{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Classify Neural Manifold Topology"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set-up + Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working directory:  /home/facosta/neurometry/neurometry\n",
      "Directory added to path:  /home/facosta/neurometry\n",
      "Directory added to path:  /home/facosta/neurometry/neurometry\n",
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n",
      "The jupyter_black extension is already loaded. To reload it, use:\n",
      "  %reload_ext jupyter_black\n"
     ]
    }
   ],
   "source": [
    "import setup\n",
    "\n",
    "setup.main()\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%load_ext jupyter_black\n",
    "\n",
    "import os\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch\n",
    "\n",
    "os.environ[\"GEOMSTATS_BACKEND\"] = \"pytorch\"\n",
    "import geomstats.backend as gs\n",
    "import neurometry.datasets.synthetic as synthetic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "noise level: 0.71%\n"
     ]
    }
   ],
   "source": [
    "import neurometry.datasets.synthetic as synthetic\n",
    "\n",
    "circle_task_points = synthetic.hypersphere(1, 1000)\n",
    "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n",
    "    points=circle_task_points,\n",
    "    encoding_dim=10,\n",
    "    nonlinearity=\"sigmoid\",\n",
    "    scales=gs.ones(10),\n",
    "    poisson_multiplier=100,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
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     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot noisy_points and manifold_points in 3D with plotly\n",
    "\n",
    "import plotly.graph_objects as go\n",
    "\n",
    "fig = go.Figure()\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=circle_noisy_points[:, 0],\n",
    "        y=circle_noisy_points[:, 1],\n",
    "        z=circle_noisy_points[:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3),\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=circle_manifold_points[:, 0],\n",
    "        y=circle_manifold_points[:, 1],\n",
    "        z=circle_manifold_points[:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3),\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "from neurometry.estimators.topology.persistent_homology import compute_diagrams_shuffle\n",
    "\n",
    "\n",
    "import neurometry.datasets.synthetic as synthetic\n",
    "\n",
    "circle_task_points = synthetic.hypersphere(1, 1000)\n",
    "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n",
    "    points=circle_task_points,\n",
    "    encoding_dim=10,\n",
    "    nonlinearity=\"sigmoid\",\n",
    "    scales=gs.ones(10),\n",
    "    poisson_multiplier=100,\n",
    ")\n",
    "\n",
    "num_shuffles = 100\n",
    "\n",
    "circle_noisy_diagrams = compute_diagrams_shuffle(\n",
    "    circle_noisy_points, num_shuffles=num_shuffles, homology_dimensions=[0, 1, 2]\n",
    ")\n",
    "\n",
    "\n",
    "from gtda.diagrams import PersistenceEntropy\n",
    "\n",
    "circle_PE = PersistenceEntropy()\n",
    "\n",
    "circle_features = circle_PE.fit_transform(circle_noisy_diagrams)\n",
    "\n",
    "# manifold_diagrams = compute_diagrams_shuffle(manifold_points, num_shuffles=num_shuffles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = noisy_points\n",
    "\n",
    "\n",
    "def _shuffle_entries(data, rng):\n",
    "    return np.array([rng.permutation(row) for row in data])\n",
    "\n",
    "\n",
    "seed = 0\n",
    "rng = np.random.default_rng(seed)\n",
    "shuffled_Xs = [_shuffle_entries(X, rng) for _ in range(num_shuffles)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
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       "                            \n",
       "var gd = document.getElementById('b002dd44-9735-4463-91a0-ef7f7a400613');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
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       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.graph_objects as go\n",
    "\n",
    "fig = go.Figure()\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=X[:, 0],\n",
