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "0.96211070091611983" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dist(vecs[wordidx[\"avalanche\"]], vecs[wordidx[\"antique\"]])" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "#### Bias" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "There is a lot of opportunity for bias:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "0.50985148631697985" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dist(vecs[wordidx[\"man\"]], vecs[wordidx[\"genius\"]])" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "0.6897833082810727" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dist(vecs[wordidx[\"woman\"]], vecs[wordidx[\"genius\"]])" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "I just checked the distance between pairs of words, because this is a quick and simple way to illustrate the concept. It is also a very **noisy** approach, and **researchers approach this problem in more systematic ways**.\n", "\n", "I talk about bias in much greater depth in [this workshop](https://www.youtube.com/watch?v=25nC0n9ERq4)." ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "### Visualizations" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "Let's visualize some words!\n", "\n", "We will use [Plotly](https://plot.ly/), a Python library to make interactive graphs (note: everything below is done without creating an account, with the free, offline version of Plotly)." ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "#### Methods" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "import plotly\n", "import plotly.graph_objs as go \n", "from IPython.display import IFrame" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "def plotly_3d(Y, cat_labels, filename=\"temp-plot.html\"):\n", " trace_dict = {}\n", " for i, label in enumerate(cat_labels):\n", " trace_dict[i] = go.Scatter3d(\n", " x=Y[i*5:(i+1)*5, 0],\n", " y=Y[i*5:(i+1)*5, 1],\n", " z=Y[i*5:(i+1)*5, 2],\n", " mode='markers',\n", " marker=dict(\n", " size=8,\n", " line=dict(\n", " color='rgba('+ str(i*40) + ',' + str(i*40) + ',' + str(i*40) + ', 0.14)',\n", " width=0.5\n", " ),\n", " opacity=0.8\n", " ),\n", " text = my_words[i*5:(i+1)*5],\n", " name = label\n", " )\n", "\n", " data = [item for item in trace_dict.values()]\n", " layout = go.Layout(\n", " margin=dict(\n", " l=0,\n", " r=0,\n", " b=0,\n", " t=0\n", " )\n", " )\n", "\n", " plotly.offline.plot({\n", " \"data\": data,\n", " \"layout\": layout,\n", " }, filename=filename)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "def plotly_2d(Y, cat_labels, filename=\"temp-plot.html\"):\n", " trace_dict = {}\n", " for i, label in enumerate(cat_labels):\n", " trace_dict[i] = go.Scatter(\n", " x=Y[i*5:(i+1)*5, 0],\n", " y=Y[i*5:(i+1)*5, 1],\n", " mode='markers',\n", " marker=dict(\n", " size=8,\n", " line=dict(\n", " color='rgba('+ str(i*40) + ',' + str(i*40) + ',' + str(i*40) + ', 0.14)',\n", " width=0.5\n", " ),\n", " opacity=0.8\n", " ),\n", " text = my_words[i*5:(i+1)*5],\n", " name = label\n", " )\n", "\n", " data = [item for item in trace_dict.values()]\n", " layout = go.Layout(\n", " margin=dict(\n", " l=0,\n", " r=0,\n", " b=0,\n", " t=0\n", " )\n", " )\n", "\n", " plotly.offline.plot({\n", " \"data\": data,\n", " \"layout\": layout\n", " }, filename=filename)" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "This method will pick out the 3 dimensions that best separate our categories from one another (stored in `dist_btwn_cats`), while minimizing the distance of the words within a given category (stored in `dist_within_cats`)." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "def get_components(data, categories, word_indices):\n", " num_components = 30\n", " pca = decomposition.PCA(n_components=num_components).fit(data.T)\n", " all_components = pca.components_\n", " centroids = {}\n", " print(all_components.shape)\n", " for i, category in enumerate(categories):\n", " cen = np.mean(all_components[:, i*5:(i+1)*5], axis = 1)\n", " dist_within_cats = np.sum(np.abs(np.expand_dims(cen, axis=1) - all_components[:, i*5:(i+1)*5]), axis=1)\n", " centroids[category] = cen\n", " dist_btwn_cats = np.zeros(num_components)\n", " for category1, averages1 in centroids.items():\n", " for category2, averages2 in centroids.items():\n", " dist_btwn_cats += abs(averages1 - averages2)\n", " clusterness = dist_btwn_cats / dist_within_cats\n", " comp_indices = np.argpartition(clusterness, -3)[-3:]\n", " return all_components[comp_indices]" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "### Preparing the Data" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "Let's plot words from a few different categories:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "my_words = [\n", " \"maggot\", \"flea\", \"tarantula\", \"bedbug\", \"mosquito\", \n", " \"violin\", \"cello\", \"flute\", \"harp\", \"mandolin\",\n", " \"joy\", \"love\", \"peace\", \"pleasure\", \"wonderful\",\n", " \"agony\", \"terrible\", \"horrible\", \"nasty\", \"failure\", \n", " \"physics\", \"chemistry\", \"science\", \"technology\", \"engineering\",\n", " \"poetry\", \"art\", \"literature\", \"dance\", \"symphony\",\n", " ]" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "categories = [\n", " \"bugs\", \"music\", \n", " \"pleasant\", \"unpleasant\", \n", " \"science\", \"arts\"\n", " ]" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "Again, we need to look up the indices of our words using the wordidx dictionary:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "my_word_indices = np.array([wordidx[word] for word in my_words])" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "(30, 100)" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vecs[my_word_indices].shape" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "Now, we will make a set combining our words with the first 10,000 words in our entire set of words (some of the words will already be in there), and create a matrix of their embeddings." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "(10030, 100)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "embeddings = np.concatenate((vecs[my_word_indices], vecs[:10000,:]), axis=0); embeddings.shape" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "### Viewing the words in 3D" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "The words are in 100 dimensions and we need a way to visualize them in 3D. \n", "\n", "We will use Principal Component Analysis (PCA), a widely used technique with many applications, including visualizing high-dimensional data sets in a lower dimension!" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "#### PCA" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "from collections import defaultdict\n", "from sklearn import decomposition" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "hidden": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(30, 10030)\n" ] } ], "source": [ "components = get_components(embeddings, categories, my_word_indices)\n", "plotly_3d(components.T[:len(my_words),:], categories, \"pca.html\")" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "hidden": true, "scrolled": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "IFrame('pca.html', width=600, height=400)" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true, "hidden": true }, "source": [ "### Random Projections" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "**Johnson-Lindenstrauss Lemma**: ([from wikipedia](https://en.wikipedia.org/wiki/Johnson%E2%80%93Lindenstrauss_lemma)) a small set of points in a high-dimensional space can be embedded into a space of much lower dimension in such a way that distances between the points are nearly preserved (proof uses random projections).\n", "\n", "It is useful to be able to reduce dimensionality of data in a way that **preserves distances**. The Johnson\u2013Lindenstrauss lemma is a classic result of this type." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "(10030, 100)" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "embeddings.shape" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "(10030, 40)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rand_proj = embeddings @ np.random.normal(size=(embeddings.shape[1], 40)); rand_proj.shape" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "hidden": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(30, 10030)\n" ] } ], "source": [ "# pca = decomposition.PCA(n_components=3).fit(rand_proj.T)\n", "# components = pca.components_\n", "components = get_components(rand_proj, categories, my_word_indices)\n", "plotly_3d(components.T[:len(my_words),:], categories, \"pca-rand-proj.html\")" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "hidden": true, "scrolled": true }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "IFrame('pca-rand-proj.html', width=600, height=400)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Part 2: Random SVD for Background Removal" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Our goal today**: ![background removal](images/surveillance3.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Load and Format the Data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use the real video 003 dataset from [BMC 2012 Background Models Challenge Dataset](http://bmc.iut-auvergne.com/?page_id=24)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Import needed libraries:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import imageio\n", "imageio.plugins.ffmpeg.download()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "scrolled": true }, "outputs": [], "source": [ "import moviepy.editor as mpe\n", "import numpy as np\n", "import scipy\n", "\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "scale = 0.50 # Adjust scale to change resolution of image\n", "dims = (int(240 * scale), int(320 * scale))\n", "fps = 60 # frames per second" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "M = np.load(\"movie/med_res_surveillance_matrix_60fps.npy\")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(120, 160) (19200, 6000)\n" ] } ], "source": [ "print(dims, M.shape)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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AZ/1IKgOMOmVUpAygs1ug2lB0pge6dq5ImBzNfplcx1mMhiv2sTNvryNiTH12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\nSUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(M[:,140], dims), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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4ikxBiqIgFAoZ7swbCbOyREyM/d5pOCn0mtXBSRBHQADo6uqqEagJeEIxC55W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hW4CG0ZHByE0+kEAHoiaWlpKXJzcxNoACski4RJth3C4TD6+voQDAbR09ODD33oQwnvsc+yY0NU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\n/VUtIzf/VMtetSMOUpj08oM9Fz/LwhLRTbPob1BtvdFopnSr9JdhhsUj9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12, 12))\n", "plt.imshow(M, cmap='gray')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the future, you can just load what you've saved:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "U = np.load(\"U.npy\")\n", "s = np.load(\"s.npy\")\n", "V = np.load(\"V.npy\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What do $U$, $S$, and $V$ look like?" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((19200, 6000), (6000,), (6000, 6000))" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U.shape, s.shape, V.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check that they are a decomposition of M" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "reconstructed_matrix = U @ np.diag(s) @ V" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(M, reconstructed_matrix)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "They are! :-)" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true }, "source": [ "### Removing the background" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "low_rank = np.expand_dims(U[:,0], 1) * s[0] * np.expand_dims(V[0,:], 0)" ] }, { "cell_type": "code", "execution_count": 360, "metadata": { "hidden": true, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 360, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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XQM5K4ESpaboIoWr691LRwhdK7Ht8nRXSdvOWRfUBrLknJg57e3vDmTNn5i7GrFjygO8N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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12, 12))\n", "plt.imshow(low_rank, cmap='gray')" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "hidden": true }, "outputs": [ { "data": { "image/png": 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j1pNlmV89jbKioqLiLcRcME3KZaYR6msgCa44ekKlfqoMxQXVfedwZ3IfoGu+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\n3idayeJgbmxsdBQkmeH/NM9M7+tL2/dMFJFLo4+/ra2t1NRF25Qxcjd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(low_rank[:,0], dims), cmap='gray');" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "How do we get the people from here?" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "hidden": true, "scrolled": true }, "outputs": [ { "data": { "image/png": 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/zufM2Az5vlfPJ/cliwM1eLt4FLutbKRLPemHnjRba28B8ETv/SOttTeqc3rv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\n9s80s9Ls+ZwJz4u+eywxN3hciCPoBwA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(M[:,0] - low_rank[:,0], dims), cmap='gray');" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true }, "source": [ "### Speed of SVD for different size matrices" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "s is the diagonal of a *diagonal matrix*" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "np.set_printoptions(suppress=True, precision=4)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "import timeit\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "m_array = np.array([100, int(1e3), int(1e4)])\n", "n_array = np.array([100, int(1e3), int(1e4)])" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "index = pd.MultiIndex.from_product([m_array, n_array], names=['# rows', '# cols'])" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "pd.options.display.float_format = '{:,.3f}'.format\n", "df = pd.DataFrame(index=m_array, columns=n_array)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "# %%prun\n", "for m in m_array:\n", " for n in n_array: \n", " A = np.random.uniform(-40,40,[m,n]) \n", " t = timeit.timeit('np.linalg.svd(A, full_matrices=False)', number=3, globals=globals())\n", " df.set_value(m, n, t)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "hidden": true, "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " 100 1000 10000\n", "100 0.006 0.009 0.043\n", "1000 0.004 0.259 0.992\n", "10000 0.019 0.984 218.726" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df/3" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### That's pretty neat!!! but..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Downside: this was really slow (also, we threw away a lot of our calculation)**" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 5min 38s, sys: 1.53 s, total: 5min 40s\n", "Wall time: 57.1 s\n" ] } ], "source": [ "%time u, s, v = np.linalg.svd(M, full_matrices=False)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(19200, 6000)" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Simplest Version of Randomized SVD" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Idea**: Let's use a smaller matrix!\n", "\n", "We haven't found a better general SVD method, we'll just use the method we have on a smaller matrix that has approximately the same range as our original matrix." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def simple_randomized_svd(M, k=10):\n", " m, n = M.shape\n", " transpose = False\n", " if m < n:\n", " transpose = True\n", " M = M.T\n", " \n", " rand_matrix = np.random.normal(size=(M.shape[1], k)) # short side by k\n", " Q, _ = np.linalg.qr(M @ rand_matrix, mode='reduced') # long side by k\n", " smaller_matrix = Q.T @ M # k by short side\n", " U_hat, s, V = np.linalg.svd(smaller_matrix, full_matrices=False)\n", " U = Q @ U_hat\n", " \n", " if transpose:\n", " return V.T, s.T, U.T\n", " else:\n", " return U, s, V" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 3.06 s, sys: 268 ms, total: 3.33 s\n", "Wall time: 789 ms\n" ] } ], "source": [ "%time u, s, v = simple_randomized_svd(M, 10)" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": true, "scrolled": true }, "outputs": [], "source": [ "U_rand, s_rand, V_rand = simple_randomized_svd(M, 10)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": true }, "outputs": [], "source": [ "low_rank = np.expand_dims(U_rand[:,0], 1) * s_rand[0] * np.expand_dims(V_rand[0,:], 0)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": 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B3Y2yoqKi4k3EXDBN2mWynJo8Btidgfbu3dsRwvqMrWFlPqv07cPtzEYZmctX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\nM4J7a9Xb2mfnUZRSOp5dZ39RRJAzVyDfI8gZq6oOnO1pO9L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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(low_rank[:,0], dims), cmap='gray');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How do we get the people from here?" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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nhhlh6ZdmKeUVAB6utf5tKeUlXppaay2luNy5lHI9gOsB4MSJE/vWn3o3RZ3T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\nQD31inzwXn5RQLRVRg/GMsqBgYGBCViZZZSRRCS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(M[:,0] - low_rank[:,0], dims), cmap='gray');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### What this method is doing" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rand_matrix = np.random.normal(size=(M.shape[1], 10))" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(6000, 10)" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rand_matrix.shape" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "image/png": 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DPafLQHESm41KabkvI/HMsjCrwvuW9x73nHuTu+J0IViGzc8XQ0IoZmsLLu91OGoKf/gd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\nz4mfoVtEERRpMaP9jHKz1iHXpTNjwj2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(rand_matrix[:4900,0], (70,70)), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(19200, 10)" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "temp = M @ rand_matrix; temp.shape" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "image/png": 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0GeoKxFmtevP12O3t7Srk0MfdZDLpx9errx7vYfjaa6/NtOHpp5/u7/9Xv/pV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\ngfbSbGhoaFgC/x8KpxT2Z1sHjQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(temp[:,0], dims), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "image/png": 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oSxwDHwvC3dFY/tbWVttWrtz8TlZ+fHycrdhkC9r/UkxRZ8Kz2VlGR5dLKYsr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\n6keD8k984hMA5s1rgJOYns4OqCR6/vnnAZys5GSjHvfPA1BE0bKd4UW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(temp[:,1], dims), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(19200, 10)" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Q, _ = np.linalg.qr(M @ rand_matrix, mode='reduced'); Q.shape" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-3.8163916471489756e-17" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.dot(Q[:,0], Q[:,1])" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "image/png": 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0GeoKxFmtevP12O3t7Srk0MfdZDLpx9errx7vYfjaa6/NtOHpp5/u7/9Xv/pV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\ngfbSbGhoaFgC/x8KpxT2Z1sHjQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(Q[:,0], dims), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "image/png": 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z+YxGo6kXBHTDKdV1hoNFtzPAtFsRy3N3Fv7Q19fXO1sY34apoYX3UvnuxpDj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\nKioqFkCdNCsqKioWwP8PyALLgCQcFfsAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(Q[:,1], dims), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(10, 6000)" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "smaller_matrix = Q.T @ M; smaller_matrix.shape" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "collapsed": true }, "outputs": [], "source": [ "U_hat, s, V = np.linalg.svd(smaller_matrix, full_matrices=False)" ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": true }, "outputs": [], "source": [ "U = Q @ U_hat" ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "image/png": 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ZZkVFRcUUmAmmCXTDDp1tEJpIgisOnXF9xdawMl9VMh2W3jNaCTNDiOtbJtEh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\nG65LdstupGt2Jtbn3kRmQZak7eU9nAVFllmyGQ1l5DVZGjq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(U[:,0], dims), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": true }, "outputs": [], "source": [ "reconstructed_small_M = U @ np.diag(s) @ V" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the people:" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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RWC/6sZhmKeU6AP8VgPfT4bcD+MD8/x8A8I7jtJFIJBKrhOMyzX8K4B8CeA4d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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(M[:,0] - reconstructed_small_M[:,0], dims), cmap='gray');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Timing Comparison" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn import decomposition\n", "import fbpca" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Full SVD:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 5min 38s, sys: 1.53 s, total: 5min 40s\n", "Wall time: 57.1 s\n" ] } ], "source": [ "%time u, s, v = np.linalg.svd(M, full_matrices=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our (overly simplified) randomized_svd from above:" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 2.37 s, sys: 160 ms, total: 2.53 s\n", "Wall time: 641 ms\n" ] } ], "source": [ "%time u, s, v = simple_randomized_svd(M, 10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Scikit learn:" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 19.2 s, sys: 1.44 s, total: 20.7 s\n", "Wall time: 3.67 s\n" ] } ], "source": [ "%time u, s, v = decomposition.randomized_svd(M, 10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Randomized SVD from Facebook's library fbpca:" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 7.28 s, sys: 424 ms, total: 7.7 s\n", "Wall time: 1.37 s\n" ] } ], "source": [ "%time u, s, v = fbpca.pca(M, 10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I would choose fbpca, since it's faster than sklearn but more robust and more accurate than our simple implementation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are some results from [Facebook Research](https://research.fb.com/fast-randomized-svd/):\n", "\n", "\"\"" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true }, "source": [ "#### Time and Accuracy vary with k" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "import timeit\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "U_rand, s_rand, V_rand = fbpca.pca(M, 700, raw=True)\n", "reconstructed = U_rand @ np.diag(s_rand) @ V_rand" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "1.1065914828881536e-07" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.norm(M - reconstructed)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "hidden": true }, "outputs": [ { "data": { "image/png": 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S31WWx61yPb5/aWmps2LzdoxWn30OHJcfunNsfX09fc/HoTLNioqKiikwE0yT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\nR9pymFnewzNLGSbYoJPJ+6+y6Mx5El0/u0+gKwN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(reconstructed[:,140], dims), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "pd.options.display.float_format = '{:,.2f}'.format\n", "k_values = np.arange(100,1000,100)\n", "df_rand = pd.DataFrame(index=[\"time\", \"error\"], columns=k_values)\n", "\n", "# df_rand = pd.read_pickle(\"svd_df\")" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "for k in k_values:\n", " U_rand, s_rand, V_rand = fbpca.pca(M, k, raw=True)\n", " reconstructed = U_rand @ np.diag(s_rand) @ V_rand\n", " df_rand.set_value(\"error\", k, np.linalg.norm(M - reconstructed))\n", " t = timeit.timeit('fbpca.pca(M, k)', number=3, globals=globals())\n", " df_rand.set_value(\"time\", k, t/3)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "df_rand.to_pickle(\"df_rand\")" ] }, { "cell_type": "code", "execution_count": 117, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/html": [ "
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time2.072.573.456.447.999.0210.2411.7013.3010.87
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" ], "text/plain": [ " 100 200 300 400 500 600 700 800 \\\n", "time 2.07 2.57 3.45 6.44 7.99 9.02 10.24 11.70 \n", "error 58,997.27 37,539.54 26,569.89 18,769.37 12,559.34 6,936.17 0.00 0.00 \n", "\n", " 900 1000 \n", "time 13.30 10.87 \n", "error 0.00 0.00 " ] }, "execution_count": 117, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df_rand" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "df = pd.DataFrame(index=[\"error\"], columns=k_values)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "for k in k_values:\n", " reconstructed = U[:,:k] @ np.diag(s[:k]) @ V[:k,:]\n", " df.set_value(\"error\", k, np.linalg.norm(M - reconstructed))" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "df.to_pickle(\"df\")" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "hidden": true }, "outputs": [ { "data": { "image/png": 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PP5Y4TqkCbj3bbtB1QQRcGcDuz07T+JkQHCLWzPpKuUj8D/Fl7nPUc5x1f52QOmfdX+Z5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\nusxsh5mNIfSExks6Nm1dki4AVpvZW+2tk+b3CJw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax1 = plt.subplots()\n", "ax1.plot(df.columns, df_rand.loc[\"time\"].values, 'b-', label=\"randomized SVD time\")\n", "ax1.plot(df.columns, np.tile([57], 9), 'g-', label=\"SVD time\")\n", "ax1.set_xlabel('k: # of singular values')\n", "# Make the y-axis label, ticks and tick labels match the line color.\n", "ax1.set_ylabel('time', color='b')\n", "ax1.tick_params('y', colors='b')\n", "ax1.legend(loc = 0)\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(df.columns, df_rand.loc[\"error\"].values, 'r--', label=\"randomized SVD error\")\n", "ax2.plot(df.columns, df.loc[\"error\"].values, 'm--', label=\"SVD error\")\n", "ax2.set_ylabel('error', color='r')\n", "ax2.tick_params('y', colors='r')\n", "ax2.legend(loc=1)\n", "\n", "#fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Math Details" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Process behind Randomized SVD" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is a process to calculate a truncated SVD, described in [Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions](https://arxiv.org/pdf/0909.4061.pdf) and [summarized in this blog post](https://research.fb.com/fast-randomized-svd/):\n", "\n", "1\\. Compute an approximation to the range of $A$. That is, we want $Q$ with $r$ orthonormal columns such that $$A \\approx QQ^TA$$\n", "\n", "\n", "2\\. Construct $B = Q^T A$, which is small ($r\\times n$)\n", "\n", "\n", "3\\. Compute the SVD of $B$ by standard methods (fast since $B$ is smaller than $A$), $B = S\\,\\Sigma V^T$\n", "\n", "4\\. Since $$ A \\approx Q Q^T A = Q (S\\,\\Sigma V^T)$$ if we set $U = QS$, then we have a low rank approximation $A \\approx U \\Sigma V^T$." ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true }, "source": [ "#### So how do we find $Q$ (in step 1)?" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "To estimate the range of $A$, we can just take a bunch of random vectors $w_i$, evaluate the subspace formed by $Aw_i$. We can form a matrix $W$ with the $w_i$ as it's columns. Now, we take the QR decomposition of $AW = QR$, then the columns of $Q$ form an orthonormal basis for $AW$, which is the range of $A$.\n", "\n", "Since the matrix $AW$ of the product has far more rows than columns and therefore, approximately, orthonormal columns. This is simple probability - with lots of rows, and few columns, it's unlikely that the columns are linearly dependent." ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true }, "source": [ "#### Why M ~ Q Q.T M" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "We are trying to find a matrix Q such that $M \\approx Q Q^T M$. We are interested in the range of $M$, let's call this $MX$. $Q$ has orthonormal columns so $Q^TQ = I$ (but $QQ^T$ isn't $I$, since $Q$ is rectangular)\n", "\n", "$$ QR = MX $$\n", "$$ QQ^TQR = QQ^TMX $$\n", "$$ QR = QQ^TMX $$\n", "so...\n", "$$ MX = QQ^TMX $$\n", "\n", "If $X$ is the identity, we'd be done (but then $X$ would be too big, and we wouldn't get the speed up we're looking for). In our problem, $X$ is just a small random matrix. The Johnson-Lindenstrauss Lemma provides some justification of why this works." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### The QR Decomposition" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will be learning about the QR decomposition **in depth** later on. For now, you just need to know that $A = QR$, where $Q$ consists of orthonormal columns, and $R$ is upper triangular. Trefethen says that the QR decomposition is the most important idea in numerical linear algebra! We will definitely be returning to it." ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true }, "source": [ "#### How should we choose $r$?" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "Suppose our matrix has 100 columns, and we want 5 columns in U and V. To be safe, we should project our matrix onto an orthogonal basis with a few more rows and columns than 5 (let's use 15). At the end, we will just grab the first 5 columns of U and V\n", "\n", "So even although our projection was only approximate, by making it a bit bigger than we need, we can make up for the loss of accuracy (since we're only taking a subset later). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### How this is different from random mean" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(4800, 2)" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "test = M @ np.random.normal(size=(M.shape[1], 2)); test.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Random mean:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": 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W4dIM3bIJTkcEhhqMW/pAdSa3qmFv9UGn8TltdUo5M3dNVz6stwSFW9lRcTGH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\nQh6OIYQwQh6OIYQwQh6OIYQwwv8HsXDOfE53XhEAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(test[:,0], dims), cmap='gray');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mean image:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(M.mean(axis=1), dims), cmap='gray')" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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Uq6zcSv/rE8Z5rDaIVy5CrWzaSuNTc8v3s88ui+q5ze22stJnlpJN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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(test[:,1], dims), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ut, st, vt = np.linalg.svd(test, full_matrices=False)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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Wom0LwW+OxhjTgSdHY4zpwJOjMcZ0MPVQHqU9ZSZNI+LjtLQbpX+o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\nDjw5GmNMB54cjTGmA0+OxhjTwf8HdZ+QVOXxnJAAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(smaller_matrix[0,:], dims), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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Lw46ybsf2cehMvv84PCfPC2t6q1bVyXJ5JcDWioyqariCQ42yvZze2Be/ORpj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\naC3voWxX+6q4x1aM65BVIDN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(smaller_matrix[1,:], dims), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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6Wot7lHKJUKF9fK4KBVOuMy2uRTXdTrmxKJQOq8LLmBaXIKVZtezY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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(M[:,140], dims), cmap='gray');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Part 