{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# PCA tutorial for the python scientific environment\n", "\n", "An extremely simple tutorial. Most of the value is in doing the exercises.\n", "\n", "### Contact us\n", "Bradley Akitake, Mark Histed - code@histedlab.org\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Initialize this notebook - must run this cell before doing anything else\n", "\n", "You will get a console window that allows you to type throw-away commands in without having to put them in a cell.\n", "As of June 2016 (Jupyter 4.1.0, qtconsole 4.2.1), you will need to hit enter a few times in the console window to see a prompt." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "#load python modules\n", "import matplotlib as mpl\n", "import scipy.io as sio\n", "import seaborn as sns \n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import sys\n", "from __future__ import print_function # backward compat in case we are using python 2\n", "\n", "#shortcuts for commonly used numpy features\n", "a_ = np.asarray\n", "r_ = np.r_\n", "\n", "%qtconsole # start a console window\n", "\n", "# this does seem to work on Python 2 for now, so leave the below\n", "#if not sys.version_info.major == 3:\n", "# raise RuntimeError('Cannot use this notebook on Python 2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---------\n", "# First, look at the waveform data so we can get a sense of what PCA will do\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1) Load data, display some of it" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'__version__': '1.0', '__header__': b'MATLAB 5.0 MAT-file, Platform: MACI64, Created on: Tue Jul 23 13:47:02 2013', '__globals__': [], 'wfUnitN': array([[0, 3, 0, ..., 3, 3, 2]], dtype=uint8), 'wfTs': array([[ 7.86666667e-03, 3.48000000e-02, 6.72000000e-02, ...,\n", " 7.25167187e+03, 7.25168730e+03, 7.25172890e+03]]), 'pow2Ix': array([[0, 0, 0, ..., 0, 0, 0]], dtype=uint8), 'pow1Ix': array([[0, 0, 0, ..., 0, 0, 0]], dtype=uint8), 'noiseStd': array([[ 14.91224382]]), 'wfMat': array([[ 10, 7, 10, ..., -13, 7, 7],\n", " [ -3, 9, 10, ..., -8, -2, -2],\n", " [-14, 10, 6, ..., -3, 4, -5],\n", " ..., \n", " [-10, -3, -15, ..., 8, -1, 20],\n", " [-11, -8, -5, ..., -9, -6, 13],\n", " [-20, 1, -8, ..., -10, -4, 13]], dtype=int16), 'wireN': array([[1]], dtype=uint8)}\n" ] } ], "source": [ "# load data from matlab file\n", "mat_contents = sio.loadmat('WaveformData/wfData-wire0.mat')\n", "print(mat_contents)\n", "unitWfArr = mat_contents['wfMat']\n", "wfTsS = mat_contents['wfTs']\n", "\n", "# we know the data is sampled at around 30kHz, so create a timept label vector\n", "(nWfTimepts, nWfs) = np.shape(unitWfArr)\n", "timeptMs = np.r_[0:nWfTimepts] / 30000.0 * 1000.0# load data\n", "\n", "# Below: output of print statements above" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Waveform data variable definitions\n", "- **unitWfArr** is a matrix of shape (nWfTimepoints, nWfs)\n", " - Here those lengths are: 48 timepoints, 395k waveforms (recorded over two hours or so)\n", "- **wfTsS** is a vector (len nWfs) that labels the start time of each of the 395k waveforms. \n", " - Each value of wfTsV is a timestamp in seconds\n", "- **timeptMs** is a vector (len nWfTimepoints) that labels the time of each sample within the waveform in ms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot the waveform timestamps for the first 100 waveforms. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(48, 395156)\n", "(1, 395156)\n", "7251.7289\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# show sizes/shapes of the loaded data\n", "print(np.shape(unitWfArr))\n", "\n", "print(np.shape(wfTsS))\n", "print(np.max(wfTsS))\n", "\n", "# example plot of waveform timestamps\n", "plt.plot(wfTsS[0,0:100], '.')\n", "plt.title('First 100 waveform timestamps')\n", "plt.xlabel('Waveform number')\n", "plt.ylabel('Time of wf (sec)')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot some example waveforms and the mean\n", "\n", "The Y-axes of waveforms are in arbitrary units - ADC (sample) units -- which we could convert to mV." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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b+fXBWybx0pzNrJBsFq0/xNmTWj+WUXN1kcsyLcoz1ZITohk3rAdfrzlY8965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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gs = mpl.gridspec.GridSpec(2,2) # set up the multi-panel plot\n", "figH = plt.figure(figsize=8*a_((1,0.75))) # make figure, using a slightly larger size\n", "yLims = 120*a_([-1,1]) # hardcode ylim value for all plots\n", "\n", "#Plot a single waveform\n", "axH = plt.subplot(gs[0,0]) # create axes for the first plot, using gridspec indexing\n", "plt.plot(timeptMs, unitWfArr[:,1], '.-')\n", "plt.xlabel('sample time (ms)')\n", "plt.ylim(yLims)\n", "plt.title('One example waveform')\n", "\n", "#Plot the average of all waveforms\n", "axH = plt.subplot(gs[0,1]) # second plot, new index in gridspec array\n", "plt.plot(timeptMs, np.mean(unitWfArr, axis=1), '.-')\n", "plt.xlabel('sample time (ms)')\n", "plt.ylim(yLims)\n", "plt.title('Mean over all %d waveforms' % nWfs)\n", "\n", "#Plot overlay of first 100 waveforms\n", "axH = plt.subplot(gs[1,0]) # 3rd plot\n", "plt.plot(timeptMs, unitWfArr[:,0:100])\n", "plt.xlabel('sample time (ms)')\n", "plt.ylim(yLims)\n", "plt.title('First 100 example waveforms')\n", "\n", "plt.tight_layout() # move plots around to prevent any label overlap" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Notes from above plot\n", "- you can see that the mean waveform is small, but there are a few large waveforms\n", "\n", "------------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Exercise (viewing data)\n", "\n", "1. Create a two-panel figure that shows waveforms 1000-1100 and the mean of waveforms 1000-1100\n", "2. Bonus points: add 3rd panel to the figure that shows the standard deviation across waveforms. It should plot twice the standard deviation above and below the mean waveform at each timepoint. \n", "\n", "**Example std dev plots, on other kinds of data **\n", "\n", "\n", "