    "        y=X[:, 1],\n",
    "        z=X[:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3),\n",
    "    )\n",
    ")\n",
    "\n",
    "i = 5\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=shuffled_Xs[i][:, 0],\n",
    "        y=shuffled_Xs[i][:, 1],\n",
    "        z=shuffled_Xs[i][:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3),\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
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                       {\"responsive\": true}                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('f6812aac-2dae-4cc9-82b5-75180cb2aa10');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })                };                });            </script>        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from gtda.plotting import plot_diagram\n",
    "\n",
    "plot_diagram(noisy_diagrams[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_diagram(noisy_diagrams[70])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "from gtda.diagrams import PersistenceEntropy\n",
    "\n",
    "circle_PE = PersistenceEntropy()\n",
    "\n",
    "circle_features = circle_PE.fit_transform(circle_noisy_diagrams)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
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       "                            \n",
       "var gd = document.getElementById('67cc471e-7990-40ff-9cbc-e3c385c2a0e1');\n",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3d plot with plotly\n",
    "fig = go.Figure()\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=features[1:, 0],\n",
    "        y=features[1:, 1],\n",
    "        z=features[1:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3, color=\"blue\"),\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=[features[0, 0]],\n",
    "        y=[features[0, 1]],\n",
    "        z=[features[0, 2]],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3, color=\"red\"),\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x1000 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from neurometry.estimators.topology.plotting import plot_all_barcodes_with_null\n",
    "\n",
    "plot_all_barcodes_with_null(\n",
    "    noisy_diagrams, \"noisy\", diagrams_2=manifold_diagrams, dataset_name_2=\"manifold\"\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _get_lifespan_from_diagram(diagram):\n",
    "    birth = diagram[:, 0]\n",
    "    death = diagram[:, 1]\n",
    "    if np.isfinite(death).any():\n",
    "        inf_value = 3 * np.max(death[death != np.inf])\n",
    "    else:\n",
    "        inf_value = 1000\n",
    "    death[death == np.inf] = inf_value\n",
    "    lifespan = death - birth\n",
    "    indices = np.argsort(-lifespan)[:20]\n",
    "\n",
    "    return lifespan[indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate_betti_numbers(points, num_shuffles, homology_dimensions=(0, 1, 2)):\n",
    "    all_diagrams = compute_diagrams_shuffle(\n",
    "        points, num_shuffles=num_shuffles, homology_dimensions=homology_dimensions\n",
    "    )\n",
    "    diagram = all_diagrams[0]\n",
    "    shuffled_diagrams = all_diagrams[1:]\n",
    "\n",
    "    betti_numbers = {dim: None for dim in homology_dimensions}\n",
    "\n",
    "    for dim in homology_dimensions:\n",
    "        filtered_diagram = diagram[diagram[:, 2] == dim]\n",
    "        lifespan = _get_lifespan_from_diagram(filtered_diagram)\n",
    "        filtered_shuffled_diagrams = np.array(\n",
    "            [\n",
    "                shuffled_diagrams[i, shuffled_diagrams[i, :, 2] == 1]\n",
    "                for i in range(shuffled_diagrams.shape[0])\n",
    "            ]\n",
    "        )\n",
    "        betti_number = []\n",
    "        for diag in filtered_shuffled_diagrams:\n",
    "            shuffled_lifespan = _get_lifespan_from_diagram(diag)\n",
    "            significant_features = (lifespan > shuffled_lifespan).astype(int)\n",
    "            betti_number.append(sum(significant_features))\n",
    "        betti_numbers[dim] = (np.mean(betti_number), np.std(betti_number))\n",
    "\n",
    "    return betti_numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: (1.28, 2.209434316742636), 1: (1.0, 0.0), 2: (0.0, 0.0)}\n"
     ]
    }
   ],
   "source": [
    "betti_numbers = estimate_betti_numbers(\n",
    "    manifold_points, num_shuffles=100, homology_dimensions=(0, 1, 2)\n",
    ")\n",
    "print(betti_numbers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "homology_dimensions = (0, 1)\n",
    "points = manifold_points\n",
    "num_shuffles = 100\n",
    "\n",
    "all_diagrams = compute_diagrams_shuffle(\n",
    "    points, num_shuffles=num_shuffles, homology_dimensions=homology_dimensions\n",
    ")\n",
    "\n",
    "plot_all_barcodes_with_null(all_diagrams, \"manifold\")\n",
    "\n",
    "\n",
    "diagram = all_diagrams[0]\n",
    "lifespan = _get_lifespan_from_diagram(diagram)\n",
    "shuffled_diagrams = all_diagrams[1:]\n",
    "\n",
    "betti_numbers = {dim: None for dim in homology_dimensions}\n",
    "\n",
    "for dim in homology_dimensions:\n",
    "    betti_number = []\n",
    "    for shuffled_diagram in shuffled_diagrams:\n",
    "        shuffled_lifespan = _get_lifespan_from_diagram(shuffled_diagram)\n",
    "        significant_features = (lifespan > shuffled_lifespan).astype(int)\n",
    "        betti_number.append(sum(significant_features))\n",
    "    betti_numbers[dim] = np.mean(betti_number)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_betti_numbers(diagrams):\n",
    "    original_diagram = diagrams[0]\n",
    "    shuffled_diagrams = diagrams[1:]\n",
    "\n",
    "    dims = np.unique(original_diagram[:, 2]).astype(int)\n",
    "\n",
    "    betti_numbers = {dim: None for dim in dims}\n",
    "    for i, dim in enumerate(dims):\n",
    "        diagram_dim = original_diagram[original_diagram[:, 2] == dim]\n",
    "        null_diagram_dim = shuffled_diagrams[:, :, 2] == dim\n",
    "        null_diagram = shuffled_diagrams[null_diagram_dim]\n",
    "\n",
    "        null_lifespans_dim = _get_lifespan_from_diagram(null_diagram)\n",
    "        lifespans_dim = _get_lifespan_from_diagram(diagram_dim)\n",
    "\n",
    "        comparison = (lifespans_dim > null_lifespans_dim).astype(int)\n",
    "\n",
    "        betti_numbers[dim] = sum(comparison)\n",
    "\n",
    "    return betti_numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "betti = get_betti_numbers(noisy_diagrams)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0, 1: 5, 2: 2}"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "betti"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classify circle, sphere, torus point clouds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "import neurometry.datasets.synthetic as synthetic\n",
    "from neurometry.estimators.topology.persistent_homology import compute_diagrams_shuffle\n",
    "from gtda.diagrams import PersistenceEntropy\n",
    "\n",
    "num_points = 1000\n",
    "encoding_dim = 10\n",
    "poisson_multiplier = 100\n",
    "homology_dimensions = [0, 1, 2]\n",
    "num_shuffles = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "noise level: 0.71%\n"
     ]
    }
   ],
   "source": [
    "circle_task_points = synthetic.hypersphere(1, num_points)\n",
    "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n",
    "    points=circle_task_points,\n",
    "    encoding_dim=encoding_dim,\n",
    "    nonlinearity=\"sigmoid\",\n",
    "    scales=gs.ones(encoding_dim),\n",
    "    poisson_multiplier=poisson_multiplier,\n",
    ")\n",
    "\n",
    "\n",
    "circle_noisy_diagrams = compute_diagrams_shuffle(\n",
    "    circle_noisy_points,\n",
    "    num_shuffles=num_shuffles,\n",
    "    homology_dimensions=homology_dimensions,\n",
    ")\n",
    "\n",
    "circle_PE = PersistenceEntropy()\n",
    "\n",
    "circle_features = circle_PE.fit_transform(circle_noisy_diagrams)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "noise level: 0.71%\n"
     ]
    }
   ],
   "source": [
    "sphere_task_points = synthetic.hypersphere(2, num_points)\n",
    "sphere_noisy_points, sphere_manifold_points = synthetic.synthetic_neural_manifold(\n",
    "    points=sphere_task_points,\n",
    "    encoding_dim=encoding_dim,\n",
    "    nonlinearity=\"sigmoid\",\n",
    "    scales=gs.ones(encoding_dim),\n",
    "    poisson_multiplier=poisson_multiplier,\n",
    ")\n",
    "\n",
    "sphere_noisy_diagrams = compute_diagrams_shuffle(\n",
    "    sphere_noisy_points,\n",
    "    num_shuffles=num_shuffles,\n",
    "    homology_dimensions=homology_dimensions,\n",
    ")\n",
    "\n",
    "sphere_PE = PersistenceEntropy()\n",
    "sphere_features = sphere_PE.fit_transform(sphere_noisy_diagrams)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "noise level: 0.71%\n"
     ]
    }
   ],
   "source": [
    "torus_task_points = synthetic.hypertorus(2, num_points)\n",
    "torus_noisy_points, torus_manifold_points = synthetic.synthetic_neural_manifold(\n",
    "    points=torus_task_points,\n",
    "    encoding_dim=encoding_dim,\n",
    "    nonlinearity=\"sigmoid\",\n",
    "    scales=gs.ones(encoding_dim),\n",
    "    poisson_multiplier=poisson_multiplier,\n",
    ")\n",
    "\n",
    "torus_noisy_diagrams = compute_diagrams_shuffle(\n",
    "    torus_noisy_points,\n",
    "    num_shuffles=num_shuffles,\n",
    "    homology_dimensions=homology_dimensions,\n",
    ")\n",
    "\n",
    "torus_PE = PersistenceEntropy()\n",
    "\n",
    "torus_features = torus_PE.fit_transform(torus_noisy_diagrams)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
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                       {\"responsive\": true}                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('03175875-422d-41e7-9b4c-8536f45300c5');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })                };                });            </script>        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3d plot with plotly\n",
    "fig = go.Figure()\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=circle_features[1:, 0],\n",
    "        y=circle_features[1:, 1],\n",
    "        z=circle_features[1:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3, color=\"lightpink\"),\n",
    "        name=\"Shuffled Circle\",\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=[circle_features[0, 0]],\n",
    "        y=[circle_features[0, 1]],\n",
    "        z=[circle_features[0, 2]],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3, color=\"deeppink\"),\n",
    "        name=\"Circle\",\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=sphere_features[1:, 0],\n",
    "        y=sphere_features[1:, 1],\n",
    "        z=sphere_features[1:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3, color=\"lightgreen\"),\n",
    "        name=\"Shuffled Sphere\",\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=[sphere_features[0, 0]],\n",
    "        y=[sphere_features[0, 1]],\n",
    "        z=[sphere_features[0, 2]],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3, color=\"darkgreen\"),\n",
    "        name=\"Sphere\",\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=torus_features[1:, 0],\n",
    "        y=torus_features[1:, 1],\n",
    "        z=torus_features[1:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3, color=\"lightblue\"),\n",
    "        name=\"Shuffled Torus\",\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=[torus_features[0, 0]],\n",
    "        y=[torus_features[0, 1]],\n",
    "        z=[torus_features[0, 2]],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3, color=\"darkblue\"),\n",
    "        name=\"Torus\",\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classifier score: 1.0\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-3 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-3 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-3 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-3 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-3 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-3 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-3 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-3 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-3 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>TopologicalClassifier(num_samples=10, poisson_multiplier=100, reduce_dim=True)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator  sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label  sk-toggleable__label-arrow \">&nbsp;TopologicalClassifier<span class=\"sk-estimator-doc-link \">i<span>Not fitted</span></span></label><div class=\"sk-toggleable__content \"><pre>TopologicalClassifier(num_samples=10, poisson_multiplier=100, reduce_dim=True)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "TopologicalClassifier(num_samples=10, poisson_multiplier=100, reduce_dim=True)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_points = 500\n",
    "encoding_dim = 10\n",
    "poisson_multiplier = 100\n",
    "\n",
    "\n",
    "test_task_points = synthetic.hypertorus(2, 400)\n",
    "test_noisy_points, test_manifold_points = synthetic.synthetic_neural_manifold(\n",
    "    points=test_task_points,\n",
    "    encoding_dim=encoding_dim,\n",
    "    nonlinearity=\"sigmoid\",\n",
    "    scales=gs.ones(encoding_dim),\n",
    "    poisson_multiplier=poisson_multiplier,\n",
    ")\n",
    "\n",
    "from neurometry.estimators.topology.persistent_homology import TopologicalClassifier\n",
    "\n",
    "num_samples = 10\n",
    "\n",
    "TC = TopologicalClassifier(\n",
    "    num_samples=num_samples, poisson_multiplier=poisson_multiplier, reduce_dim=True\n",
    ")\n",
    "TC.fit(test_noisy_points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "TC.predict(test_noisy_points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.base import BaseEstimator, ClassifierMixin\n",
    "\n",
    "\n",
    "class TopologicalClassifier(ClassifierMixin, BaseEstimator):\n",
    "    def __init__(\n",
    "        self,\n",
    "        num_samples,\n",
    "        poisson_multiplier,\n",
    "        homology_dimensions=[0, 1, 2],\n",
    "        reduce_dim=False,\n",
    "    ):\n",
    "        self.num_samples = num_samples\n",
    "        self.poisson_multiplier = poisson_multiplier\n",
    "        self.homology_dimensions = homology_dimensions\n",
    "        self.reduce_dim = reduce_dim\n",
    "        self.classifier = RandomForestClassifier()\n",
    "\n",
    "    def _generate_ref_data(self, input_data):\n",
    "        num_points = input_data.shape[0]\n",
    "        encoding_dim = input_data.shape[1]\n",
    "        circle_task_points = synthetic.hypersphere(1, num_points)\n",
    "        circle_point_clouds = []\n",
    "        for i in range(self.num_samples):\n",
    "            circle_noisy_points, _ = synthetic.synthetic_neural_manifold(\n",
    "                points=circle_task_points,\n",
    "                encoding_dim=encoding_dim,\n",
    "                nonlinearity=\"sigmoid\",\n",
    "                scales=gs.ones(encoding_dim),\n",
    "                poisson_multiplier=self.poisson_multiplier,\n",
    "            )\n",
    "            circle_point_clouds.append(circle_noisy_points)\n",
    "\n",
    "        sphere_task_points = synthetic.hypersphere(2, num_points)\n",
    "        sphere_point_clouds = []\n",
    "        for i in range(num_samples):\n",
    "            sphere_noisy_points, _ = synthetic.synthetic_neural_manifold(\n",
    "                points=sphere_task_points,\n",
    "                encoding_dim=encoding_dim,\n",
    "                nonlinearity=\"sigmoid\",\n",
    "                scales=gs.ones(encoding_dim),\n",
    "                poisson_multiplier=self.poisson_multiplier,\n",
    "            )\n",
    "            sphere_point_clouds.append(sphere_noisy_points)\n",
    "\n",
    "        torus_task_points = synthetic.hypertorus(2, num_points)\n",
    "        torus_point_clouds = []\n",
    "        for i in range(num_samples):\n",
    "            torus_noisy_points, _ = synthetic.synthetic_neural_manifold(\n",
    "                points=torus_task_points,\n",
    "                encoding_dim=encoding_dim,\n",
    "                nonlinearity=\"sigmoid\",\n",
    "                scales=gs.ones(encoding_dim),\n",
    "                poisson_multiplier=self.poisson_multiplier,\n",
    "            )\n",
    "            torus_point_clouds.append(torus_noisy_points)\n",
    "\n",
    "        klein_bottle_task_points = synthetic.klein_bottle(num_points)\n",
    "        klein_bottle_point_clouds = []\n",
    "        for i in range(num_samples):\n",
    "            klein_bottle_noisy_points, _ = synthetic.synthetic_neural_manifold(\n",
    "                points=klein_bottle_task_points,\n",
    "                encoding_dim=encoding_dim,\n",
    "                nonlinearity=\"sigmoid\",\n",
    "                scales=gs.ones(encoding_dim),\n",
    "                poisson_multiplier=self.poisson_multiplier,\n",
    "            )\n",
    "            klein_bottle_point_clouds.append(klein_bottle_noisy_points)\n",
    "\n",
    "        circle_labels = np.zeros(num_samples)\n",
    "        sphere_labels = np.ones(num_samples)\n",
    "        torus_labels = 2 * np.ones(num_samples)\n",
    "        klein_bottle_labels = 3 * np.ones(num_samples)\n",
    "        ref_labels = np.concatenate(\n",
    "            [\n",
    "                circle_labels,\n",
    "                sphere_labels,\n",
    "                torus_labels,\n",
    "                klein_bottle_labels,\n",
    "            ]\n",
    "        )\n",
    "\n",
    "        ref_point_clouds = [\n",
    "            *circle_point_clouds,\n",
    "            *sphere_point_clouds,\n",
    "            *torus_point_clouds,\n",
    "            *klein_bottle_point_clouds,\n",
    "        ]\n",
    "\n",
    "        return ref_point_clouds, ref_labels\n",
    "\n",
    "    def _compute_topo_features(self, diagrams):\n",
    "        PE = PersistenceEntropy()\n",
    "        features = PE.fit_transform(diagrams)\n",
    "        return features\n",
    "\n",
    "    def fit(self, X, y=None):\n",
    "        ref_point_clouds, ref_labels = self._generate_ref_data(X)\n",
    "        if self.reduce_dim:\n",
    "            pca = PCA(n_components=10)\n",
    "            ref_point_clouds = [\n",
    "                pca.fit_transform(point_cloud) for point_cloud in ref_point_clouds\n",
    "            ]\n",
    "        ref_diagrams = compute_persistence_diagrams(\n",
    "            ref_point_clouds, homology_dimensions=self.homology_dimensions\n",
    "        )\n",
    "        ref_features = self._compute_topo_features(ref_diagrams)\n",
    "        X_ref_train, X_ref_valid, y_ref_train, y_ref_valid = train_test_split(\n",
    "            ref_features, ref_labels\n",
    "        )\n",
    "        self.classifier.fit(X_ref_train, y_ref_train)\n",
    "        print(f\"Classifier score: {self.classifier.score(X_ref_valid, y_ref_valid)}\")\n",
    "        return self\n",
    "\n",
    "    def predict(self, X):\n",
    "        if self.reduce_dim:\n",
    "            pca = PCA(n_components=10)\n",
    "            X = pca.fit_transform(X)\n",
    "        diagram = compute_persistence_diagrams(\n",
    "            [X], homology_dimensions=self.homology_dimensions\n",
    "        )\n",
    "        features = self._compute_topo_features(diagram)\n",
    "        return self.classifier.predict(features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_task_points = synthetic.hypertorus(2, 400)\n",
    "test_noisy_points, test_manifold_points = synthetic.synthetic_neural_manifold(\n",
    "    points=test_task_points,\n",
    "    encoding_dim=5,\n",
    "    nonlinearity=\"sigmoid\",\n",
    "    scales=gs.ones(10),\n",
    "    poisson_multiplier=100,\n",
    ")\n",
    "\n",
    "TC = TopologicalClassifier(num_samples=10, poisson_multiplier=100, reduce_dim=True)\n",
    "TC.fit(test_noisy_points)"
   ]
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example color mapping\n",
    "color_map = {0: \"darkblue\", 1: \"deeppink\", 2: \"limegreen\", 3: \"orange\"}\n",
    "colors = [color_map[label] for label in labels]\n",
    "\n",
    "names = {0: \"Circle\", 1: \"Sphere\", 2: \"Torus\", 3: \"Klein Bottle\"}\n",
    "\n",
    "# Create a figure\n",
    "fig = go.Figure()\n",
    "\n",
    "# Add the trace with colored markers based on labels\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(\n",
    "        x=features[:, 0],\n",
    "        y=features[:, 1],\n",
    "        z=features[:, 2],\n",
    "        mode=\"markers\",\n",
    "        marker=dict(size=3, color=colors),\n",
    "        showlegend=False,\n",
    "    )\n",
    ")\n",
    "\n",
    "# Manually add the legend entries\n",
    "for label, color in color_map.items():\n",
    "    fig.add_trace(\n",
    "        go.Scatter3d(\n",
    "            x=[None],\n",
    "            y=[None],\n",
    "            z=[None],\n",
    "            mode=\"markers\",\n",
    "            marker=dict(size=3, color=color),\n",
    "            showlegend=True,\n",
    "            name=f\"{names[label]}\",\n",
    "        )\n",
    "    )\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_valid, y_train, y_valid = train_test_split(features, labels)\n",
    "model = RandomForestClassifier()\n",
    "model.fit(X_train, y_train)\n",
    "model.score(X_valid, y_valid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "ename": "AssertionError",
     "evalue": "scales must have same shape as tensor",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[9], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m test_task_points \u001b[38;5;241m=\u001b[39m synthetic\u001b[38;5;241m.\u001b[39mhypertorus(\u001b[38;5;241m2\u001b[39m, \u001b[38;5;241m400\u001b[39m)\n\u001b[0;32m----> 2\u001b[0m test_noisy_points, test_manifold_points \u001b[38;5;241m=\u001b[39m \u001b[43msynthetic\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msynthetic_neural_manifold\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[43m    \u001b[49m\u001b[43mpoints\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mtest_task_points\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m      4\u001b[0m \u001b[43m    \u001b[49m\u001b[43mencoding_dim\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m      5\u001b[0m \u001b[43m    \u001b[49m\u001b[43mnonlinearity\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43msigmoid\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m      6\u001b[0m \u001b[43m    \u001b[49m\u001b[43mscales\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mgs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mones\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m10\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m      7\u001b[0m \u001b[43m    \u001b[49m\u001b[43mpoisson_multiplier\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m100\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m      8\u001b[0m \u001b[43m)\u001b[49m\n\u001b[1;32m     10\u001b[0m TC\u001b[38;5;241m.\u001b[39mfit(test_noisy_points)\n",
      "File \u001b[0;32m~/neurometry/neurometry/datasets/synthetic.py:42\u001b[0m, in \u001b[0;36msynthetic_neural_manifold\u001b[0;34m(points, encoding_dim, nonlinearity, poisson_multiplier, ref_frequency, **kwargs)\u001b[0m\n\u001b[1;32m     40\u001b[0m encoding_matrix \u001b[38;5;241m=\u001b[39m random_encoding_matrix(manifold_extrinsic_dim, encoding_dim)\n\u001b[1;32m     41\u001b[0m encoded_points \u001b[38;5;241m=\u001b[39m encode_points(points, encoding_matrix)\n\u001b[0;32m---> 42\u001b[0m manifold_points \u001b[38;5;241m=\u001b[39m ref_frequency \u001b[38;5;241m*\u001b[39m \u001b[43mapply_nonlinearity\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m     43\u001b[0m \u001b[43m    \u001b[49m\u001b[43mencoded_points\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnonlinearity\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\n\u001b[1;32m     44\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     45\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m     46\u001b[0m     noisy_points \u001b[38;5;241m=\u001b[39m poisson_spikes(manifold_points, poisson_multiplier)\n",
      "File \u001b[0;32m~/neurometry/neurometry/datasets/synthetic.py:218\u001b[0m, in \u001b[0;36mapply_nonlinearity\u001b[0;34m(encoded_points, nonlinearity, **kwargs)\u001b[0m\n\u001b[1;32m    216\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m relu(encoded_points, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m    217\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m nonlinearity \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124msigmoid\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n\u001b[0;32m--> 218\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mscaled_sigmoid\u001b[49m\u001b[43m(\u001b[49m\u001b[43mencoded_points\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    219\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m nonlinearity \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mtanh\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n\u001b[1;32m    220\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m scaled_tanh(encoded_points, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n",
      "File \u001b[0;32m~/neurometry/neurometry/datasets/synthetic.py:231\u001b[0m, in \u001b[0;36mscaled_sigmoid\u001b[0;34m(tensor, scales)\u001b[0m\n\u001b[1;32m    230\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mscaled_sigmoid\u001b[39m(tensor, scales):\n\u001b[0;32m--> 231\u001b[0m     \u001b[38;5;28;01massert\u001b[39;00m tensor\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m1\u001b[39m] \u001b[38;5;241m==\u001b[39m scales\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m0\u001b[39m], \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mscales must have same shape as tensor\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    232\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;241m1\u001b[39m \u001b[38;5;241m/\u001b[39m (\u001b[38;5;241m1\u001b[39m \u001b[38;5;241m+\u001b[39m gs\u001b[38;5;241m.\u001b[39mexp(\u001b[38;5;241m-\u001b[39mscales \u001b[38;5;241m*\u001b[39m tensor))\n",
      "\u001b[0;31mAssertionError\u001b[0m: scales must have same shape as tensor"
     ]
    }
   ],
   "source": [
    "test_task_points = synthetic.hypertorus(2, 400)\n",
    "test_noisy_points, test_manifold_points = synthetic.synthetic_neural_manifold(\n",
    "    points=test_task_points,\n",
    "    encoding_dim=5,\n",
    "    nonlinearity=\"sigmoid\",\n",
    "    scales=gs.ones(10),\n",
    "    poisson_multiplier=100,\n",
    ")\n",
    "\n",
    "TC.fit(test_noisy_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NOTE: Try different coefficients to distinguish between torus and klein bottle?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: (19.814, 0.7066852198822331), 1: (13.214, 2.555817677378416)}\n"
     ]
    }
   ],
   "source": [
    "betti_numbers = estimate_betti_numbers(\n",
    "    manifold_points, num_shuffles=500, homology_dimensions=(0, 1)\n",
    ")\n",
    "print(betti_numbers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x1500 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_shuffles = 10\n",
    "\n",
    "noisy_diagrams = compute_diagrams_shuffle(\n",
    "    noisy_points, num_shuffles=num_shuffles, homology_dimensions=(0, 1, 2)\n",
    ")\n",
    "\n",
    "manifold_diagrams = compute_diagrams_shuffle(\n",
    "    manifold_points, num_shuffles=num_shuffles, homology_dimensions=(0, 1, 2)\n",
    ")\n",
    "\n",
    "plot_all_barcodes_with_null(\n",
    "    noisy_diagrams, \"noisy\", diagrams_2=manifold_diagrams, dataset_name_2=\"manifold\"\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 0, 1: 5, 2: 2}\n"
     ]
    }
   ],
   "source": [
    "betti = get_betti_numbers(noisy_diagrams)\n",
    "print(betti)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TODO: FIX get_betti_numbers FUNCTION!!!!\n",
    "\n",
    "Also: how to deal with betti 0 ? There should be a single \"significant\" feature?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "sphere_1_betti = {0: 1, 1: 1, 2: 0}\n",
    "torus_2_betti = {0: 1, 1: 2, 2: 1}\n",
    "sphere_2_betti = {0: 1, 1: 0, 2: 1}\n",
    "\n",
    "# if betti == sphere_1_betti:\n",
    "#     print(\"The manifold is a ring\") ----> use ring VAE\n",
    "\n",
    "\n",
    "# elif betti == torus_2_betti:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "neurometry",
   "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": "3.11.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}