06-VectorizingPersistenceDiagrams.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vectorizing Persistence Diagrams\n",
    "\n",
    "In this notebook, we'll analyze a synthetic dataset and a real dataset using vectorized TDA signatures. Specifically, we'll turn persistence diagrams into persistence images and use these as features in a standard machine learning pipeline. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import standard packages for linear algebra and statistics\n",
    "import numpy as np\n",
    "from sklearn import datasets\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.model_selection import train_test_split\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Import a package to time computations\n",
    "import time\n",
    "\n",
    "# Import specialized TDA packages\n",
    "from ripser import Rips\n",
    "from persim import PersImage\n",
    "\n",
    "# Package for including a figure in the notebook\n",
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1: Synthetic Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is an expanded version of the demonstration available at https://github.com/scikit-tda/persim. I added more parameters to the experiment and more explanation for everything.\n",
    "\n",
    "This notebook shows how you can use persistent homology and persistence images to classify datasets.  We construct datasets from two classes, one just noise and the other noise with a big circle in the middle. We then compute persistence diagrams with [Ripser.py](https://github.com/scikit-tda/ripser.py) and convert them to persistence images with [PersIm](https://github.com/scikit-tda/persim). Using these persistence images, we build classifier using Support Vector Machines."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing the dataset\n",
    "\n",
    "We will construct a data set consisting of several pointclouds which are just noise and several pointclouds which are noise on top of a noisy circle. The goal is to see whether tools from persistent homology can be used to classify the data into two categories. \n",
    "\n",
    "This is synthetic data, but one can imagine realistic tasks along these lines; e.g. https://en.wikipedia.org/wiki/Transmission_electron_cryomicroscopy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Cryo EM](data/Cryoem_groel.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We begin by defining a function which generates a noisy point cloud sampled from a sphere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_spherical(npoints, scale=1, ndim=2):\n",
    "    vec = np.random.randn(ndim, npoints)\n",
    "    vec /= np.linalg.norm(vec, axis=0)\n",
    "    vec = scale*np.transpose(vec)\n",
    "    return vec\n",
    "\n",
    "def noisy_sphere(npoints, scale=1, noiseLevel=0.3, offset = 0, ndim=2):\n",
    "    \"\"\"\n",
    "    npoints = number of points sampled\n",
    "    scale = radius of the sphere being sampled\n",
    "    noiseLevel = how \"noisy\" the samples are\n",
    "    offset = shifts the circle in the (1,1,...,1) direction\n",
    "    \"\"\"\n",
    "    data = sample_spherical(npoints,scale, ndim)+scale*noiseLevel*np.random.random((npoints,ndim)) + offset*np.ones(ndim)\n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = noisy_sphere(200, scale=20, offset=30)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(121)\n",
    "ax1.plot(data[:, 0], data[:, 1], 'ob');\n",
    "ax1.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we define a function which produces a noisy point cloud in space, with a given scale, in a given dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def noise(N, scale, ndim=2):\n",
    "    return scale * np.random.random((N, 2)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we construct our data set. There are lots of parameters to change to produce different experiments. In general we generate samples of random noise and samples of random noise with noisy circles embedded in them. We can change numbers of samples, how noisy everything is, size and location of the circles, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We first define a bunch of parameters for the experiment\n",
    "total_samples = 200 # Number of samples in our experiment\n",
    "samples_per_class = int(total_samples / 2) \n",
    "# Number of samples which are just noise. We will do our experiment taking an equal number each type of sample.\n",
    "npoints = 400\n",
    "# Number of points in each point cloud sample.\n",
    "circle_noise_level = 0.4 # Noise level for the circles.\n",
    "snr = 0.25\n",
    "# Signal-to-noise ratio. For the images containing circles, this is the percentage of points that belong to the circle.\n",
    "noise_scale = 150 # How large the noisy point cloud is\n",
    "circle_scale = 30 # How large the noisy circle is. Should be chosen relative to the noise_scale.\n",
    "\n",
    "# Generate the pure noise samples\n",
    "just_noise = [noise(npoints, noise_scale) for _ in range(samples_per_class)]\n",
    "\n",
    "# Generate the noise+circle samples\n",
    "with_circle = [np.concatenate((noisy_sphere(int(snr*npoints), noiseLevel = circle_noise_level, scale=circle_scale, offset=(0.2*np.random.random()+0.4)*noise_scale), noise(npoints-int(snr*npoints), noise_scale)))\n",
    "               for _ in range(samples_per_class)]\n",
    "\n",
    "# Combine all the samples into one list.\n",
    "datas = []\n",
    "datas.extend(just_noise)\n",
    "datas.extend(with_circle)\n",
    "\n",
    "# Define labels. Pure noise samples are labeled with 0, noise+circles are labeled with 1.\n",
    "# These labels will be used to train/test our classifyer.\n",
    "labels = np.zeros(total_samples)\n",
    "labels[samples_per_class:] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the data. We'll plot a random pure noise sample and a random circle+noise sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 2)\n",
    "fig.set_size_inches(10,5)\n",
    "\n",
    "random_sample_choice = np.random.randint(100) # Pick a number between 0 and 100.\n",
    "\n",
    "xs, ys = just_noise[random_sample_choice][:,0], just_noise[random_sample_choice][:,1]\n",
    "axs[0].scatter(xs, ys)\n",
    "axs[0].set_title(\"Example noise dataset\")\n",
    "axs[0].set_aspect('equal', 'box')\n",
    "\n",
    "xs_, ys_ = with_circle[random_sample_choice][:,0], with_circle[random_sample_choice][:,1]\n",
    "axs[1].scatter(xs_, ys_)\n",
    "axs[1].set_title(\"Example noise with circle dataset\")\n",
    "axs[1].set_aspect('equal', 'box')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute persistent homology of each dataset\n",
    "\n",
    "Generate the persistence diagram of $H_1$ for each of the datasets generated above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rips(maxdim=1, thresh=inf, coeff=2, do_cocycles=False, n_perm = None, verbose=True)\n",
      "CPU times: user 2min 40s, sys: 12.9 s, total: 2min 53s\n",
      "Wall time: 41.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "rips = Rips(maxdim=1, coeff=2); # Apply ripser with Z_2 coefficients, up to dimension 1.\n",
    "diagrams = [rips.fit_transform(data) for data in datas]\n",
    "diagrams_h1 = [rips.fit_transform(data)[1] for data in datas]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot persistence diagrams for a random choice of noise sample and a random choice of circle+noise. We'll use the \"lifetime\" plot style option because this is a step in the process of creating persistence images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "plt.subplot(121)\n",
    "\n",
    "random_sample = np.random.randint(50)\n",
    "\n",
    "rips.plot(diagrams_h1[random_sample], show=False, legend=False, lifetime=True)\n",
    "plt.title(\"PD of $H_1$ for just noise\")\n",
    "\n",
    "plt.subplot(122)\n",
    "rips.plot(diagrams_h1[-random_sample], show=False, legend=False, lifetime=True)\n",
    "plt.title(\"PD of $H_1$ for circle w/ noise\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute persistence images\n",
    "\n",
    "We will discuss the definition of a persistence image in class. The 'persim' package is made to handle persistence images. Recall from class that we need to choose a resolution and a variance for the Gaussians. The weight function is automatically chosen to be linearly increasing in the $y$-direction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PersImage(pixels=(20, 20), spread=1, specs=None, kernel_type=\"gaussian\", weighting_type=\"linear\")\n",
      "CPU times: user 5.69 s, sys: 89.4 ms, total: 5.78 s\n",
      "Wall time: 5.93 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "pim = PersImage(pixels=(20,20), spread=1)\n",
    "imgs = pim.transform(diagrams_h1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at the persistence images. We should interpret each image as the pixelated plot of a function $\\mathbb{R}^2 \\rightarrow \\mathbb{R}$, with colors corresponding to height of the plot. Such a plot can be understood as a vector: by reshaping the 20-pixel-by-20-pixel image into a list of 400 numbers, we can think of it as a vector in $\\mathbb{R}^{400}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1500x750 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,7.5))\n",
    "\n",
    "for i in range(4):\n",
    "    ax = plt.subplot(240+i+1)\n",
    "    pim.show(imgs[i], ax)\n",
    "    plt.title(\"PI of $H_1$ for noise\")\n",
    "\n",
    "for i in range(4):\n",
    "    ax = plt.subplot(240+i+5)\n",
    "    pim.show(imgs[-(i+1)], ax)\n",
    "    plt.title(\"PI of $H_1$ for circle w/ noise\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classify the datasets from the persistence images\n",
    "\n",
    "Now we'll train a classifier on the vectorized persistence diagrams. We first flatten each persistence image so that it is really represented as a vector in $\\mathbb{R}^{400}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "imgs_array = np.array([img.flatten() for img in imgs])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we randomly divide our data into a training set and a testing set (with labels for each)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(imgs_array, labels, test_size=0.20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we train a Support Vector Machines classifier on the training set. Roughly, SVM looks for a $399$-dimensional affine hyperplane in $\\mathbb{R}^{400}$ which best separates the two classes in the training data set. This hyperplane can then be used to guess the label of unseen data from the testing dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(kernel='linear')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "modelSVM = SVC(kernel=\"linear\") # Defines the model with optional parameters\n",
    "\n",
    "modelSVM.fit(X_train, y_train) # Trains the model on the training data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can run the trained classifier on the unseen testing data to see how well it performs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.95"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "modelSVM.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model performs extremely well!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The hyperplane we found in the training stage is determined by a normal vector (plus a bias). This is a $400$-dimensional vector, which we can reshape back into an image to get an idea of how the classifier distinguishes the classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "classifying_image = np.copy(modelSVM.coef_).reshape((20,20))\n",
    "plt.imshow(classifying_image,cmap = plt.cm.RdBu)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing to a  Naive Baseline\n",
    "\n",
    "To test whether this performance is a result of the efficacy of logistic regression, or the persistence image representation is actually useful, let's try to classify with a more naive approach.\n",
    "\n",
    "Each sample in our data set is an npoints-by-2 array. We could flatten each of these to get a vector in $\\mathbb{R}^{2 \\cdot \\mbox{npoints}}$, then run the same regression procedure to see if logistic regression can classify these vectors. \n",
    "\n",
    "First we flatten the data, split into training and test sets and perform regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Naive SVM score: 0.575\n"
     ]
    }
   ],
   "source": [
    "datas_array = np.array([sample.flatten() for sample in datas])\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(datas_array, labels, test_size=0.20, random_state=42)\n",
    "\n",
    "modelSVM = SVC(kernel=\"linear\") # Defines the model with optional parameters\n",
    "modelSVM.fit(X_train, y_train) # Trains the model on the training data\n",
    "\n",
    "print('Naive SVM score:', modelSVM.score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At least the result is better than random guessing...\n",
    "\n",
    "We can visualize the classifying vector learned by logistic regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "classifying_image = np.copy(modelSVM.coef_).reshape((400,2))\n",
    "\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(121)\n",
    "ax1.plot(classifying_image[:, 0], classifying_image[:, 1],'ob')\n",
    "ax1.axis('equal'); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: Classifying Weighted Graphs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset is also simulated, but comes from a more realistic source. The data comes from a set of ~400 *districting plans* for the state of Pennsylvania---each districting plan is a partition of Pennsylvania into 18 (path connected) districts, each of which has the same population (up to a small tolerance). \n",
    "\n",
    "To get a persistence diagram from a districting plan:\n",
    "- The districting plan is converted into an adjacency graph for the districts\n",
    "- nodes are weighted by, say, Republican vote share in a given election\n",
    "- each edge is assigned the maximum value of its neighboring nodes, so that we get an overall filtration of the graph (considered as a simplicial complex)\n",
    "- sublevel set degree-0 persistent homology is run on the resulting filtered simplicial complex\n",
    "\n",
    "This is illustrated in the figure below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](data/districting.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Studying statistics of the space of all districting plans is an important part of treating the *gerrymandering problem*, which is the problem that districts can be drawn adversarily to favor one party over the other, regardless of the vote distribution in the state. In the paper https://arxiv.org/abs/2007.02390, we use these TDA signatures as proxies for districting plans in order to simplify statistical analyses. \n",
    "\n",
    "Unfortunately, the space of districting plans is extremely large and complicated. Ensembles of districting plans are generated via various Markov chain algorithms which can be used to explore the space of potential plans.\n",
    "\n",
    "In this dataset, we have generated plans in two classes. Each class used a Markov chain which aimed to maximize the number of districts one by either Republicans or Democrats in a given election. Our task is to see if these plans can be classified by their topological signatures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Read in the Data\n",
    "\n",
    "The persistence diagrams for the weighted graphs are precomputed and saved. So all we have to do is load in the persistence features from the csv files in the data folder. The data is stored in csv files with the most persistent feature for all plans stored in the first file, second most persistent feature in another file, etc. The classes are a bit unbalanced here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "barcodes = []\n",
    "\n",
    "for j in range(6):\n",
    "    fileName = \"data/50biased_\"+str(j)+\".csv\"\n",
    "    file = np.genfromtxt(fileName,delimiter=',')\n",
    "    barcodes.append(file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Combine the various classes into barcodes for the democrat-biased plans..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "dem_barcodes = []\n",
    "\n",
    "for j in range(1,243):\n",
    "    barcode = []\n",
    "    for k in range(6):\n",
    "        bar = barcodes[k][j,1:3]\n",
    "        barcode.append(bar)\n",
    "    dem_barcodes.append(np.array(barcode))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...and the republican-biased plans."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "rep_barcodes = []\n",
    "\n",
    "for j in range(243,431):\n",
    "    barcode = []\n",
    "    for k in range(6):\n",
    "        bar = barcodes[k][j,1:3]\n",
    "        barcode.append(bar)\n",
    "    rep_barcodes.append(np.array(barcode))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Combine them into one big list of barcodes and record the labels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_barcodes = dem_barcodes + rep_barcodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = [0]*len(dem_barcodes)+[1]*len(rep_barcodes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create persistence images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "plt.subplot(121)\n",
    "\n",
    "random_sample = np.random.randint(50)\n",
    "\n",
    "rips.plot(all_barcodes[random_sample], show=False, legend=False, lifetime=True)\n",
    "plt.title(\"PD of Democratic Plan\")\n",
    "\n",
    "plt.subplot(122)\n",
    "rips.plot(all_barcodes[-random_sample], show=False, legend=False, lifetime=True)\n",
    "plt.title(\"PD Republican Plan\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PersImage(pixels=[30, 30], spread=0.01, specs=None, kernel_type=\"gaussian\", weighting_type=\"linear\")\n"
     ]
    }
   ],
   "source": [
    "pim = PersImage(pixels=[30,30], spread=0.01)\n",
    "imgs = pim.transform(all_barcodes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the persistence images as pixelated heat maps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1500x750 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,7.5))\n",
    "\n",
    "for i in range(4):\n",
    "    ax = plt.subplot(240+i+1)\n",
    "    pim.show(imgs[20+i], ax)\n",
    "    plt.title(\"PI of Democrat Plan\")\n",
    "\n",
    "for i in range(4):\n",
    "    ax = plt.subplot(240+i+5)\n",
    "    pim.show(imgs[-(i+20)], ax)\n",
    "    plt.title(\"PI of Republican Plan\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classification\n",
    "\n",
    "As before, we will flatten the images into 1d arrays (vectors)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "imgs_array = np.array([img.flatten() for img in imgs])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a training and testing set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing set size: 129\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(imgs_array, y, test_size=0.3, random_state=3, stratify = y)\n",
    "print('Testing set size:',len(y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we train and test a SVM model, as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9069767441860465"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "modelSVM = SVC(kernel=\"linear\")\n",
    "modelSVM.fit(X_train, y_train)\n",
    "\n",
    "modelSVM.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a fairly subtle classification problem, but the TDA signatures seem to do a good job of capturing the differences in these weighted graphs. Changing the `random_state` variable above gives different results, but one can get a more robust statistic by running this over several splits of the data and averaging.\n",
    "\n",
    "This can be improved with some feature tuning. For example, observe that the most persistent point is pretty much the same across all plans---this is Philadelphia. Removing highly persistent points from all diagrams actually has a positive effect on classification for this example. \n",
    "\n",
    "**Unofficial HW:** See if you can improve this classification rate with some tuning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As above, we can reshape the coefficients of the SVM classification vector to get an idea of how classification works here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "classifying_image = modelSVM.coef_.reshape((30,30))\n",
    "plt.imshow(classifying_image, cmap = plt.cm.RdBu)\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}