This is one way to plot std devs/variance/errorbars

\n", "
This is a second way to plot them

" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# add your exercise code here" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "-----\n", "### Now we have plotted all the raw data, move on to PCA\n", "\n", "------\n", "\n", "# PCA demo \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Run the PCA analysis. What is PCA? Generating a covariance matrix and diagonalizing it\n", "\n", "- To show the PCA result, we plot projections back onto the first 2 eigenvectors" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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4aynlbwtxvblEtlFEepjmlRtPtJT+1tHNReaeIlff/pyhOOpqa+gb1FaaNTUe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\nVq06bgSFrozzWbFWomCxj8l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EIfibG+oYHrPWdVrYFkAc1mpqvxvjuru0ID/zLqV/WDOL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\nxAfQIrQ2Jl6/BLgdqAEekFI+U57hKQqN3fy02CF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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# remove mean\n", "unitWfArrZM = unitWfArr - np.mean(unitWfArr, axis=1, keepdims=True) # keepdims: preserve broadcasting\n", "# compute covariance matrix\n", "covM = np.cov(unitWfArrZM[:,0:200000]) # compute over a subset of waveforms to save memory\n", "# diagonalize cov matrix (compute eigenvalues and right eigenvectors of a square array)\n", "(eigVal, eigVect) = np.linalg.eig(covM)\n", "# project back onto first two eigenvectors (dot product of two arrays)\n", "d0=np.dot(unitWfArr.T, eigVect[:,0:4])\n", "\n", "desNs = r_[0:1000]\n", "plt.plot(d0[desNs,0], d0[desNs,1], '.')\n", "plt.xlabel('first eigenvector')\n", "plt.ylabel('second eigenvector')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is PCA doing? Generating eigenvalues and eigenvectors in descending order of captured data variance. Below: explore those eigenvectors" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9XLjutqW88fcc3vjHWfr6Bkd83CejR6oJj4e8/Xn52VM01HaSlhVOdLw/779e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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# To get a sense of what those eigenvectors look like, \n", "# make a figure projecting the data onto different eigenvector pairs\n", "\n", "gs = mpl.gridspec.GridSpec(3,3) # set up the multi-panel plot\n", "fig = plt.figure(figsize=8*a_((1,0.75))) # make figure, using a slightly larger size\n", "\n", "#Plot eigenvalues\n", "ax = plt.subplot(gs[0,0])\n", "plt.plot(eigVal)\n", "plt.yscale('log')\n", "plt.ylabel('log magnitude')\n", "plt.title('eigenvalue magnitude')\n", "\n", "#Plot eigenvectors\n", "ax = plt.subplot(gs[0,1])\n", "plt.plot(eigVect[:,0:4]) # vectors 1 thru 4\n", "plt.title('eigenvectors 1-4')\n", " \n", "#Plot eigenvectors 1 and 2\n", "ax = plt.subplot(gs[1,1])\n", "plt.plot(eigVect[:,0:2]) # vectors 1 and 2\n", "plt.title('eigenvectors 1 and 2')\n", "\n", "#Plot in ev space\n", "ax = plt.subplot(gs[1,0]) \n", "plt.plot(d0[desNs,0], d0[desNs,1], '.')\n", "plt.xlabel('first eigenvector')\n", "plt.ylabel('2nd eigenvector')\n", "plt.title('projection onto evs 1 and 2')\n", "\n", "\n", "plt.tight_layout() # move plots around to prevent any label overlap" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## 2. Exercise (PCA)\n", "\n", "1. Other eigenvectors.\n", " 1. Plot the first and third eigenvector\n", " 2. Plot the projection onto the 1st and 3d eigenvector\n", " 3. Compare it to the 1st and second eigenvector. Is the 3rd eigenvector useful? What does it tell us? Write a bit of text answering these questions. You may learn more about this by looking at the waveforms (below)\n", " 4. Do the same for the fourth eigenvector\n", "\n", "1. Extract waveforms based on clusters.\n", " 1. define the center of the clusters in the projection onto evs 1 and 2. There are two clusters.\n", " 2. pull out 10 or so waveforms near the center of each of the two clusters.\n", " 3. plot the 10 waveforms from each cluster.\n", " 4. plot the mean of those waveforms, w/ errorbars given by $2 \\cdot \\sigma$ (standard deviation).\n", " 5. Interpret the clusters by writing some text - what have we learned by working with projections onto two eigenvectors? How do the waveforms cluster? How do the clusters relate to the eigenvectors you plotted? What features of the data are captured by which eigenvectors? What value do the first and second eigenvectors have for sorting waveforms into clusters?\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# add your exercise code here. Use more cells if necessary." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }