Neural_NCPD_Synthetic_low_noise.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Details\n",
    "\n",
    "The notebook contains the synthetic data experiment with low noise (sigma^2 = 0.05). Due to the non-convexity of the HNCPD task, results will vary run to run, so the results from this notebook will not exactly match those in the paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# loading packages and functions\n",
    "import sys\n",
    "import itertools\n",
    "from utils import *\n",
    "\n",
    "sys.path.append(\"./src\")\n",
    "import torch\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from NNCPD import NNCPD, weights_H, Energy_Loss_Tensor, Recon_Loss, L21_Norm, outer_product, outer_product_np, PTF, random_NNCPD, Fro_Norm\n",
    "from lsqnonneg_module import LsqNonneg\n",
    "from trainNNCPD import train\n",
    "#\n",
    "import torch.nn as nn\n",
    "from torch.autograd import Variable\n",
    "from writer import Writer\n",
    "\n",
    "from sklearn.decomposition import NMF\n",
    "\n",
    "import tensorly as tl\n",
    "from tensorly import unfold as tl_unfold\n",
    "from tensorly.decomposition import parafac, non_negative_parafac"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate Data Tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "## set the network parameters\n",
    "torch.set_default_tensor_type(torch.DoubleTensor)\n",
    "\n",
    "X = get_synthetic_tensor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_original = get_synthetic_tensor(noise=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize Original Data Tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_tensor(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = torch.from_numpy(X)\n",
    "X_np = np.asarray(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run Neural NCPD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jvendrow/.local/lib/python3.6/site-packages/torch/nn/_reduction.py:43: UserWarning: size_average and reduce args will be deprecated, please use reduction='sum' instead.\n",
      "  warnings.warn(warning.format(ret))\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c079509aed9540a5bd33024c9873a866"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d4f1ccd8245b4a899f18e41b4f6859fd"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dd87f73f816444b997c98a9315c72e6d"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0c7a67dd16bf4df79b381fed24e763f4"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3167f62203164745a71b6cca9b4164fe"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e5d2bb3c8bd84e929d6840de3970350b"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d8c74656968948689b97fe6df3300668"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e9ef0bcbf3b44c3789d80e1588a5b5b0"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5cf6415ad96a41c2972130fcf761284a"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "431fb89aefb14561b27d3836f3e57730"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# unsupervised case,one layer\n",
    "r=7\n",
    "n1,n2,n3 = X.shape\n",
    "\n",
    "num_trials = 10\n",
    "histories = []\n",
    "\n",
    "for i in range(num_trials):\n",
    "    \n",
    "    torch.manual_seed(i)\n",
    "\n",
    "    net = NNCPD([n1, 4, 2],[n2, 4, 2],[n3, 4, 2])\n",
    "    loss_func = Energy_Loss_Tensor()\n",
    "    h = train(net, X, loss_func, r, epoch = 7500, lr1 = 0, lr2 = 50)\n",
    "    histories.append(h)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the loss curve\n",
    "histories[0].plot_scalar('loss')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "S_trues = get_synthetic_gt_topics()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Topic Modeling Loss 7 to 2 (average, best, worst): 0.04310424175371318 0.002637882416244456 0.2153776277997652\n",
