quick_start.ipynb

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    "# Quick start\n",
    "This notebook contains quick-start code for running the extension method and the analogous bars method.\n",
    "\n",
    "### Contents\n",
    "1. Quick start for extension method comparing two VR barcodes\n",
    "2. Quick start for similarity-centric analogous bars method\n",
    "\n",
    "See notebooks in `examples` directory for more details."
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      "┌ Warning: ORCA.jl has been deprecated and all savefig functionality\n",
      "│ has been implemented directly in PlotlyBase itself.\n",
      "│ \n",
      "│ By implementing in PlotlyBase.jl, the savefig routines are automatically\n",
      "│ available to PlotlyJS.jl also.\n",
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   "source": [
    "include(\"extension_method.jl\")"
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  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "changing-parking",
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   "outputs": [],
   "source": [
    "using .ext\n",
    "using Distances\n",
    "using Eirene\n",
    "using Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "three-burst",
   "metadata": {},
   "source": [
    "# 1. Quick start for extension method comparing two VR barcodes"
   ]
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   "id": "incorporated-companion",
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    "# generate random point cloud\n",
    "P = rand(3, 50)\n",
    "\n",
    "# compute two different distance matrices\n",
    "D_Z = pairwise(Euclidean(), P, dims = 2)\n",
    "D_Y = pairwise(Cityblock(), P, dims = 2)\n",
    "\n",
    "# run Eirene \n",
    "C_Z = eirene(D_Z, record = \"all\")\n",
    "C_Y = eirene(D_Y, record = \"all\")\n",
    "\n",
    "# plot barcodes\n",
    "barcode_Z = barcode(C_Z, dim = 1)\n",
    "barcode_Y = barcode(C_Y, dim = 1)\n",
    "p1 = plot_barcode(barcode_Z, title = \"barcode(VR(Z))\")\n",
    "p2 = plot_barcode(barcode_Y, title = \"barcode(VR(Y))\")\n",
    "plot(p1, p2, layout = grid(2,1))"
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    "# select a bar of interest and run extension \n",
    "Z_bar = 12\n",
    "extension = run_extension_VR_to_VR_bar(C_Z = C_Z, D_Z = D_Z, C_Y = C_Y, D_Y = D_Y, Z_bar = Z_bar, dim = 1);"
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      "*** Parameter key, value pair *** \n",
      "key: 1 parameter: 0.518738 \n",
      "key: 2 parameter: 0.522099 \n",
      "key: 3 parameter: 0.583422 \n"
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      "Select a key for parameter 1\n"
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      "Selected parameter: 0.5187378547288659\n",
      "\n",
      "Baseline bars extension at selected parameter: [15, 18]\n",
      "\n",
      "*** Offset bar extensions at selected parameter *** \n",
      "key: 1 offset bar extension: [4, 19, 18]\n",
      "key: 2 offset bar extension: [12]\n",
      "key: 3 offset bar extension: [18]\n",
      "key: 4 offset bar extension: [14, 19]\n",
      "key: 5 offset bar extension: [3]\n",
      "key: 6 offset bar extension: [11]\n",
      "key: 7 offset bar extension: [19, 18]\n",
      "key: 8 offset bar extension: [9]\n"
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      "\n",
      "Select keys for offset bar extensions. \n",
      "Leave blank to select none. \n",
      "To select multiple keys, separate keys with space. ex) 1 2 3 :  \n"
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    "# explore baseline and offset bar extensions\n",
    "return_extension_results_at_parameter(extension)"
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   "source": [
    "# find all cycle extensions and bar extensions under fixed interval decomposition of barcode(VR(Y))\n",
    "CE, BE_fixed = find_CE_BE(extension)\n",
    "\n",
    "# find alternative bar extensions for a specific bar extension\n",
    "param = extension[\"epsilon_0\"]\n",
    "bar_ext = BE_fixed[param][0]\n",
    "alt_ext = find_alternative_bar_extension(extension, param, bar_extension = bar_ext);"
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  {
   "cell_type": "markdown",
   "id": "agricultural-excitement",
   "metadata": {},
   "source": [
    "# 2. Quick start for similarity-centric analogous bars method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "muslim-praise",
   "metadata": {},
   "outputs": [],
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    "# generate random point cloud\n",
    "P = rand(3, 50)\n",
    "Q = rand(3, 50)\n",
    "\n",
    "# compute distance matrices\n",
    "D_P = pairwise(Euclidean(), P, dims = 2)\n",
    "D_Q = pairwise(Euclidean(), Q, dims = 2)\n",
    "D_P_Q = pairwise(Euclidean(), P, Q, dims = 2)\n",
    "D_Q_P = pairwise(Euclidean(), Q, P, dims = 2);"
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  {
   "cell_type": "markdown",
   "id": "regular-hunter",
   "metadata": {},
   "source": [
    "Run persistence on the VR filtration and the Witness filtration"
   ]
  },
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   "cell_type": "code",
   "execution_count": 34,
   "id": "polish-weekend",
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   "source": [
    "# Compute Vietoris-Rips persistence on two regions\n",
    "dim = 1\n",
    "VR_P = eirene(D_P, record = \"all\", maxdim = dim)\n",
    "VR_Q = eirene(D_Q, record = \"all\", maxdim = dim)\n",
    "\n",
    "# compute Witness persistence\n",
    "W_P = compute_Witness_persistence(D_P_Q, maxdim = dim)\n",
    "W_Q = compute_Witness_persistence(D_Q_P, maxdim = dim)\n",
    "\n",
    "# plot all four barcodes\n",
    "barcode_VR_P = barcode(VR_P, dim = 1)\n",
    "barcode_W_P = barcode(W_P[\"eirene_output\"], dim = 1)\n",
    "barcode_W_Q = barcode(W_Q[\"eirene_output\"], dim = 1)\n",
    "barcode_VR_Q = barcode(VR_Q, dim = 1)\n",
    "\n",
    "# plot\n",
    "p1 = plot_barcode(barcode_VR_P, title = \"Barcode(VR(P))\")\n",
    "p2 = plot_barcode(barcode_W_P, title = \"Barcode(W(P,Q))\")\n",
    "p3 = plot_barcode(barcode_W_Q, title = \"Barcode(W(Q,P))\")\n",
    "p4 = plot_barcode(barcode_VR_Q, title = \"Barcode(VR(Q))\")\n",
    "plot(p1, p2, p3, p4, layout = grid(4,1), size = (500, 700))"
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   "cell_type": "markdown",
   "id": "rational-strip",
   "metadata": {},
   "source": [
    "Select a bar of interest in `barcode(W(P,Q))` and run persistence"
   ]
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  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "suburban-classification",
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   "source": [
    "# select bar\n",
    "W_P_bar = 15\n",
    "\n",
    "# run extension\n",
    "extension_P, extension_Q = run_similarity_analogous(VR_P = VR_P,\n",
    "                                                    D_P = D_P,\n",
    "                                                    VR_Q = VR_Q,\n",
    "                                                    D_Q = D_Q,\n",
    "                                                    W_PQ = W_P,\n",
    "                                                    W_PQ_bar = W_P_bar,\n",
    "                                                    dim = 1);"
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   "cell_type": "markdown",
   "id": "surprised-shoulder",
   "metadata": {},
   "source": [
    "Plot the baseline bar extensions to `barcode(VR(P))` and `barcode(VR(Q))`"
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  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "disturbed-finance",
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