{ "metadata": { "name": "", "signature": "sha256:85803ac598aef29d5de2555d7ee246f55a8ccbe8c5b71fd2c09f0e19e0428563" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Matrix Algebra\n", "====\n", "\n", "Date: October 14, 2014\n", "\n", "Copyright (c) 2014 Rafael A. Irizarry MIT License" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# special IPython command to prepare the notebook for matplotlib\n", "%matplotlib inline \n", "\n", "import numpy as np\n", "import scipy\n", "import pandas as pd # pandas\n", "import matplotlib.pyplot as plt # module for plotting \n", "from mpl_toolkits.mplot3d import Axes3D #3D plotting\n", "import datetime as dt # module for manipulating dates and times\n", "\n", "import requests \n", "import scipy.stats as stats\n", "import statsmodels.api as sm\n", "from scipy.stats import binom\n", "from __future__ import division\n", "import re\n", "from StringIO import StringIO\n", "from zipfile import ZipFile \n", "from pandas import read_csv\n", "from urllib import urlopen\n", "\n", "import sklearn\n", "import sklearn.preprocessing\n", "import sklearn.datasets\n", "\n", "#nice defaults for matplotlib\n", "from matplotlib import rcParams\n", "\n", "dark2_colors = [(0.10588235294117647, 0.6196078431372549, 0.4666666666666667),\n", " (0.8509803921568627, 0.37254901960784315, 0.00784313725490196),\n", " (0.4588235294117647, 0.4392156862745098, 0.7019607843137254),\n", " (0.9058823529411765, 0.1607843137254902, 0.5411764705882353),\n", " (0.4, 0.6509803921568628, 0.11764705882352941),\n", " (0.9019607843137255, 0.6705882352941176, 0.00784313725490196),\n", " (0.6509803921568628, 0.4627450980392157, 0.11372549019607843),\n", " (0.4, 0.4, 0.4)]\n", "\n", "rcParams['figure.figsize'] = (10, 6)\n", "rcParams['figure.dpi'] = 150\n", "rcParams['axes.color_cycle'] = dark2_colors\n", "rcParams['lines.linewidth'] = 2\n", "rcParams['axes.grid'] = True\n", "rcParams['axes.facecolor'] = '#eeeeee'\n", "rcParams['font.size'] = 14\n", "rcParams['patch.edgecolor'] = 'none'" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 392 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Motivation\n", "====" ] }, { "cell_type": "code", "collapsed": false, "input": [ "url_exprs = \"https://raw.githubusercontent.com/cs109/2014_data/master/exprs_GSE5859.csv\"\n", "X = pd.read_csv(url_exprs, index_col=0)\n", "\n", "url_sampleinfo = \"https://raw.githubusercontent.com/cs109/2014_data/master/sampleinfo_GSE5859.csv\"\n", "sampleid = pd.read_csv(url_sampleinfo)\n", "\n", "a = list(sampleid.filename)\n", "b = list(X.columns)\n", "matchIndex = [b.index(x) for x in a]\n", "X = X[matchIndex]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 393 }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", " Our data is usually saved in matrices. \n", "\n", "\n", "\n", "In the gene expression example data, $X$, was $8793 \\times 208$.\n", "\n", "\n", "Say you want to compute the average of each column:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "A = np.repeat(1/float(X.shape[0]), X.shape[0]).reshape(1, X.shape[0])\n", "colmeans = np.dot(A, X)\n", "print \"Column averages:\",np.round(colmeans,2)[0]\n", "pd.DataFrame(np.array([X.columns.values, np.round(colmeans,2)[0]]).transpose(), \n", " columns = [\"Gene\", \"Average\"]).head(15)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Column averages: [ 5.74 5.75 5.69 5.73 5.72 5.72 5.72 5.75 5.62 5.73 5.72 5.72\n", " 5.62 5.71 5.68 5.7 5.71 5.74 5.71 5.72 5.69 5.71 5.76 5.71\n", " 5.74 5.71 5.71 5.71 5.71 5.72 5.71 5.69 5.74 5.73 5.73 5.73\n", " 5.73 5.75 5.75 5.7 5.81 5.84 5.72 5.68 5.72 5.7 5.73 5.74\n", " 5.81 5.73 5.74 5.73 5.69 5.72 5.69 5.7 5.7 5.71 5.72 5.71\n", " 5.74 5.71 5.71 5.74 5.7 5.72 5.71 5.73 5.73 5.69 5.7 5.72\n", " 5.73 5.69 5.72 5.73 5.73 5.72 5.72 5.69 5.73 5.69 5.73 5.72\n", " 5.75 5.75 5.73 5.75 5.72 5.72 5.73 5.72 5.72 5.71 5.74 5.71\n", " 5.69 5.65 5.68 