      "Topic Modeling Loss 7 to 4 (average, best, worst): 0.04211838800164144 0.0023534462714323973 0.205795638325977\n",
      "Topic Modeling Loss 4 to 2 (average, best, worst): 0.04223941408098822 0.005845247203841973 0.2502222760931831\n",
      "\n",
      "Relative Recon Loss Rank 7 (average, best, worst): 0.09631970490841361 0.09631970490840853 0.09631970490841732\n",
      "Relative Recon Loss Rank 4 (average, best, worst): 0.2306551768042581 0.2171728210713715 0.3519589280455683\n",
      "Relative Recon Loss Rank 2 (average, best, worst): 0.53034785052147 0.5303409676047632 0.5303601632486924\n"
     ]
    }
   ],
   "source": [
    "all_topic_losses, all_recon_losses = measure_all(histories, X_np, S_trues, kind=\"Neural\")\n",
    "\n",
    "handle_losses(all_recon_losses, all_topic_losses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Topic Modeling Loss 7 to 2 (average, best, worst): 0.04310424175371318 0.002637882416244456 0.2153776277997652\n",
      "Topic Modeling Loss 7 to 4 (average, best, worst): 0.04211838800164144 0.0023534462714323973 0.205795638325977\n",
      "Topic Modeling Loss 4 to 2 (average, best, worst): 0.04223941408098822 0.005845247203841973 0.2502222760931831\n",
      "\n",
      "Relative Recon Loss Rank 7 (average, best, worst): 0.1187897713361051 0.11878977133610057 0.11878977133610837\n",
      "Relative Recon Loss Rank 4 (average, best, worst): 0.2524510019193263 0.2385528113335064 0.3771243698510093\n",
      "Relative Recon Loss Rank 2 (average, best, worst): 0.5628380756843907 0.562687334654858 0.5632015113766597\n"
     ]
    }
   ],
   "source": [
    "all_topic_losses, all_recon_losses = measure_all(histories, X_original, S_trues, kind=\"Neural\")\n",
    "\n",
    "handle_losses(all_recon_losses, all_topic_losses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def standard_HNCPD(X, ranks, seed=0):\n",
    "    \n",
    "    np.random.seed(2)\n",
    "    factors_tl = non_negative_parafac(X, ranks[0])\n",
    "    \n",
    "    X_1 =  factors_tl[0]\n",
    "    X_2 =  factors_tl[1]\n",
    "    X_3 =  factors_tl[2]\n",
    "    \n",
    "    factors = [[X_1], [X_2], [X_3]]\n",
    "    \n",
    "    for i in range(1, len(ranks)):\n",
    "        r = ranks[i]\n",
    "        for j in range(3):\n",
    "            model = NMF(n_components=r, init='random', random_state=seed, max_iter=300, solver='mu')\n",
    "            A = model.fit_transform(factors[j][2*i-2])\n",
    "            S = model.components_\n",
    "\n",
    "            factors[j].append(A)\n",
    "            factors[j].append(S)\n",
    "            \n",
    "    return factors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_trials = 10\n",
    "all_factors = []\n",
    "for i in range(num_trials):\n",
    "    factors = standard_HNCPD(X_np, [7,4,2], seed=i)\n",
    "    all_factors.append(factors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Topic Modeling Loss 7 to 2 (average, best, worst): 0.10575072361742997 0.009766357175004165 0.2843265404695422\n",
      "Topic Modeling Loss 7 to 4 (average, best, worst): 0.10093002773034329 0.008824998649549803 0.1987577306994643\n",
      "Topic Modeling Loss 4 to 2 (average, best, worst): 0.18925579316578658 0.014433730333846068 0.28436942439735485\n",
      "\n",
      "Relative Recon Loss Rank 7 (average, best, worst): 0.09631970490841418 0.09631970490840637 0.09631970490841901\n",
      "Relative Recon Loss Rank 4 (average, best, worst): 0.4682536676182603 0.46647599733882583 0.469993477149036\n",
      "Relative Recon Loss Rank 2 (average, best, worst): 0.8152656799281802 0.6491065026309738 0.9154293006189043\n"
     ]
    }
   ],
   "source": [
    "all_topic_losses, all_recon_losses = measure_all(all_factors, X_np, S_trues, kind=\"Standard\")\n",
    "\n",
