Tuto-GUDHI-simplicial-complexes-from-data-points.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "# TDA  with Python using the Gudhi Library  \n",
    "\n",
    "# Building simplicial complexes from a point cloud : Rips and Alpha complexes "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Authors:** F. Chazal and B. Michel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pickle as pickle\n",
    "import gudhi as gd  \n",
    "from pylab import *\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TDA typically aims at extracting topological signatures from a point cloud in $\\mathbb R^d$ or in a general metric space. [Simplicial complexes](https://en.wikipedia.org/wiki/Simplicial_complex) are used in computational geometry to infer topological signatures from a point cloud.\n",
    "\n",
    "This tutorial explains how to build [Vietoris-Rips complexes](https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex)  and [alpha complexes](https://en.wikipedia.org/wiki/Alpha_shape#Alpha_complex) from a data point in $\\mathbb R ^d$.\n",
    "\n",
    "![title](https://upload.wikimedia.org/wikipedia/commons/thumb/d/d0/VR_complex.svg/600px-VR_complex.svg.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The walk of 3 persons A, B and C, has been recorded using the accelerometer sensor of a smartphone in their pocket, giving rise to 3 multivariate time series in $\\mathbb R ^d$: each time series represents the 3 coordinates of the acceleration of the corresponding walker in a coordinate system attached to the sensor. \n",
    "\n",
    "Notice that the smartphone was carried in a possibly different position for each person and thus these time series cannot be compared coordinates by coordinates.\n",
    "\n",
    "Using a sliding window, each serie have been splitted in a list of 100 times series made of 200 consecutive points, that are stored in `data_A`, `data_B` and `data_C`.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We load the data with the pickle module :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = open(\"./datasets/data_acc\",\"rb\")\n",
    "data = pickle.load(f)    \n",
    "f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A'\n",
      " 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A'\n",
      " 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A'\n",
      " 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A'\n",
      " 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A'\n",
      " 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'A' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B'\n",
      " 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B'\n",
      " 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B'\n",
      " 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B'\n",
      " 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B'\n",
      " 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B' 'B'\n",
      " 'B' 'B' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C'\n",
      " 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C'\n",
      " 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C'\n",
      " 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C'\n",
      " 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C'\n",
      " 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C' 'C']\n"
     ]
    }
   ],
   "source": [
    "data_A = data[0]\n",
    "data_B = data[1] \n",
    "data_C = data[2]\n",
    "label  = data[3]\n",
    "print(label)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The object <code>data_A</code> is a list of 100 time series of the 3d acceleration for Walker A, let's have a look at the dimensions of <code>data_A</code>:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 200, 3)\n"
     ]
    }
   ],
   "source": [
    "print(np.shape(data_A))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now represent the trajectory of accelerations for the first trajectory of walker A :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_A_sample = data_A[0]\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection = '3d')\n",
    "ax.scatter(data_A_sample[:, 0], data_A_sample[:, 1], data_A_sample[:, 2]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vietoris-Rips complex\n",
    "\n",
    "\n",
    "The [$\\alpha$-Rips complex](https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex) of a point cloud $\\mathbb X$ in $(\\mathbb R^d,\\| \\|_2)$  is an [abstract simplicial complex](https://en.wikipedia.org/wiki/Abstract_simplicial_complex) that can be defined  by forming a simplex for every finite subset of $\\mathbb X$ that has diameter at most $\\alpha$. \n",
    "\n",
    "Definition of diameter here?\n",
    "\n",
    "Vietoris-Rips complexes can be defined for any metric space from the  matrix of pairwise distances (see this [notebook](https://github.com/GUDHI/TDA-tutorial/blob/master/Tuto-GUDHI-simplicial-complexes-from-distance-matrix.ipynb)).\n",
    "\n",
    "In order to efficiently compute an $\\alpha$-Rips complex, one can start by building a topological graph with:\n",
    "\n",
    "- as many vertices as there are points; and,\n",
    "- as edges only pairs of points whose distance is smaller than or equal to $\\alpha$.\n",
    "\n",
    "In other words, it corresponds to the [1-skeleton](https://en.wikipedia.org/wiki/N-skeleton) of the point cloud, with upper-bounded edge length. In GUDHI, this is performed via the `RipsComplex()` function (see the [Documentation](https://gudhi.inria.fr/python/latest/rips_complex_user.html) for details on the syntax):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "skeleton = gd.RipsComplex(points = data_A_sample, max_edge_length = 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `max_edge_length` parameter is the maximal diameter: only edges of length smaller than or equal to this value are included in the 1-skeleton.\n",
    "\n",
    "From the $\\alpha$-*truncated* 1-skeleton, it is then possible to add higher dimensional simplices to the simplicial complex, subject to the condition that all their faces are already in the complex. Their filtration value is then defined as the maximum filtration value of its faces which matches their diameter by design. This process necessarily yields the desired $\\alpha$-Rips complex since filtration values can never exceeds $\\alpha$ in this way. \n",
    "\n",
    "In practice, one should define a maximal dimension of simplicies to be added to the Rips complex for computational reasons. In GUDHI, this is achieved through the `create_simplex_tree()` method of the `RipsComplex` class which takes the argument `max_dimension` to limit the tree:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "Rips_simplex_tree_sample = skeleton.create_simplex_tree(max_dimension = 3) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `max_dimension` parameter is the maximum dimension of the simplices included in the filtration. The result is a simplex tree, of dimension 3 in this example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rips_simplex_tree_sample.dimension()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the methods of the simplex tree object to describe the Rips filtration. For instance, we can check that the 200 points of `data_A_sample` are all vertices of the Rips filtration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rips_simplex_tree_sample.num_vertices()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of simplices in the Rips complex is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27851"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rips_simplex_tree_sample.num_simplices()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that this is actually the number of simplices in the \"last\" Rips complex of the filtration, namely with parameter $\\alpha=$ `max_edge_length=`0.2. \n",
    "\n",
    "Notice that the number of simplices in a Rips complex increases very fast with the number of points and the dimension. AND THE $\\alpha$ ??"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's compute the list of simplices in the Rips complex with the `get_filtration() ` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "rips_generator = Rips_simplex_tree_sample.get_filtration()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "Let's print the 300 first elements in the list:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "([0], 0.0)\n",
      "([1], 0.0)\n",
      "([2], 0.0)\n",
      "([3], 0.0)\n",
      "([4], 0.0)\n",
      "([5], 0.0)\n",
      "([6], 0.0)\n",
      "([7], 0.0)\n",
      "([8], 0.0)\n",
      "([9], 0.0)\n",
      "([10], 0.0)\n",
      "([11], 0.0)\n",
      "([12], 0.0)\n",
      "([13], 0.0)\n",
      "([14], 0.0)\n",
      "([15], 0.0)\n",
      "([16], 0.0)\n",
      "([17], 0.0)\n",
      "([18], 0.0)\n",
      "([19], 0.0)\n",
      "([20], 0.0)\n",
      "([21], 0.0)\n",
      "([22], 0.0)\n",
      "([23], 0.0)\n",
      "([24], 0.0)\n",
      "([25], 0.0)\n",
      "([26], 0.0)\n",
      "([27], 0.0)\n",
      "([28], 0.0)\n",
      "([29], 0.0)\n",
      "([30], 0.0)\n",
      "([31], 0.0)\n",
      "([32], 0.0)\n",
      "([33], 0.0)\n",
      "([34], 0.0)\n",
      "([35], 0.0)\n",
      "([36], 0.0)\n",
      "([37], 0.0)\n",
      "([38], 0.0)\n",
      "([39], 0.0)\n",
      "([40], 0.0)\n",
      "([41], 0.0)\n",
      "([42], 0.0)\n",
      "([43], 0.0)\n",
      "([44], 0.0)\n",
      "([45], 0.0)\n",
      "([46], 0.0)\n",
      "([47], 0.0)\n",
      "([48], 0.0)\n",
      "([49], 0.0)\n",
      "([50], 0.0)\n",
      "([51], 0.0)\n",
      "([52], 0.0)\n",
      "([53], 0.0)\n",
      "([54], 0.0)\n",
      "([55], 0.0)\n",
      "([56], 0.0)\n",
      "([57], 0.0)\n",
      "([58], 0.0)\n",
      "([59], 0.0)\n",
      "([60], 0.0)\n",
      "([61], 0.0)\n",
      "([62], 0.0)\n",
      "([63], 0.0)\n",
      "([64], 0.0)\n",
      "([65], 0.0)\n",
      "([66], 0.0)\n",
      "([67], 0.0)\n",
      "([68], 0.0)\n",
      "([69], 0.0)\n",
      "([70], 0.0)\n",
      "([71], 0.0)\n",
      "([72], 0.0)\n",
      "([73], 0.0)\n",
      "([74], 0.0)\n",
      "([75], 0.0)\n",
      "([76], 0.0)\n",
      "([77], 0.0)\n",
      "([78], 0.0)\n",
      "([79], 0.0)\n",
      "([80], 0.0)\n",
      "([81], 0.0)\n",
      "([82], 0.0)\n",
      "([83], 0.0)\n",
      "([84], 0.0)\n",
      "([85], 0.0)\n",
      "([86], 0.0)\n",
      "([87], 0.0)\n",
      "([88], 0.0)\n",
      "([89], 0.0)\n",
      "([90], 0.0)\n",
      "([91], 0.0)\n",
      "([92], 0.0)\n",
      "([93], 0.0)\n",
      "([94], 0.0)\n",
      "([95], 0.0)\n",
      "([96], 0.0)\n",
      "([97], 0.0)\n",
      "([98], 0.0)\n",
      "([99], 0.0)\n",
      "([100], 0.0)\n",
      "([101], 0.0)\n",
      "([102], 0.0)\n",
      "([103], 0.0)\n",
      "([104], 0.0)\n",
      "([105], 0.0)\n",
      "([106], 0.0)\n",
      "([107], 0.0)\n",
      "([108], 0.0)\n",
      "([109], 0.0)\n",
      "([110], 0.0)\n",
      "([111], 0.0)\n",
      "([112], 0.0)\n",
      "([113], 0.0)\n",
      "([114], 0.0)\n",
      "([115], 0.0)\n",
      "([116], 0.0)\n",
      "([117], 0.0)\n",
      "([118], 0.0)\n",
      "([119], 0.0)\n",
      "([120], 0.0)\n",
      "([121], 0.0)\n",
      "([122], 0.0)\n",
      "([123], 0.0)\n",
      "([124], 0.0)\n",
      "([125], 0.0)\n",
      "([126], 0.0)\n",
      "([127], 0.0)\n",
      "([128], 0.0)\n",
      "([129], 0.0)\n",
      "([130], 0.0)\n",
      "([131], 0.0)\n",
      "([132], 0.0)\n",
      "([133], 0.0)\n",
      "([134], 0.0)\n",
      "([135], 0.0)\n",
      "([136], 0.0)\n",
      "([137], 0.0)\n",
      "([138], 0.0)\n",
      "([139], 0.0)\n",
      "([140], 0.0)\n",
      "([141], 0.0)\n",
      "([142], 0.0)\n",
      "([143], 0.0)\n",
      "([144], 0.0)\n",
      "([145], 0.0)\n",
      "([146], 0.0)\n",
      "([147], 0.0)\n",
      "([148], 0.0)\n",
      "([149], 0.0)\n",
      "([150], 0.0)\n",
      "([151], 0.0)\n",
      "([152], 0.0)\n",
      "([153], 0.0)\n",
      "([154], 0.0)\n",
      "([155], 0.0)\n",
      "([156], 0.0)\n",
      "([157], 0.0)\n",
      "([158], 0.0)\n",
      "([159], 0.0)\n",
      "([160], 0.0)\n",
      "([161], 0.0)\n",
      "([162], 0.0)\n",
      "([163], 0.0)\n",
      "([164], 0.0)\n",
      "([165], 0.0)\n",
      "([166], 0.0)\n",
      "([167], 0.0)\n",
      "([168], 0.0)\n",
      "([169], 0.0)\n",
      "([170], 0.0)\n",
      "([171], 0.0)\n",
      "([172], 0.0)\n",
      "([173], 0.0)\n",
      "([174], 0.0)\n",
      "([175], 0.0)\n",
      "([176], 0.0)\n",
      "([177], 0.0)\n",
      "([178], 0.0)\n",
      "([179], 0.0)\n",
      "([180], 0.0)\n",
      "([181], 0.0)\n",
      "([182], 0.0)\n",
      "([183], 0.0)\n",
      "([184], 0.0)\n",
      "([185], 0.0)\n",
      "([186], 0.0)\n",
      "([187], 0.0)\n",
      "([188], 0.0)\n",
      "([189], 0.0)\n",
      "([190], 0.0)\n",
      "([191], 0.0)\n",
      "([192], 0.0)\n",
      "([193], 0.0)\n",
      "([194], 0.0)\n",
      "([195], 0.0)\n",
      "([196], 0.0)\n",
      "([197], 0.0)\n",
      "([198], 0.0)\n",
      "([199], 0.0)\n",
      "([6, 34], 0.010037972604067026)\n",
      "([95, 120], 0.011934283430520687)\n",
      "([24, 108], 0.017975277911620735)\n",
      "([151, 177], 0.018713766643837386)\n",
      "([79, 106], 0.018944080262710026)\n",
      "([42, 43], 0.02139398300924822)\n",
      "([81, 136], 0.02153918522135876)\n",
      "([4, 191], 0.022836281768273937)\n",
      "([156, 186], 0.02404079478719446)\n",
      "([52, 190], 0.02528062297491887)\n",
      "([47, 185], 0.02543660160084278)\n",
      "([4, 53], 0.02656518191166776)\n",
      "([137, 165], 0.026689955732447364)\n",
      "([12, 68], 0.027999307509293882)\n",
      "([23, 51], 0.028305883664001743)\n",
      "([10, 38], 0.030244785153807872)\n",
      "([54, 165], 0.030334711041972974)\n",
      "([163, 190], 0.030841760585284376)\n",
      "([53, 191], 0.03269553417517446)\n",
      "([4, 53, 191], 0.03269553417517446)\n",
      "([48, 155], 0.03270191445466141)\n",
      "([97, 154], 0.033380721157578334)\n",
      "([42, 181], 0.03371579898207958)\n",
      "([21, 181], 0.034473350301356065)\n",
      "([16, 99], 0.035402079628179935)\n",
      "([43, 181], 0.03604829516079782)\n",
      "([42, 43, 181], 0.03604829516079782)\n",
      "([40, 174], 0.03635244907843206)\n",
      "([122, 149], 0.036790327465245506)\n",
      "([108, 190], 0.037527917767976426)\n",
      "([96, 178], 0.038341942830274006)\n",
      "([52, 108], 0.03848452715053156)\n",
      "([52, 108, 190], 0.03848452715053156)\n",
      "([107, 190], 0.03952421033999288)\n",
      "([125, 180], 0.04042591259328599)\n",
      "([10, 94], 0.04086899075093489)\n",
      "([39, 178], 0.041456725944049144)\n",
      "([79, 162], 0.04152965660826004)\n",
      "([24, 164], 0.041682370973830186)\n",
      "([80, 136], 0.042696594676859156)\n",
      "([6, 10], 0.04296810997705157)\n",
      "([65, 68], 0.043114058785969134)\n",
      "([49, 104], 0.044036842087052615)\n",
      "([85, 198], 0.04441595016432722)\n",
      "([92, 151], 0.044417584119355306)\n",
      "([9, 123], 0.04474070645396651)\n",
      "([25, 80], 0.044775941184971184)\n",
      "([24, 190], 0.04503018556479643)\n",
      "([24, 108, 190], 0.04503018556479643)\n",
      "([108, 164], 0.04509993323720115)\n",
      "([24, 108, 164], 0.04509993323720115)\n",
      "([120, 177], 0.0452854613645483)\n",
      "([21, 43], 0.04536807662883676)\n",
      "([21, 43, 181], 0.04536807662883676)\n",
      "([54, 137], 0.045461176546587496)\n",
      "([54, 137, 165], 0.045461176546587496)\n",
      "([52, 163], 0.04621308427274681)\n",
      "([52, 163, 190], 0.04621308427274681)\n",
      "([95, 177], 0.04646166650046034)\n",
      "([95, 120, 177], 0.04646166650046034)\n",
      "([37, 123], 0.04669949572532886)\n",
      "([43, 71], 0.04670615440174885)\n",
      "([106, 162], 0.046711459461249945)\n",
      "([79, 106, 162], 0.046711459461249945)\n",
      "([23, 53], 0.046858285510675696)\n",
      "([37, 150], 0.04704462724902802)\n",
      "([39, 92], 0.04705525816526781)\n",
      "([8, 147], 0.04728024972438278)\n",
      "([120, 175], 0.04745268912295697)\n",
      "([52, 107], 0.04796088461444387)\n",
      "([52, 107, 190], 0.04796088461444387)\n",
      "([159, 186], 0.049566945306322815)\n",
      "([25, 136], 0.049588833581765135)\n",
      "([25, 80, 136], 0.049588833581765135)\n",
      "([10, 34], 0.049595510048793735)\n",
      "([6, 10, 34], 0.049595510048793735)\n",
      "([23, 134], 0.04963560183980849)\n",
      "([55, 166], 0.05056851213947273)\n",
      "([4, 136], 0.050702254644147744)\n",
      "([80, 81], 0.05071354281649033)\n",
      "([80, 81, 136], 0.05071354281649033)\n",
      "([100, 156], 0.051819557360131926)\n",
      "([135, 136], 0.052141185592581234)\n",
      "([107, 163], 0.05222368637888371)\n",
      "([52, 107, 163], 0.05222368637888371)\n",
      "([107, 163, 190], 0.05222368637888371)\n",
      "([52, 107, 163, 190], 0.05222368637888371)\n",
      "([50, 161], 0.052446656995465385)\n",
      "([70, 125], 0.05251374992323431)\n",
      "([79, 134], 0.052579455550623565)\n",
      "([49, 187], 0.052584575552152)\n",
      "([106, 134], 0.05290928140695164)\n",
      "([79, 106, 134], 0.05290928140695164)\n",
      "([24, 52], 0.05308009651460706)\n",
      "([24, 52, 108], 0.05308009651460706)\n",
      "([24, 52, 190], 0.05308009651460706)\n",
      "([24, 52, 108, 190], 0.05308009651460706)\n",
      "([120, 178], 0.05312372783417972)\n",
      "([63, 90], 0.05346525304344867)\n",
      "([95, 175], 0.053922095267153705)\n"
     ]
    }
   ],
   "source": [
    "rips_list = list(rips_generator)\n",
    "for splx in rips_list[0:300] :\n",
    "    print(splx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "The filtration value is the diameter of the simplex, which is zero for the vertices of course. The first edge in the filtration is `[6, 34]`, these two points are the two closest points in `data_A_sample`, at distance $0.0100$ of each other. If you scroll down, you will see that the first triangle is `[4, 53, 191]`, for the filtration value $0.0327$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "### Alpha complex "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "The [alpha complex](https://en.wikipedia.org/wiki/Alpha_shape#Alpha_complex) is a simplicial complex built from the finite cells of a [Delaunay triangulation](https://en.wikipedia.org/wiki/Delaunay_triangulation). Alpha complexes contain less simplices than Rips complexes and so they can be a better option. They are sub-complexes of the Delaunay complex and, as such, they are geometric simpicial complexes.\n",
    "\n",
    "The `AlphaComplex()` function directly computes the simplex tree representing the alpha complex:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha_complex = gd.AlphaComplex(points = data_A_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "st_alpha = alpha_complex.create_simplex_tree(max_alpha_square = 0.2**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Talk about `max_alpha_square` ?\n",
    "\n",
    "Talk about `default_filtration_value` ?\n",
    "\n",
    "The point cloud `data_A_sample` belongs to $\\mathbb R^3$ and so does the Alpha Complex:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "st_alpha.dimension()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As for the Rips complex, the 200 points of `data_A_sample` are all vertices of the Alpha complex :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "st_alpha.num_vertices()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the number of simplices in the Alpha complex is smaller than for the Rips complex:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3334"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "st_alpha.num_simplices()"
   ]
  }
 ],
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