ICML 2024 Manifold Learning Figures.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "from sklearn import metrics\n",
    "import scipy as sp\n",
    "from scipy.spatial import distance_matrix\n",
    "\n",
    "import pdb\n",
    "\n",
    "from diffusion_functions import *\n",
    "from semi_supervised_manifold_learning import *\n",
    "from animate_diffusion import animate_diffusion\n",
    "\n",
    "# commands for displaying animations in jupyter notebook\n",
    "from IPython.display import HTML\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Helper functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def format_axes(ax, titlestring):\n",
    "    # figure formatting\n",
    "    ax.spines[\"top\"].set_visible(False)\n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)\n",
    "    ax.axis('off')\n",
    "    if not titlestring==None:\n",
    "        ax.set_title(titlestring)\n",
    "    return\n",
    "\n",
    "def plot_label_comparison_colorful(ax, label_vector, data_matrix, titlestring=None):\n",
    "    threshold = 0 \n",
    "    label_estimates = label_vector#make_sweep_cut(label_vector, threshold)\n",
    "\n",
    "    im = ax.scatter(data_matrix[:,0],data_matrix[:,1],c=label_estimates)\n",
    "    plt.colorbar(im, ax=ax)\n",
    "    \n",
    "    format_axes(ax,titlestring)\n",
    "    return\n",
    "\n",
    "def plot_label_comparison_binary(ax, label_vector, data_matrix, titlestring=None, \n",
    "                                 objective_function = sweep_cut_classification_error):\n",
    "    \n",
    "    cut_val, threshold = find_min_sweepcut(label_vector,100,objective_function, orthogonality_constraint = 'auto')\n",
    "    label_estimates = make_sweep_cut(label_vector, threshold)\n",
    "    \n",
    "    classification_error = sweep_cut_classification_error(label_estimates)\n",
    "    orthogonality_error = np.abs(np.sum(label_estimates)/len(label_estimates))\n",
    "\n",
    "    im = ax.scatter(data_matrix[:,0],data_matrix[:,1],c=label_estimates)\n",
    "    plt.colorbar(im, ax=ax)\n",
    "    \n",
    "    subtitle = f'\\n Threshold = {threshold:.3f}. Cut objective = {cut_val:.3f} \\n Class. error = {classification_error:.3f} \\n Orthog. error = {orthogonality_error:.3f}'\n",
    "    format_axes(ax,titlestring+subtitle)\n",
    "    return\n",
    "\n",
    "def plot_AUC_hist(AUC_vals, titlestring = None):\n",
    "    plt.rcParams.update({'font.size': 15})\n",
    "    # get bin parameters for consistent scaling of both datasets without displaying\n",
    "    _, first_bins, _ = plt.hist([[v[1] for v in AUC_vals], [v[0] for v in AUC_vals]])\n",
    "    plt.clf()\n",
    "    \n",
    "    fig, ax = plt.subplots(figsize = (6, 5))\n",
    "    ax.hist([v[1] for v in AUC_vals], bins = first_bins, alpha=0.5, edgecolor = 'black', label = 'graph')\n",
    "    ax.hist([v[0] for v in AUC_vals], bins = first_bins, alpha=0.5, edgecolor = 'black', label='hypergraph')\n",
    "    \n",
    "    # figure formatting \n",
    "    ax.set_title(titlestring)\n",
    "    ax.spines[\"top\"].set_visible(False)\n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.tick_params(axis='x', labelsize=15)\n",
    "    ax.tick_params(axis='y', labelsize=15)\n",
    "    ax.legend()\n",
    "    if False:\n",
    "        ax.set_ylabel('Frequency')\n",
    "        ax.set_xlabel('AUC value')\n",
    "    plt.show()\n",
    "    return\n",
    "\n",
    "def compare_ROC_curves(hypergraph_x, graph_x):\n",
    "    n = len(hypergraph_x)\n",
    "    labels = np.hstack([np.full(shape=int(n/2),fill_value = -1),np.full(shape=int(n/2),fill_value = 1)])\n",
    "    \n",
    "    plt.plot(figsize=(15, 15))\n",
    "    for x, legend_val in [(graph_x, 'graph'),(hypergraph_x, 'hypergraph')]:\n",
    "        fpr, tpr, thresholds = metrics.roc_curve(labels, x, pos_label=1)\n",
    "        plt.plot(fpr, tpr, label = legend_val)\n",
    "    \n",
    "    graph_auc_score = metrics.roc_auc_score(labels, graph_x)\n",
    "    hypergraph_auc_score = metrics.roc_auc_score(labels, hypergraph_x)\n",
    "    \n",
    "    plt.legend()\n",
    "    plt.title('ROC curves \\n hyper AUC score = '+str(hypergraph_auc_score)+' \\n graph AUC score = '+str(graph_auc_score))\n",
    "    plt.show()\n",
    "    return"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Concentric spheres in increasing dimensions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization in 2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate new data\n",
    "_, data_matrix = generate_concentric_highdim(ambient_dim = 2,verbose = False)\n",
    "n = data_matrix.shape[0]\n",
    "\n",
    "num_rand_seeds = int(0.05*n)\n",
    "x0 = np.full(shape=(n, 1), fill_value=0)\n",
    "random_seeds = np.random.choice(np.arange(n), size=num_rand_seeds)\n",
    "x0[random_seeds[random_seeds < n / 2]] = -1\n",
    "x0[random_seeds[random_seeds > n / 2]] = 1\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (6,6))\n",
    "# formatting\n",
    "unlabeled_idxs = (x0==0).reshape(n,)\n",
    "plt.scatter(data_matrix[unlabeled_idxs,0], data_matrix[unlabeled_idxs,1],marker=\"x\",c='grey')\n",
    "# Reversed colorscheme for spheres\n",
    "pos_idxs = (x0==-1).reshape(n,)\n",
    "plt.scatter(data_matrix[pos_idxs,0], data_matrix[pos_idxs,1],marker=\"o\",c='red')\n",