3: Random SVD for Topic Modeling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Randomized SVD" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Reminder: full SVD is **slow**. This is the calculation we did above using Scipy's Linalg SVD:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "vectors = np.load(\"topics/vectors.npy\")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2034, 26576)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vectors.shape" ] }, { "cell_type": "code", "execution_count": 344, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 27.2 s, sys: 812 ms, total: 28 s\n", "Wall time: 27.9 s\n" ] } ], "source": [ "%time U, s, Vh = linalg.svd(vectors, full_matrices=False)" ] }, { "cell_type": "code", "execution_count": 345, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(2034, 2034) (2034,) (2034, 26576)\n" ] } ], "source": [ "print(U.shape, s.shape, Vh.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fortunately, there is a faster way:" ] }, { "cell_type": "code", "execution_count": 175, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 144 ms, sys: 8 ms, total: 152 ms\n", "Wall time: 154 ms\n" ] } ], "source": [ "%time u, s, v = decomposition.randomized_svd(vectors, 5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The runtime complexity for SVD is $\\mathcal{O}(\\text{min}(m^2 n,\\; m n^2))$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question**: How can we speed things up? (without new breakthroughs in SVD research)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Idea**: Let's use a smaller matrix (with smaller $n$)!\n", "\n", "Instead of calculating the SVD on our full matrix $A$ which is $m \\times n$, let's use $B = A Q$, which is just $m \\times r$ and $r << n$\n", "\n", "We haven't found a better general SVD method, we are just using the method we have on a smaller matrix." ] }, { "cell_type": "code", "execution_count": 175, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 144 ms, sys: 8 ms, total: 152 ms\n", "Wall time: 154 ms\n" ] } ], "source": [ "%time u, s, v = decomposition.randomized_svd(vectors, 5)" ] }, { "cell_type": "code", "execution_count": 177, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((2034, 5), (5,), (5, 26576))" ] }, "execution_count": 177, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u.shape, s.shape, v.shape" ] }, { "cell_type": "code", "execution_count": 178, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['jpeg image edu file graphics images gif data',\n", " 'jpeg gif file color quality image jfif format',\n", " 'space jesus launch god people satellite matthew atheists',\n", " 'jesus god matthew people atheists atheism does graphics',\n", " 'image data processing analysis software available tools display']" ] }, "execution_count": 178, "metadata": {}, "output_type": "execute_result" } ], "source": [ "show_topics(v)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Randomized SVD, version 2" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy import linalg" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The method `randomized_range_finder` finds an orthonormal matrix whose range approximates the range of A (step 1 in our algorithm above). To do so, we use the LU and QR factorizations, both of which we will be covering in depth later.\n", "\n", "I am using the [scikit-learn.extmath.randomized_svd source code](https://github.com/scikit-learn/scikit-learn/blob/14031f65d144e3966113d3daec836e443c6d7a5b/sklearn/utils/extmath.py) as a guide." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# computes an orthonormal matrix whose range approximates the range of A\n", "# power_iteration_normalizer can be safe_sparse_dot (fast but unstable), LU (imbetween), or QR (slow but most accurate)\n", "def randomized_range_finder(A, size, n_iter=5):\n", " Q = np.random.normal(size=(A.shape[1], size))\n", " \n", " for i in range(n_iter):\n", " Q, _ = linalg.lu(A @ Q, permute_l=True)\n", " Q, _ = linalg.lu(A.T @ Q, permute_l=True)\n", " \n", " Q, _ = linalg.qr(A @ Q, mode='economic')\n", " return Q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here's our randomized SVD method:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def randomized_svd(M, n_components, n_oversamples=10, n_iter=4):\n", " \n", " n_random = n_components + n_oversamples\n", " \n", " Q = randomized_range_finder(M, n_random, n_iter)\n", " print(Q.shape)\n", " # project M to the (k + p) dimensional space using the basis vectors\n", " B = Q.T @ M\n", " print(B.shape)\n", " # compute the SVD on the thin matrix: (k + p) wide\n", " Uhat, s, V = linalg.svd(B, full_matrices=False)\n", " del B\n", " U = Q @ Uhat\n", " print(U.shape)\n", " \n", " return U[:, :n_components], s[:n_components], V[:n_components, :]" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(2034, 15)\n", "(15, 26576)\n", "(2034, 15)\n" ] } ], "source": [ "u, s, v = randomized_svd(vectors, 5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Test" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2034, 26576)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vectors.shape" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(26576, 10)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Q = np.random.normal(size=(vectors.shape[1], 10)); Q.shape" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2034, 