5.73 5.74 5.74 5.74 5.73 5.73 5.74 5.75 5.74\n", " 5.75 5.73 5.73 5.73 5.73 5.74 5.68 5.73 5.74 5.74 5.73 5.73\n", " 5.73 5.72 5.72 5.73 5.74 5.74 5.73 5.73 5.75 5.73 5.74 5.74\n", " 5.73 5.74 5.73 5.73 5.73 5.74 5.74 5.73 5.73 5.73 5.75 5.74\n", " 5.74 5.74 5.74 5.73 5.74 5.75 5.76 5.74 5.74 5.74 5.75 5.72\n", " 5.75 5.72 5.72 5.75 5.71 5.73 5.73 5.73 5.75 5.73 5.75 5.73\n", " 5.74 5.73 5.74 5.75 5.73 5.73 5.73 5.73 5.74 5.75 5.74 5.74\n", " 5.74 5.74 5.74 5.74 5.75 5.75 5.74 5.75 5.75 5.76 5.75 5.74\n", " 5.75 5.74 5.75 5.74 5.76 5.75 5.75 5.75 5.76 5.75 5.75 5.76\n", " 5.74 5.73 5.74 5.73]\n" ] }, { "html": [ "
\n", " | Gene | \n", "Average | \n", "
---|---|---|
0 | \n", "GSM25349.CEL.gz | \n", "5.74 | \n", "
1 | \n", "GSM25350.CEL.gz | \n", "5.75 | \n", "
2 | \n", "GSM25356.CEL.gz | \n", "5.69 | \n", "
3 | \n", "GSM25357.CEL.gz | \n", "5.73 | \n", "
4 | \n", "GSM25358.CEL.gz | \n", "5.72 | \n", "
5 | \n", "GSM25359.CEL.gz | \n", "5.72 | \n", "
6 | \n", "GSM25360.CEL.gz | \n", "5.72 | \n", "
7 | \n", "GSM25361.CEL.gz | \n", "5.75 | \n", "
8 | \n", "GSM25377.CEL.gz | \n", "5.62 | \n", "
9 | \n", "GSM25378.CEL.gz | \n", "5.73 | \n", "
10 | \n", "GSM25385.CEL.gz | \n", "5.72 | \n", "
11 | \n", "GSM25386.CEL.gz | \n", "5.72 | \n", "
12 | \n", "GSM25399.CEL.gz | \n", "5.62 | \n", "
13 | \n", "GSM25400.CEL.gz | \n", "5.71 | \n", "
14 | \n", "GSM25401.CEL.gz | \n", "5.68 | \n", "
15 rows \u00d7 2 columns
\n", "\n", " | GSM25349.CEL.gz | \n", "GSM25350.CEL.gz | \n", "GSM25356.CEL.gz | \n", "GSM25357.CEL.gz | \n", "GSM25358.CEL.gz | \n", "GSM25359.CEL.gz | \n", "GSM25360.CEL.gz | \n", "GSM25361.CEL.gz | \n", "GSM25377.CEL.gz | \n", "GSM25378.CEL.gz | \n", "GSM25385.CEL.gz | \n", "GSM25386.CEL.gz | \n", "GSM25399.CEL.gz | \n", "GSM25400.CEL.gz | \n", "GSM25401.CEL.gz | \n", "GSM25402.CEL.gz | \n", "GSM25409.CEL.gz | \n", "GSM25410.CEL.gz | \n", "GSM25426.CEL.gz | \n", "GSM25427.CEL.gz | \n", "\n", " |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "0.004808 | \n", "... | \n", "
1 | \n", "0.008197 | \n", "0.008197 | \n", "0.008197 | \n", "0.008197 | \n", "0.008197 | \n", "0.008197 | \n", "-0.011628 | \n", "0.008197 | \n", "0.008197 | \n", "0.008197 | \n", "0.008197 | \n", "0.008197 | \n", "-0.011628 | \n", "-0.011628 | \n", "0.008197 | \n", "-0.011628 | \n", "0.008197 | \n", "-0.011628 | \n", "0.008197 | \n", "0.008197 | \n", "... | \n", "
2 rows \u00d7 208 columns
\n", "\n", " | R | \n", "Singles | \n", "HR | \n", "BB | \n", "
---|---|---|---|---|
437 | \n", "505 | \n", "997 | \n", "11 | \n", "344 | \n", "
1366 | \n", "744 | \n", "902 | \n", "189 | \n", "681 | \n", "
1367 | \n", "683 | \n", "989 | \n", "90 | \n", "580 | \n", "
1377 | \n", "817 | \n", "1041 | \n", "199 | \n", "584 | \n", "
1379 | \n", "718 | \n", "973 | \n", "137 | \n", "602 | \n", "
5 rows \u00d7 4 columns
\n", " X = U[:,0] d[0,0] Vh[0,:]
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Singular Value Decomposition\n",
"#U are the left singular vectors\n",
"#d are the singular values\n",
"#U*d gives PCA scores\n",
"#V are the right singular vectors -- PCA loadings\n",
"U, d, Vh = scipy.linalg.svd(Y, full_matrices=False)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 410
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Print the eigenvalues:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print np.round(d, 6)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 22.872792 0. 0. 0. 0. ]\n"
]
}
],
"prompt_number": 411
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"U1 = U[:,0].reshape(100,1)\n",
"dV1 = (d[0] * Vh[0,:].reshape(1,5))\n",
"newY = np.dot(U1, dV1)\n",
"print dV1"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[[-10.22902343 -10.22902343 -10.22902343 -10.22902343 -10.22902343]]\n"
]
}
],
"prompt_number": 412
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"np.round(np.abs(Y-newY).max(),6)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 413,
"text": [
"0.0"
]
}
],
"prompt_number": 413
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Motivating SVD\n",
"====\n",
"Consider this simple linear combination:\n",
"\n",
"$$ \\Delta_j = (Y_{1,j}, \\dots, Y_{N,j})'(1/N_1,\\dots,1/N_1,-1/N_2,\\dots,-1/N_2) =$$ \n",
"\n",
"$$\\frac{1}{N_1}\\sum_{i=1}^{N_1} Y_{i,j} - \\frac{1}{N_2}\\sum_{i=N_1+1}^{N} Y_{i,j}, N_2=N-N_1$$\n",
"\n",
"Try to find the $N_1$ that maximizes the variance\n",
"\n",
"$$\n",
"\\frac{1}{p}\\sum_{j=1}^p \\Delta_j^2\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Back to gene expression example"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"url_exprs = \"https://raw.githubusercontent.com/cs109/2014_data/master/exprs_GSE5859.csv\"\n",
"exprs = pd.read_csv(url_exprs, index_col=0)\n",
"\n",
"url_sampleinfo = \"https://raw.githubusercontent.com/cs109/2014_data/master/sampleinfo_GSE5859.csv\"\n",
"sampleinfo = pd.read_csv(url_sampleinfo)\n",
"## Re-order the columns in the `exprs` DataFrame to match the order of the file names in the `sampleinfo` DataFrame.\n",
"fns = list(sampleinfo.filename)\n",
"cns = list(exprs.columns)\n",
"matchIndex = [cns.index(x) for x in fns]\n",
"exprs = exprs[matchIndex]\n",
"\n",
"##Add a column to the `sampleinfo` DataFrame titled `days` containing the days since October 31, 2002.\n",
"sampleinfo[\"date\"] = pd.to_datetime(sampleinfo.date)\n",
"oct31 = dt.datetime(2002,10,31,0,0)\n",
"\n",
"sampleinfo[\"days\"] = map(lambda x: (x - oct31).days, sampleinfo.date)\n",
"\n",
"##Subset for CEU only samples only. \n",
"sampleinfoCEU = sampleinfo[sampleinfo.ethnicity == \"CEU\"]\n",
"exprsCEU = exprs[sampleinfoCEU.filename]\n",
"\n",
"###Remove the mean\n",
"X = exprsCEU.apply(lambda x: x - exprsCEU.mean(axis=1), \\\n",
" axis = 0)\n",
"X=X.T\n",
"X.shape"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 415,
"text": [
"(102, 8793)"
]
}
],
"prompt_number": 415
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** SVD **"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Singular Value Decomposition\n",
"#U are the left singular vectors\n",
"#d are the singular values\n",
"#U*d gives PCA scores\n",
"#V are the right singular vectors -- PCA loadings\n",
"U, d, Vh = scipy.linalg.svd(X,full_matrices=False)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 416
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Vh.shape"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 417,
"text": [
"(102, 8793)"
]
}
],
"prompt_number": 417
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** First PC correlates with batch **"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.scatter(sampleinfoCEU.days, U.transpose()[0,:])\n",
"plt.xlabel('Date sample was processed (Number of days since Oct 31, 2012)')\n",
"plt.ylabel('PC1')\n",
"plt.title('Relationship between the PC1 and the date the samples were processed')\n",
"plt.ylim()\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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hl19+wdy5c1GpUiWUL18eERERstqqjZc5+/aUKVOwf/9+tG/fHr6+vnj48CGW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\n/wf85jg8V9V6rAAAAABJRU5ErkJggg==\n",
"text": [
"XV[:,1]V.T
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"xnew = np.dot(U.transpose()[0][None].T, [d[0]*V[0]])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 437
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.scatter(xnew[:, 0], X[:, 0])\n",
"plt.plot(xnew[:, 0],xnew[:, 0])\n",
"plt.xlabel(\"Original 1st column\")\n",
"plt.ylabel(\"Approximation\")\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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wpo+MWEchjnERx7iIY1zMicUkNxf44ANvHDzogQYNNFi6NAvly1v36+j77+WY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\nPvp18eJF9OnTB5aWlvDw8MDu3bthY2ODNWvWqNs8fno3OTlZ/XrAgAG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"text": [
"