    "neg_idxs = (x0==1).reshape(n,)\n",
    "plt.scatter(data_matrix[neg_idxs,0], data_matrix[neg_idxs,1],marker=\"o\",c='blue')\n",
    "ax.set_aspect('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## AUC Histograms for varying dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# data generation parameters\n",
    "r_inner=1\n",
    "r_outer=2\n",
    "pts_per_community=300\n",
    "noise_level=0.4\n",
    "\n",
    "n = 2*pts_per_community\n",
    "labels = np.hstack([np.full(shape=int(n/2),fill_value = -1),np.full(shape=int(n/2),fill_value = 1)])\n",
    "\n",
    "node_weight_method = 'gaussian_to_central_neighbor'\n",
    "order = 2\n",
    "\n",
    "# experimental procedure parameters\n",
    "k = 5\n",
    "num_trials = 50\n",
    "PPR_iterations = 50\n",
    "\n",
    "for ambient_dim in [4,7]:\n",
    "    AUC_vals = []\n",
    "    for trial in range(num_trials):\n",
    "        graph_x, hypergraph_x, _ = compare_estimated_labels('PPR',\n",
    "                                    generate_data = generate_concentric_highdim,\n",
    "                                    k = 5,\n",
    "                                    num_iterations = PPR_iterations,\n",
    "                                    diffusion_step_size=None,\n",
    "                                    titlestring=None,\n",
    "                                    node_weight_method=node_weight_method,\n",
    "                                    order=order\n",
    "                                    )\n",
    "\n",
    "        graph_auc_score = metrics.roc_auc_score(labels, graph_x)\n",
    "        hypergraph_auc_score = metrics.roc_auc_score(labels, hypergraph_x)\n",
    "            \n",
    "        AUC_vals.append((hypergraph_auc_score, graph_auc_score))\n",
    "    plot_AUC_hist(AUC_vals) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Concentric Hyperrectangles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate new data\n",
    "inner_sidelengths=[1, 3, 1, 1, 1, 1, 1, 1]\n",
    "outer_sidelengths=[2, 4, 2, 2, 2, 2, 2, 2]\n",
    "_, data_matrix = generate_concentric_highdim_rectangles(inner_sidelengths = inner_sidelengths[:2],\n",
    "                                                        outer_sidelengths = outer_sidelengths[:2],\n",
    "                                                        verbose = False)\n",
    "n = data_matrix.shape[0]\n",
    "\n",
    "num_rand_seeds = int(0.05*n)\n",
    "x0 = np.full(shape=(n, 1), fill_value=0)\n",
    "random_seeds = np.random.choice(np.arange(n), size=num_rand_seeds)\n",
    "x0[random_seeds[random_seeds < n / 2]] = -1\n",
    "x0[random_seeds[random_seeds > n / 2]] = 1\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (6,6))\n",
    "# formatting\n",
    "unlabeled_idxs = (x0==0).reshape(n,)\n",
    "plt.scatter(data_matrix[unlabeled_idxs,0], data_matrix[unlabeled_idxs,1],marker=\"x\",c='grey')\n",
    "pos_idxs = (x0==1).reshape(n,)\n",
    "plt.scatter(data_matrix[pos_idxs,0], data_matrix[pos_idxs,1],marker=\"o\",c='red')\n",
    "neg_idxs = (x0==-1).reshape(n,)\n",
    "plt.scatter(data_matrix[neg_idxs,0], data_matrix[neg_idxs,1],marker=\"o\",c='blue')\n",
    "ax.set_aspect('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n",
      "Using degree regularizer\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pts_per_community = 300\n",
    "n = 2*pts_per_community\n",
    "labels = np.hstack([np.full(shape=int(n/2),fill_value = -1),np.full(shape=int(n/2),fill_value = 1)])\n",
    "\n",
    "\n",
    "node_weight_method = None\n",
    "order = 2\n",
    "inner_sidelengths=[1, 3, 1, 1, 1, 1, 1, 1]\n",
    "outer_sidelengths=[2, 4, 2, 2, 2, 2, 2, 2]\n",
    "\n",
    "# experimental procedure parameters\n",
    "k = 5\n",
    "num_trials = 50\n",
    "PPR_iterations = 50\n",
    "\n",
    "for ambient_dim in [2]:\n",
    "    dimension_dependent_data_generation = lambda verbose: generate_concentric_highdim_rectangles(verbose = False,\n",
    "                                                        inner_sidelengths = inner_sidelengths[:ambient_dim],\n",
    "                                                        outer_sidelengths = outer_sidelengths[:ambient_dim])\n",
    "    AUC_vals = []\n",
    "    for trial in range(num_trials):\n",
    "        graph_x, hypergraph_x, _ = compare_estimated_labels('PPR',\n",
    "                                    generate_data = dimension_dependent_data_generation,\n",
    "                                    k = 5,\n",
    "                                    num_iterations = PPR_iterations,\n",
    "                                    diffusion_step_size=None,\n",
    "                                    titlestring=None,\n",
    "                                    node_weight_method=node_weight_method,\n",
    "                                    order = order\n",
    "                                    )\n",
    "\n",
    "        graph_auc_score = metrics.roc_auc_score(labels, graph_x)\n",
    "        hypergraph_auc_score = metrics.roc_auc_score(labels, hypergraph_x)\n",
    "            \n",
    "        AUC_vals.append((hypergraph_auc_score, graph_auc_score))\n",
    "    plot_AUC_hist(AUC_vals) "
   ]
  },
  {
   "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": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}