    "handle_losses(all_recon_losses, all_topic_losses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Topic Modeling Loss 7 to 2 (average, best, worst): 0.10575072361742997 0.009766357175004165 0.2843265404695422\n",
      "Topic Modeling Loss 7 to 4 (average, best, worst): 0.10093002773034329 0.008824998649549803 0.1987577306994643\n",
      "Topic Modeling Loss 4 to 2 (average, best, worst): 0.18925579316578658 0.014433730333846068 0.28436942439735485\n",
      "\n",
      "Relative Recon Loss Rank 7 (average, best, worst): 0.11878977133610555 0.11878977133609872 0.11878977133610986\n",
      "Relative Recon Loss Rank 4 (average, best, worst): 0.49406419039224597 0.4901545516898462 0.4968988292025292\n",
      "Relative Recon Loss Rank 2 (average, best, worst): 0.8277137602349078 0.6833347463432453 0.9178393156775861\n"
     ]
    }
   ],
   "source": [
    "all_topic_losses, all_recon_losses = measure_all(all_factors, X_original, S_trues, kind=\"Standard\")\n",
    "\n",
    "handle_losses(all_recon_losses, all_topic_losses)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "X1 = np.asarray(histories[0].get('A_X1')[-1])\n",
    "X2 = np.asarray(histories[0].get('B_X1')[-1])\n",
    "X3 = np.asarray(histories[0].get('C_X1')[-1])\n",
    "\n",
    "\n",
    "A_A1 = np.asarray(histories[0].get('A_A1')[-1])\n",
    "A_S1 = np.asarray(histories[0].get('A_S1')[-1])\n",
    "B_A1 = np.asarray(histories[0].get('B_A1')[-1])\n",
    "B_S1 = np.asarray(histories[0].get('B_S1')[-1])\n",
    "C_A1 = np.asarray(histories[0].get('C_A1')[-1])\n",
    "C_S1 = np.asarray(histories[0].get('C_S1')[-1])\n",
    "\n",
    "A_A2 = np.asarray(histories[0].get('A_A2')[-1])\n",
    "A_S2 = np.asarray(histories[0].get('A_S2')[-1])\n",
    "B_A2 = np.asarray(histories[0].get('B_A2')[-1])\n",
    "B_S2 = np.asarray(histories[0].get('B_S2')[-1])\n",
    "C_A2 = np.asarray(histories[0].get('C_A2')[-1])\n",
    "C_S2 = np.asarray(histories[0].get('C_S2')[-1])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### All models, Rank 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative reconstruction loss: 0.0963197049084112\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "approx = outer_product_np(X1, X2, X3)\n",
    "print(\"Relative reconstruction loss:\", np.linalg.norm(np.ndarray.flatten(X_np-approx), 2)  / np.linalg.norm(np.ndarray.flatten(X_np), 2))\n",
    "display_tensor(approx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Neural NCPD, Rank 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative reconstruction loss: 0.21717879697975728\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "approx = outer_product_np(A_A1 @ A_S1, B_A1 @ B_S1, C_A1 @ C_S1)\n",
    "print(\"Relative reconstruction loss:\", np.linalg.norm(np.ndarray.flatten(X_np-approx), 2)  / np.linalg.norm(np.ndarray.flatten(X_np), 2))\n",
    "display_tensor(approx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Neural NCPD, Rank 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative reconstruction loss: 0.5303409676047632\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "approx = outer_product_np(A_A1 @ A_A2 @ A_S2, B_A1 @ B_A2 @ B_S2, C_A1 @ C_A2 @ C_S2)\n",
    "print(\"Relative reconstruction loss:\", np.linalg.norm(np.ndarray.flatten(X_np-approx), 2)  / np.linalg.norm(np.ndarray.flatten(X_np), 2))\n",
    "display_tensor(approx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_topic_matrices([A_S2.T, A_S1.T, A_A2], S_trues)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard HNCPD, Rank 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative reconstruction loss: 0.4668036527196204\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X1, A_A1, A_S1, A_A2, A_S2 = all_factors[0][0]\n",
    "X2, B_A1, B_S1, B_A2, B_S2 = all_factors[0][1]\n",
    "X3, C_A1, C_S1, C_A2, C_S2 = all_factors[0][2]\n",
    "\n",
    "approx = outer_product_np(A_A1 @ A_S1, B_A1 @ B_S1, C_A1 @ C_S1)\n",
    "print(\"Relative reconstruction loss:\", np.linalg.norm(np.ndarray.flatten(X_np-approx), 2)  / np.linalg.norm(np.ndarray.flatten(X_np), 2))\n",
    "display_tensor(approx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard HNCPD, Rank 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative reconstruction loss: 0.8020052038717367\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "approx = outer_product_np(A_A1 @ A_A2 @ A_S2, B_A1 @ B_A2 @ B_S2, C_A1 @ C_A2 @ C_S2)\n",
    "print(\"Relative reconstruction loss:\", np.linalg.norm(np.ndarray.flatten(X_np-approx), 2)  / np.linalg.norm(np.ndarray.flatten(X_np), 2))\n",
    "display_tensor(approx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_topic_matrices([A_S2.T, A_S1.T, A_A2], S_trues)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dislay S_true matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdYAAAFwCAYAAAAFX1qpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAH2ElEQVR4nO3dsWodRxiA0bmR3Kg0dmGBsB9BlYq8wM27xg/gC8kDxBAQKtW5UWNDihATu9mUBiMcX/jGqxXnlMsy+xc7fOwVjHbLsgwAoPHT2gMAwGMirAAQElYACAkrAISEFQBCwgoAodNjbn729GR5dfFk1izj9uZs2tpjjPHv+Gd8Xj7tpj6EVW39Hd06e+zhmr03KlvaY3+Pvz4sy/L86+tHhfXVxZPx9nDRTfWV/fnltLXHGOOP5fep67O+rb+jW2ePPVyz90ZlS3vst+X1u/uu+ykYAELCCgAhYQWAkLACQEhYASAkrAAQElYACAkrAISEFQBCwgoAIWEFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABASVgAICSsAhIQVAELCCgAhYQWAkLACQEhYASAkrAAQElYACAkrAISEFQBCwgoAIWEFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBIHS69gBQur05G/vzy2nrH+6up609xpg6O/Bj+GIFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABASVgAICSsAhIQVAELCCgAhYQWAkLACQEhYASAkrAAQElYACAkrAISEFQBCwgoAIWEFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABA6XXsAAOa7vTkb+/PLtcf4X4e767VH+G4nL+6/7osVAELCCgAhYQWAkLACQEhYASAkrAAQElYACAkrAISEFQBCwgoAIWEFgNBRZwXPPmty9hmRV/uPU9fn8Zt91uqPOCd1C+fFwpb5YgWAkLACQEhYASAkrAAQElYACAkrAISEFQBCwgoAIWEFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABASVgAICSsAhIQVAELCCgAhYQWAkLACQEhYASAkrAAQElYACAkrAISEFQBCwgoAIWEFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABASVgAICSsAhIQVAEKnaw8AfLE/v5z+jMPd9bS1r/Yfp60NW+GLFQBCwgoAIWEFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABASVgAICSsAhIQVAELCCgAhYQWAkLACQEhYASAkrAAQElYACJ0ec/PP+6vx5s2vs2aZ7s+b3WHtGZhr6+/o1tljMMZuWZbvv3m3ezPGeDZvnOk+LMvyy9pDMM8jeEe3zh57oHa73fsxxru153hkXi7L8vzri0eFFQD4Nn9jBYCQsAJASFgBICSsABASVgAICSsAhIQVAELCCgAhYQWAkLACQEhYASB01H+3efb0ZHl18WTWLOP25mza2mOM8e/4Z3xePu2mPoRVbf0d3Tp77OGavTcqW9pjf4+/Ptx3CP9RYX118WS8PVx0U31lf345be0xxvhj+X3q+qxv6+/o1tljD9fsvVHZ0h77bXl9738L8lMwAISEFQBCwgoAIWEFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABASVgAICSsAhIQVAELCCgAhYQWAkLACQEhYASAkrAAQElYACAkrAISEFQBCwgoAIWEFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABASVgAICSsAhIQVAELCCgAhYQWAkLACQOh07QGgdHtzNvbnl9PWP9xdT1t7jDF1duDH8MUKACFhBYCQsAJASFgBICSsABASVgAICSsAhIQVAELCCgAhYQWAkLACQEhYASAkrAAQElYACAkrAISEFQBCwgoAIWEFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABASVgAICSsAhIQVAELCCgAhYQWAkLACQOh07QEAmO/25mzszy/XHuN/He6u1x7hu528uP+6L1YACAkrAISEFQBCwgoAIWEFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKAKGjDuGffYjz7MOXr/Yfp67P4zf7EPMfcQD5Fg5ihy3zxQoAIWEFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABASVgAICSsAhIQVAELCCgAhYQWAkLACQEhYASAkrAAQElYACAkrAISEFQBCwgoAIWEFgJCwAkBIWAEgJKwAEBJWAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABASVgAICSsAhIQVAELCCgAhYQWAkLACQEhYASAkrAAQElYACAkrAIRO1x4A+GJ/fjn9GYe762lrX+0/TlsbtsIXKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABASVgAICSsAhIQVAELCCgAhYQWAkLACQEhYASAkrAAQElYACAkrAISEFQBCwgoAIWEFgJCwAkBIWAEgJKwAENoty/L9N+9278cY7+aNM93LZVmerz0E8zyCd3Tr7LEHyt6Y4t73/aiwAgDf5qdgAAgJKwCEhBUAQsIKACFhBYCQsAJASFgBICSsABASVgAI/Qd7ILwfIj4O1AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x360 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_topic_matrices(S_trues, S_trues)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}