10)" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Q2, _ = linalg.qr(vectors @ Q, mode='economic'); Q2.shape" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2034, 10)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Q2.shape" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true }, "source": [ "#### End Test" ] }, { "cell_type": "code", "execution_count": 238, "metadata": { "hidden": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 136 ms, sys: 0 ns, total: 136 ms\n", "Wall time: 137 ms\n" ] } ], "source": [ "%time u, s, v = randomized_svd(vectors, 5)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "((2034, 5), (5,), (5, 26576))" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u.shape, s.shape, v.shape" ] }, { "cell_type": "code", "execution_count": 247, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "['jpeg image edu file graphics images gif data',\n", " 'edu graphics data space pub mail 128 3d',\n", " 'space jesus launch god people satellite matthew atheists',\n", " 'space launch satellite commercial nasa satellites market year',\n", " 'image data processing analysis software available tools display']" ] }, "execution_count": 247, "metadata": {}, "output_type": "execute_result" } ], "source": [ "show_topics(v)" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "Write a loop to calculate the error of your decomposition as you vary the # of topics. Plot the result" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true }, "source": [ "#### Answer" ] }, { "cell_type": "code", "execution_count": 248, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "#Exercise: Write a loop to calculate the error of your decomposition as you vary the # of topics\n" ] }, { "cell_type": "code", "execution_count": 242, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 242, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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YmZfFtVVnvwm0dfUFwR/5BFDX2kltaxcv7TjM0c6Tp+2fn50eCf4z3gTmFuVQ\nlp+lLqFxUtCLyJQzM4pCGRSFMrhmbuFZrx/v6ePg0W4OHO3iwNHOYNnNrkPHeHnn4eEpIiByjUB5\nQfZw67+iKDu4pWQ2cwqzKcnVMNEzKehFJObystJZNDudRbNnnPXawKBz+FgPB1q7OHi0i7qjnRwI\n3hRe2tFIW9SXwwCZaSmUF54e/sn+RqCgF5G4lho1OuiGS8Jnvd7Z209Dezf1bV3Ut3UHj8j6joaO\ns7qFznwjGPrZswuyKS/MpjQvM+G6hhT0IjKthTLTgtk+zx4hBON/I0hNMWbNyGJ2QVYk/IfeBII3\ngtkF2dNuGonpVa2IyDiN9kbQdbKfQ+09HGrvpqG9e3jZ0NbNOwfaeGFb42lTSADMyEqjvDCH8oIs\nyvKzKSvIYnZ+NmX5kTeH0hlZcTWpnIJeRJJaTkbaOa8cHjIw6DQf7z3tTeBQ8Khv6+YX+9vo6D79\newKzyG0ly/Kzgkc2swtOX868iF1ECnoRkfNITTFm5WcxKz+LZZVnjxiCSPdQY0cPjR3dNLb3cChq\n+X5zJ2/ubaHz5OmztacYzMzL4u4lZfyPuxdN6d+goBcRmaBQ5vk/Fbg7x3r6Odxx6k2gsaObQ+09\nlBVkT3l9CnoRkSlmZuRnp5OfnX7OaSWmWvx8WyAiIlNCQS8ikuAU9CIiCW7UoDezCjN71cx2mdlO\nM3s42F5kZq+Y2d5gWRh1zONmVmNme8zsjqn8A0RE5PzG0qLvB/7I3RcB1wMPmdki4DFgvbtXA+uD\n5wSvrQIWA3cCz5iZJp4WEYmRUYPe3Rvd/Z1g/TiwGygHVgJrgt3WAPcE6yuBZ929191rgRpgxWQX\nLiIiYzOuPnozqwKuBjYApe7eGLx0GCgN1suBg1GH1QfbREQkBsYc9GaWC/wL8Ii7H4t+zd0d8HMe\nOPLPe9DMNpnZpubm5vEcKiIi4zCmC6bMLJ1IyH/H3X8YbD5iZmXu3mhmZUBTsL0BqIg6fE6w7TTu\nvhpYHfz8ZjOru8C/AaAYaJnA8VNN9U2M6psY1Tcx8Vxf5Vh2skhj/Dw7RGboXwMcdfdHorb/FdDq\n7k+Z2WNAkbt/1swWA98l0i8/m8gXtdXuPnCOHz8pzGyTuy+fqp8/UapvYlTfxKi+iYn3+sZiLC36\nDwL3AdvNbGuw7U+Bp4C1ZvYAUAfcC+DuO81sLbCLyIidh6Yy5EVE5PxGDXp3fxMY6b5bt45wzBPA\nExOoS0RDmS5rAAADPElEQVREJkmiXBm7OtYFjEL1TYzqmxjVNzHxXt+oRu2jFxGR6S1RWvQiIjKC\naR30ZnZnMJ9OTTDyJ+bMbL+ZbTezrWa2Kdg24rxAF6Geb5pZk5ntiNoWN/MUjVDf582sITiHW83s\nYzGsL67nejpPfXFxDs0sy8w2mtkvg/r+ItgeL+dvpPri4vxNGneflg8gFXgfmA9kAL8EFsVBXfuB\n4jO2/SXwWLD+GPDFi1jPTcA1wI7R6gEWBecxE5gXnN/UGNT3eeCPz7FvLOorA64J1vOA94I64uIc\nnqe+uDiHRAZy5Abr6USuqr8+js7fSPXFxfmbrMd0btGvAGrcfZ+7nwSeJTLPTjwaaV6gKefubwBH\nx1jPRZ+naIT6RhKL+uJ6rqfz1DeSi12fu/uJ4Gl68HDi5/yNVN9IpuVcXtM56ON1Th0Hfmxmm83s\nwWDbSPMCxcp0mKfoD8xsW9C1M/SxPqb1xftcT2fUB3FyDs0sNbgGpwl4xd3j6vyNUB/EyfmbDNM5\n6OPVh9x9KfBRIlM63xT9okc+/8XNUKd4qyfwFSJdckuBRuBvYlvO5M/1NNnOUV/cnEN3Hwj+TcwB\nVpjZFWe8HtPzN0J9cXP+JsN0Dvoxzalzsbl7Q7BsAn5E5GPdEYvMB4SdPi9QrIxUT1ycU3c/Evzj\nGwS+xqmPxjGpz84z11PwekzP4bnqi7dzGNTUDrxK5D4VcXP+zlVfPJ6/iZjOQf8LoNrM5plZBpGb\nnayLZUFmFjKzvKF14HZgR1DX/cFu9wPPxabCYSPVsw5YZWaZZjYPqAY2XuzihgIg8GtEzmFM6jMz\nA74B7Hb3p6NeiotzOFJ98XIOzazEzAqC9WzgNuBd4uf8nbO+eDl/kybW3wZP5AF8jMgog/eBz8VB\nPfOJfCP/S2DnUE1AmMjkbnuBHxOZAO5i1fQ9Ih89+4j0Jz5wvnqAzwXncw/w0RjV90/AdmAbkX9Y\nZTGs70NEuhW2AVuDx8fi5Ryep764OIfAEmBLUMcO4M+C7fFy/kaqLy7O32Q9dGWsiEiCm85dNyIi\nMgYKehGRBKegFxFJcAp6EZEEp6AXEUlwCnoRkQSnoBcRSXAKehGRBPf/Ab3xUQZhjfpjAAAAAElF\nTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(range(0,n*step,step), error)" ] }, { "cell_type": "code", "execution_count": 175, "metadata": { "hidden": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 144 ms, sys: 8 ms, total: 152 ms\n", "Wall time: 154 ms\n" ] } ], "source": [ "%time u, s, v = decomposition.randomized_svd(vectors, 5)" ] }, { "cell_type": "code", "execution_count": 176, "metadata": { "hidden": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 2.38 s, sys: 592 ms, total: 2.97 s\n", "Wall time: 2.96 s\n" ] } ], "source": [ "%time u, s, v = decomposition.randomized_svd(vectors.todense(), 5)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "heading_collapsed": true }, "source": [ "# End" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "**Further Resources**:\n", "- [a whole course on randomized algorithms](http://www.cs.ubc.ca/~nickhar/W12/)" ] } ], "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }