mnist example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "62daafa5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from sklearn.neural_network import MLPClassifier as NN\n",
    "\n",
    "import math\n",
    "import matplotlib as mpl\n",
    "from functools import partial\n",
    "\n",
    "from sklearn.datasets import make_moons\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.neighbors import KernelDensity\n",
    "from sklearn.model_selection import GridSearchCV, LeaveOneOut\n",
    "from sklearn.gaussian_process import GaussianProcessClassifier as GPC\n",
    "from sklearn.gaussian_process.kernels import RBF\n",
    "\n",
    "from dijsktra_algorithm import Graph, dijsktra_toall\n",
    "from density_estimator import DensityEstimator\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8a173b75",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://www.python-course.eu/neural_network_mnist.php\n",
    "image_size = 28 # width and length\n",
    "no_of_different_labels = 10 #  i.e. 0, 1, 2, 3, ..., 9\n",
    "image_pixels = image_size * image_size\n",
    "data_path = \"/Users/rafaelpoyiadzi/Documents/mnist_train.csv\"\n",
    "train_data = np.loadtxt(data_path, delimiter=\",\")\n",
    "\n",
    "\n",
    "fac = 0.99 / 255\n",
    "train_imgs = np.asfarray(train_data[:, 1:]) * fac + 0.01\n",
    "train_labels = np.asfarray(train_data[:, :1]).ravel()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a10b016b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "44ffdec3",
   "metadata": {},
   "outputs": [],
   "source": [
    "indices0 = set(np.where(train_labels == 0)[0][:1000])\n",
    "indices8 = set(np.where(train_labels == 8)[0][:1000])\n",
    "\n",
    "\n",
    "indices = np.array(list(indices0.union(indices8)))\n",
    "\n",
    "X = train_imgs[indices, :]\n",
    "y = train_labels[indices]\n",
    "\n",
    "y[y==0]=0\n",
    "y[y==8]=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a7d48655",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f54bfea8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def inv_log(x):\n",
    "    return -np.log(x)\n",
    "\n",
    "def get_edges(kernel):\n",
    "    edges = []\n",
    "\n",
    "    n_samples = kernel.shape[0]\n",
    "    for i in range(n_samples):\n",
    "        for j in range(i):\n",
    "            weight = kernel[i, j]\n",
    "            if weight != 0 :\n",
    "                edges.append([i, j, weight])\n",
    "                #edges.append([str(j), str(i), weight])\n",
    "    return edges\n",
    "\n",
    "\n",
    "def get_weights(X, \n",
    "                density_scorer, \n",
    "                mode,\n",
    "                weight_func = inv_log):\n",
    "    epsilon = 0.75\n",
    "    n_samples, _ = X.shape\n",
    "    k = np.zeros((n_samples, n_samples))\n",
    "    for i in range(n_samples):\n",
    "        v0 = X[i, :].reshape(-1, 1)\n",
    "        for j in range(i):\n",
    "            v1 = X[j, :].reshape(-1, 1)\n",
    "            dist = np.linalg.norm(v0 - v1)\n",
    "            if dist <= epsilon:\n",
    "                midpoint = (v0 + v1)/2\n",
    "                density = density_scorer(midpoint.reshape(1, -1))\n",
    "                if mode == 1:\n",
    "                    k[i, j] = weight_func(np.exp(density)) * dist\n",
    "                else:\n",
    "                    k[i, j] = weight_func(sigmoid(density)) * dist\n",
    "            else:\n",
    "                k[i, j] = 0\n",
    "            k[j, i] = k[i, j]\n",
    "    return k\n",
    "\n",
    "def get_weights_kNN(\n",
    "    X, \n",
    "    n_neighbours = 20,\n",
    "    alpha=0.10,\n",
    "    weight_func = inv_log\n",
    "    ):\n",
    "    n_samples, n_ftrs = X.shape\n",
    "#     volume_sphere = get_volume_of_sphere(n_ftrs)\n",
    "#     const = (n_neighbours / (n_samples * volume_sphere))**(1/n_ftrs)\n",
    "    \n",
    "    k = np.zeros((n_samples, n_samples))\n",
    "    for i in range(n_samples):\n",
    "        v0 = X[i, :].reshape(-1, 1)\n",
    "        for j in range(n_samples):\n",
    "            v1 = X[j, :].reshape(-1, 1)\n",
    "            dist = np.linalg.norm(v0 - v1)\n",
    "            k[i, j] = dist\n",
    "        t = np.argsort(k[i, :])[(n_neighbours+1):]\n",
    "        mask = np.ix_(t)\n",
    "        k[i, mask] = 0\n",
    "        \n",
    "    for i in range(n_samples):\n",
    "        v0 = X[i, :].reshape(-1, 1)\n",
    "        for j in range(n_samples):\n",
    "            v1 = X[j, :].reshape(-1, 1)\n",
    "            if k[i, j] != 0:\n",
    "                current_value = k[i, j]\n",
    "#                 k[i, j] = current_value**alpha\n",
    "                k[i, j] = weight_func(current_value)\n",
    "    return k\n",
    "\n",
    "def get_weights_e(X, \n",
    "                 epsilon = 0.75,\n",
    "                 alpha=0.10,\n",
    "                 weight_func = inv_log):\n",
    "    n_samples, n_ftrs = X.shape\n",
    "    k = np.zeros((n_samples, n_samples))\n",
    "    for i in range(n_samples):\n",
    "        v0 = X[i, :].reshape(-1, 1)\n",
    "        for j in range(i):\n",
    "            v1 = X[j, :].reshape(-1, 1)\n",
    "            dist = np.linalg.norm(v0 - v1)\n",
    "            if dist <= epsilon:\n",
    "                k[i, j] = weight_func(current_value)\n",
    "                k[j, i] = k[i, j]\n",
    "    return k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c4e82aed",
   "metadata": {},
   "outputs": [],
   "source": [
    "clf = NN(max_iter=5000).fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fe79e185",
   "metadata": {},
   "outputs": [],
   "source": [
    "predictions = clf.predict_proba(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "82408321",
   "metadata": {},
   "outputs": [],
   "source": [
    "bandwidths = 10 ** np.linspace(-2, 0, 10)\n",
    "\n",
    "grid = GridSearchCV(\n",
    "    KernelDensity(kernel='gaussian'),\n",
    "    {'bandwidth': bandwidths},\n",
    ")\n",
    "\n",
    "grid.fit(X)\n",
    "kde = grid.best_estimator_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e64e8d6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_neighbours = 20\n",
    "n_samples, n_features = X.shape\n",
    "\n",
    "def get_volume_of_sphere(d):\n",
    "    return math.pi**(d/2)/math.gamma(d/2 + 1)\n",
    "\n",
    "volume_sphere = get_volume_of_sphere(1)\n",
    "r = (n_neighbours / (n_samples * volume_sphere))\n",
    "    \n",
    "res = {}\n",
    "for test_index in [0, 10, 20, 30, 50]:\n",
    "    res[test_index] = {}\n",
    "    for idx, alpha in enumerate([1]):  # np.linspace(0.01, 3, 9)\n",
    "    \n",
    "        kernel = get_weights_kNN(\n",
    "            X,\n",
    "            n_neighbours=int(n_neighbours),\n",
    "            weight_func=lambda x: -x*np.log(r/x)  # x**alpha\n",
    "        )\n",
    "\n",
    "        graph = Graph()\n",
    "        edges = get_edges(kernel)\n",
    "        for edge in edges:\n",
    "            graph.add_edge(*edge) \n",
    "\n",
    "        dist, paths = dijsktra_toall(graph, test_index)\n",
    "        for item, val in paths.items():\n",
    "            if (y[item] != y[test_index] \n",
    "                and predictions[item, int(y[item])] >= 0.55):\n",
    "                res[test_index][idx] = val\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "759e59a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_digits(path, _id):\n",
    "    n_digits = len(path)\n",
    "    ncols=min(10, n_digits)\n",
    "    nrows = math.ceil(n_digits / ncols)\n",
    "    _, axes = plt.subplots(nrows=nrows, ncols=ncols, figsize=(16, 4*nrows))\n",
    "    axes = axes.ravel()\n",
    "    for idx, img_idx in enumerate(path):\n",
    "        ax = axes[idx]\n",
    "        image = X[img_idx, :]\n",
    "        label = y[img_idx]\n",
    "        ax.set_axis_off()\n",
    "        ax.imshow(image.reshape(28, 28), cmap=plt.cm.gray_r, interpolation=\"nearest\")\n",
    "        ax.set_title(f\"id:{_id}, t: {label}\")\n",
    "    plt.savefig(f'example_{_id}_log.jpg', dpi=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6941fa5a",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ez7169cr6PqqNPs9ou3Vc7dq1S/t9nYZe7W2o+v524cKFnvX5fs2aNZ510m9cui9tx9fXC2393mWXXTxfdNFFWd9fIfDJIgAAAAAghINFAAAAAEBIvbahTpkyxbNOPY1q6dFJg3qhUZ12Z2bWp0+ftLcfMWKE5+7du0feHhvoxdajWk8333xzz9dff73n1ImC2mKqk06rvYUxjldeecVz3759M27fvHlzz3qR16iLuZuZLVmyJO19zJ0717NecF5pm1810haeKNrSdfDBB3tu3bp1wdax8847e+7QoUPB9lsN9LVFXxvyldqOj420pV7pKQ+50NNSdKLnO++84znOlPVqpFMxtZ1XJ6DHpX/vSZMmpd3m888/z3q/1Uzfb6VOnI9Da6q07tVu9uzZGbfRU9e0hT6qXfvII49M+lonAl977bWedWKzvndr1apVxjUVG58sAgAAAABCOFgEAAAAAITUeRuqtnz+8Y9/TLuNTqbT9qC4U9L22msvz2eccYbnc845J+32eoHMO++803NU210lO+644zzrZCalk2RnzJjhOWrSlllyGyoye/311z1rW9yiRYvSbq+PGb1AuLaqpLZ97bfffp512pbmOHQqbbWYOXOm5zitVD/96U89X3755cVYUtJFnZs0aVKU+ygXejHlOLSFPl9M3Yxn8ODBnvXx0b59+7z2O2/evLTf79+/f177rQb6+q+TSrW1d6uttoq8vbbRXX311Wm36dSpk+dLL700p3VWOj09QZ/XdYKwTpg9+uijPafWZ/HixZ7Hjh2b9v722Wef3BdbYY444gjP+t/nddddl3b7nj17ev700089t2jRwnPDhg2TbqOnxCm9D30sFus9Qzb4ZBEAAAAAEMLBIgAAAAAgpM7bULVFTieVKW1PidOmkHqxY/0YWSdDRtGP7bWdr1poK+mrr77qWS+qq21Cr732mme96HshRbVbVrK33nrL81FHHeX5q6++ynhbbS857bTT0m7TpUuX3BdXi3333bco+y1letH7UmnDvfLKK+t7CSUjzmPmmGOO8VxbC73SqcGPPfZY2m2ybYGtVtq+3bRpU89R09DjimrxatmyZV77rQZ6ysPNN9/s+Z///KdnfdykGj58uOeox4eeitSgQYMcVln5tB3xiy++8Hz//fd7/t3vfue5R48ennWKvVnye6moFu02bdrkvtgKoxNn9blkk002frY2cuRIz99++61nnUj+0EMPee7WrVvk/elpP4lEwvPbb7+dzbKLjk8WAQAAAAAhHCwCAAAAAELqpA1VL86qU7W+//57z9rymK22bdvmfNtU+jGwrq/SrF+/3rO2PP73v/9Nu32/fv08F6v1VCep3XTTTUW5j1L23nvvedZ2tyjNmjXznMsFeqN8+OGHnr/88kvP+tjQiY9Rba+VLOp5Iur7Tz75ZF73p63iUc9LHTt2zOs+yp1O+9VWN62JXtz4kUceyfo+9PVLX9d22GEHz7R0oVy9+OKLnnXq+d577512e72geOrX2s53xx13eN5tt93yXWZVGTNmjGd9fzZt2jTP+lymF3OPS98DIj1tsdb3P2effbZnPbVOp6Tqbc2Sr8CgU4eDIPCsp9OVAj5ZBAAAAACEcLAIAAAAAAjhYBEAAAAAEFK0cxbff/99zzqO+euvv/ac74jsQtHzUNauXeu5VNZXDK+88ornqPMUDznkEM8DBw4s+pp0HLGeo6W0V7xr165FX1Nd0n51zUovBfP444973meffQq2jtmzZ3tesGBBVuurZIsXL/Y8ZcoUz/o8oecTnnjiiZ71/NJcDBs2LO39Ib2omuTy362+Puiln/Q+9Dys1Es5IT29lIWO91++fLnnJk2axNrXunXrPEe9nul9tG7dOvY6q8nHH3/sWS8jpn+vSZMmeb7mmmsi99W4cWPPp556aqGWWHX00m5PPfWUZz0P7vrrr/esjx+z5HO29fnv3nvv9Vxq58eVOv3vWS8rd9ZZZ3n+5JNPPKe+fx46dKjnFStWeNb66PvvUsAniwAAAACAEA4WAQAAAAAhRWtDPf/88z3Pnz+/WHdTEA8//LDnN954ox5XUndSR/mmc+yxx3rWMdiFtHDhQs+TJ0/OuL2OiG7QoEFR1lRfUseQp6MtD506dSrYfc+dO9fz4MGD026z3Xbbeb799tsLdt/lYtmyZZ6nT5+ecXttR4zbTqejt6+44grP8+bNS7v9XXfdFWu/yJ2+PkyYMKEeV1JZtHVex8dr63vcx83UqVM966V/tIVPL2+C9A499FDPjz76qOdbb73V80UXXeRZT9tJ9dVXX3nWyyvpY6hY7ysqlb7nGTRokGe9NJNe0ieVtjlGXQ4F2dHXeT19qk+fPp4feuihpNusXLky7b701JVSqw+fLAIAAAAAQjhYBAAAAACEFK0NNY5Ro0bV231/8MEHnrWtQmnLn04GK1fayvb2229n3L5Hjx7FXI6Zmd14442e33vvvbTbnHDCCZ516mCliWpNqAvHH3+8Z23jUqNHj/bcpUuXYi+pKr3wwgue9e8dpUWLFsVcDlAWop6ztBWMlsfMOnfu7HmLLbbwPGDAgFi312nlOvle2/D0vZS2HyOz9evXez799NM919Z6etJJJ3l+8MEHPd93332eR4wYUaAVVjdte9f3qjqRtjZxt6sPfLIIAAAAAAjhYBEAAAAAEFKvbajbbrttnd6ftp7qpM8lS5Z41oue6xQ8/X65mjlzpmf9ndUee+zhWS+qmy+9MLZeyFfbUFWHDh08azteJV8Mvm3btp6//PLLtNvssssuOe//s88+S/p64sSJnufMmZP2NvoYbdeuXc73jfR04qmZ2d///veMt+nWrZvnjh07FnxNlUwnND722GOe9fUg1bhx4zLu9/e//31+C0PW/vOf/3iOatnu3r17XS2nIujjY9WqVRm3v+CCC5K+1ovDT5kyxbPW4dlnn/W8aNEiz5XwHqvYdCK3Pn+pCy+8MOnrc88917PW5KabbvKsF4DXibjIzlVXXZU2p75v1cnM+jym7dqHHXaY5969exd0nbngk0UAAAAAQAgHiwAAAACAkKK1oepUH21BVGeccYZnneyUL22f0P3qR/BKW/v04qbt27cv2JrKhbah6OStbC1cuDDp6zFjxni+8sor095GW0//9re/ea6WiymfddZZnnUqpvrhhx8y7kcfb2+++abn8ePHJ22nNVE//vGPPWsLnl5Eu9pFPafp897s2bM9L1682PPQoUM9p9ZAb6+tK9oCrBfLxkY6ofeOO+7wrBMxV6xY4fm4447zrFMcmzVrlrTf6dOne9aaDBs2zHPPnj1zW3QV07b7XOhpJdpir9M2daI5MtPHx+rVq9Nu06hRI8+1vW/Ti5Xr85q23c2dO9czbaiZDR8+PO339XSEIUOGJP1MJ3Tefffdnvv16+dZT4fQ91t6WhLS0/ezmvVxoqdemSUf+/Tt29eztqHecMMNnk8++eS0+61LfLIIAAAAAAjhYBEAAAAAEFK0NtTLL7/c87vvvutZ2xzUwQcf7FlbfXRKnbaFjho1ynPqhSzXrl3r+Y033vCsH98OHjzYs07qqsbWU6UtIn/4wx88a5uCtmxpa+O3337r+c4770za79tvv532/nRfOgmyWlpPs6WtjZ9++qlnbb3S1lGtW+rjJGqy7IknnuhZJ29io0033TTt97U99a677vKsbdlPPPFE5H709vqzs88+O/fFViGdTqptPlF1+/jjj9Nms+THiV6ovGnTpvkus6odf/zxnrV1Tlu2a3P//fen/b7Wu2XLljmurjrp30vbsfX0lIEDB3rec889I/el7weiXms++ugjz/vvv392i61CDz74YNrv/+lPf/KsbaepTjnlFM+TJ0/2rKc26OPypZde8lzXVy8oZTqJVqee6uvDxRdf7HnAgAGR+9LttA31ww8/9Ky1OvXUU3NYcf74ZBEAAAAAEMLBIgAAAAAgJEhtTUtR6w/jev755z1ry6e2pEa1X8WROplQb9+5c2fPvXr18lzI6atZyveq8jnXRCdpaoupTg6MsskmG/+/gv59405M1dvvt99+nh9++GHP9dh6Wm81UdqCoK0GUX/jJk2aeNaWIZ0wp1If61tvvbXnESNGeD7ttNPS3kcdK4maqM8//9zzr3/9a89LlizxnM/zmJlZw4YNPWt7S//+/T03aNAg6/0WSMnVJI6o5664tKY777yz56jHWR3LtyZm9VQXfT7SC1CvW7fOs07Fvuyyy5Juf8stt3jW57IZM2Z41inCdawsHyvq8MMP9/zMM8941vcOo0ePTrqNnm5y3nnneX755Zc9t2rVKu3222yzTZ4rzqjsa9K6dWvPCxYs8Pz000971sdSbdasWeP5qKOO8qzv17XVXtsiUydG56Esa7Lbbrt51qnMOiFbp57HpW3C2mav+9L7KJK0NeGTRQAAAABACAeLAAAAAICQok1DVQcddJBnnYyqEzOvvvrqnPef2r6oradjx471XI8tdSVB27H+/Oc/e9b2VP17Kd0mzoXhW7RokfS1tq7oJFpsdMIJJ3ieOXOmZ538+91333levnx52hzlmGOOSfr6ggsu8KyPGaS30047eZ40aZLnM8880/O///3vrPaZOm22a9eunvWiycid1qRnz56edVJ2bfT1RSfcIj86IbNTp06er732Ws96Yfd33nkncl96Wkk9tp5WFH2d1incY8aM8fzAAw8k3WblypWedSq9uvDCCz3XQetpRdGp2DpB+LrrrvOc+t4rjtWrV6f9/rJlyzxnOGWtqhx44IGetT03X3vvvbdnfWz94x//8FwHbahp8ckiAAAAACCEg0UAAAAAQEidTEON45577vF8/fXXe9aPePUC7oMGDfLcpk2bpH1p60oJKrnpT9oucvPNN3vWaVtTp071PGfOHM/aXqrTzxo3bpx0H/U46TSOkquJ0seGTvq77bbb0m6vF4bVKVqXXHJJEVZXNCVdE/Xmm2961nY6nby54447etb2+44dOybtq4BT5oqhbGoSRdt5Fi1a5Pnuu+/23Lt376Tb6OtLCb62lO00VKXt9VdeeaXnkSNHetbnNbPk6dF6qotOFK5HZf9YUUuXLvWsFxj/61//mrRd8+bNPR999NGedQLqpZde6rmOJzuXfU108ubuu+8e6zb6Hl9bv+PQdku9EH0BT+kqy5q88sornrt06eJZX/P1dV6n29dGHxv63Hfsscd6njx5clZrzQHTUAEAAAAA8XCwCAAAAAAIKZk21CpSlh+7VzhqUnqoSemhJqWnItpQKxCPldJT9jXRSfTjxo3zPHz4cM/z589Puk1UG6q2Rm677baedSK3tlimtoEXSNnXRCcxT5gwwbO2WDdt2jTpNjr1VOvzwgsveF6/fr1nPZ1Ic5HQhgoAAAAAiIeDRQAAAABACG2oda/sP3avQNSk9FCT0kNNSg9tqKWJx0rpoSalh5qUHtpQAQAAAADxcLAIAAAAAAjhYBEAAAAAEMLBIgAAAAAghINFAAAAAEAIB4sAAAAAgBAOFgEAAAAAIRwsAgAAAABCgkSCa1oCAAAAAJLxySIAAAAAIISDRQAAAABACAeLAAAAAIAQDhYBAAAAACEcLAIAAAAAQjhYBAAAAACE/D+G2In2EqsjiwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x288 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qT548WeVE1jnEqmVCMHPmzAn0eFsPYMVTo2j7e27atMn38WXKlCn2ueD173//W+Xhw4cHev6yZctUDtJvtVWrVirPmjUr0Ln79u2r8vvvvx/o+Thp4sSJKtu68nhdc801+dvvvfdeqMe2bM2JrdHLRJs3b87ftp8BYHsNIjMtXLhQZVvHl0rs61X7GqVTp04qx6pZtGzfxkwzY8YMlW3vwUT2Orz11lvVPlsfuWXLFpXta5Cwx/anP/1JkoF3FgEAAAAAHiwWAQAAAAAeLBYBAAAAAB4pU7No+yRasWoWo2sewla/fn3fc40bN07lChUqqPzQQw8lYlil1nPPPafyqlWrVLb3gCeyb6LtydmoUSOVBwwYoPL999+fsLFkomHDhqls61RsvYB11llnFfvcM2fOVPnmm29Wefbs2b7P//DDD1W2NTexrnmZzF4z460jjO6jKKJrFEW813A/tt8btajx27ZtW/62/T1Jtugeds2aNVP77PVmyJAhKn/22WeJG1iG2bNnj8pBa8ZL0uLFi1WO9fo1qOjP5HjxxRdDPXY6iO4tKBJ+L8OWLVuqPHDgwPztrl27+o7N1lP27Nkz1LHZ/bFeA4WFdxYBAAAAAB4sFgEAAAAAHilzG6q1bt06lSdNmhTase1bzPfee6/v/sqVK6s8dOhQlV9++WWVR40apfIVV1yhctu2bYs+2AxUvnx5lcuVK+f7eNuuokOHDirPmzdPZfvRw37sLa7bt29X2d4y++abb/rut2ODP3sLsr3lwubWrVurfOaZZ4Y2lmnTpql83XXXqfz555/7Pt/etsptqCf99NNPKtt2REF+Z0VEOnbsqLL9ePGrr7460PGi/fjjjyofP3480PPtnK1atWqxx1IaBf1Zx3LppZeqbH9vR44cWexj21tmb7zxRpVtq6V426SE/XeTyj766COVV69eHej5sVoQhHmsiy++WOWxY8eqPGXKFJXtPIhnbKXV1q1b87dta71EtsYQ8d5GHKQ9hX0dEPbYbOuOWLfFhoV3FgEAAAAAHiwWAQAAAAAeLBYBAAAAAB4pU7O4b98+lX//+9+rbFsYWK1atVL5sssuUzkrKyt/29YQ2o+mjWXixImFHlvEew9xr169VN6yZUug82WapUuXqvzll1+qbGsYH330UZXtx5l/8sknKgep+zh48KDKw4cPV3nNmjUq21or+7HJNj/77LNFHksmiK5TEBE5evSo7+ObN2+u8t///neVbRubeNj2C4MGDVLZ1hJYtuZx9OjR4QysFPjqq69Utj/HoHr06KFyPDWKYTv1VP3Prr2e7dq1S+WaNWsmfEypJN6Pgrd1g1OnTlW5evXqcR3fz5w5c1SObnEgItK7d+9Ax2vfvr3KdevWLda40kV0naL9LImgr9NitSCw7GclRP/e2dcM9nfSXtvr1aunsn3Naeekfc0D/XeyYsUKtc9eI8JsjSHi/XlHry9sTeLzzz+v8vTp0+MaW6z9yWqVYfHOIgAAAADAg8UiAAAAAMCDxSIAAAAAwCNlahaHDRumsr1H2WrWrJnKs2bNUjmRdR6nnKLX2Ndee63KtpbJfm/jxo1TuX///iGOLv3ZHkUHDhxQ+ZJLLlHZ1ihaYdYrde7cWeU+ffqo/M4776hsaxjfeOMNlW+++WaVbY1KprG1y7annWV7oJ5//vmhj6kwtWvXTtq5SrumTZuqfOedd6r8yiuvqNyoUSOVbV2yrS8Nk+3dWatWLZXt77z1888/q2x7et12221xjA72MwMSWaOYaLb+0tbClTbRn03xww8/xHUs2/vQfv7At99+q/KIESNUTuXXZZ06dSrpISRcdN1gvL0K//GPf6hsP2cklug6xTZt2qh9toYw7B6Qtr7yrbfeKsKIw8c7iwAAAAAADxaLAAAAAAAPFosAAAAAAI+UqVnctGlToMc3aNBA5VTqRWXvtbc1Kvb+6VS+N74krF692nf/X/7yl+QMpAC2583f/vY3lQcMGKCyrZe0PdT69eun8rp16+IdYlqz9+vHyvZ3qyTF6t8ZpL9npilbtqzKVapU8X387t27Vbb9Tm0tcJhatGihsu3xa+vnrTJlyqg8d+7ccAYGEfH25zv77LNVPuecc1S2rx3OOOOMYp9748aNKu/cubPYxxIRefzxx1Vu165d/vbll18e17FT0YYNG0I71rx581ReuXKlyra2uEuXLsU+1+bNm32z9cADDxT7XCIit9xyS1zPTwfRtYDx9lG01+hYbC/F6L698fZ4DDr2kqpRtHhnEQAAAADgwWIRAAAAAODBYhEAAAAA4JEyNYu2jsC64IILVI5V05JMy5cvV9n20rMaN26cyOGUOrbmpEmTJiU0ktiaN2+usp2ne/bsSeZw0o6t+cnOzlbZ1gvYnqclyY7NqlOnTpJGUvrZuvBJkyapfN1116lcrly50M796aefqhyrRhHJZa8Z119/ve/ju3XrprLtmxzEwIEDfccS1IUXXqhyPPWU6WDUqFH527aWK6jBgwerbGsYbc3i7NmzVa5UqVL+tq03t9d6+zkLa9eu9R1brLo1y77m+fWvf+37+NIg+vcyaC9Dm20Nos1jxozxPX70+RPdR3HRokWSilLnlRYAAAAAIGWwWAQAAAAAeLBYBAAAAAB4pEzNYiy33367yg8//HDCznXkyBGVbQ+v5557TuUPPvhA5ePHj/sePysrK47RZZ66deuq/Mtf/rKERhLb5MmTVY7Vb8ner57pbH1qxYoVVT58+HAyhxOq7t27l/QQSi17DZ4/f77KttbL7/fuxx9/VHno0KEq2z65QQ0fPjyu5yNc06dPLzTHqlVLtK5du6rcqFGjpJ4/2aJr8RYvXhzXsaZOnapyrJ/djBkzCt0X9jyIVdd28cUXq2zrLc8888y4zp8O4umzuGzZMpV79uwZ6Pl++0trH8VYeGcRAAAAAODBYhEAAAAA4MFiEQAAAADgkTI1i7F653300Ucq9+7dW+Xq1aurbOtO9u3bV+ix7T3Dtu7s66+/9h2bVatWLZVt76V27doFOl6m279/v8rbt29X2dY0JpK9H71///4qv/322yrH6qkzbty4EEeX/lq3bq2yrTWzNYs7duxQeefOnSrXrl07tLEdOnRI5T//+c+Bnn/ppZeGNpbSrlevXipPmTJFZVtXbnXs2FHlypUrq9y5c+dCn3vs2DGV7e90UE8//bTKv/nNb+I6Xmn0q1/9Kn/7m2++UfuGDBmisq1PtdfkdGb7gZYvX76ERlIy7rrrrvztpUuXxnWsoL0Mk3UsEW9f8Zo1a6o8bdo0lTOhRtGKfl3+29/+Vu0Lu9dhkP2xnms/d6FNmzYqp0uNosU7iwAAAAAADxaLAAAAAAAPFosAAAAAAA9n7781fHeGacmSJSpfeeWVKv/8888qV6hQQeWLLrpIZVtftH79+niHmK9MmTIq2x4uI0aMULlOnTqhnbsIEtUIKmlzwfZRtDUso0ePVnnw4MGBjh9dJ2hrDr/88kuVbZ/EJ598UuUVK1b4nusPf/iDyrZ+tWnTpr7Pj1PazwX792Pngu131bhxY5Vnzpypsq0nqFKlSv62rYPbu3evyrbObdWqVYWMOsd7772ncqdOnXwfn2CJmAtJmwevvfaaynfeeWeyTh1YdP2diMjs2bNVtvVJSZb214QuXbqobH/PwpToPou2RvGRRx5R+cEHHwz1fEbKXRNWr16dv/3qq6+qfUHr+0uyZrF+/foq2xps+3MuYSl5TYjuexlmn8R499vPnbCv6exnaLRq1UrSSKFzgXcWAQAAAAAeLBYBAAAAAB4sFgEAAAAAHilTs2gNHTpU5eHDhyft3A0aNFC5W7duKtvapRS7Jzkl7z8PokOHDiovXLhQ5UqVKqncvn37QMePrnuz/T2XL1+u8u7du32PVaNGDZVvuukmlW2dRcWKFYs8zhCk/VzYsGGDyldddZXKtq9iLC1atFA5usZx69atat+yZctUttfKqlWrqmxrqV544QWVbZ11kqVcfVIQttfqypUrVbY1jN99912xz1W2bFmVbd/ctm3bqvzAAw+obHv+htnrMwRpf02wPZNtD07rmWeeUXnXrl1FPle8NYu2vqlr164q2z6K/fr1C3T8OKX0NeHEiRMq2/7Kqcz+XO01JMWk/TUBoaFmEQAAAABQdCwWAQAAAAAeLBYBAAAAAB4pW7Noa1T69Omj8vTp0wMdr2HDhvnb9913n9pn+6LYurN4+vOUgLS//9zWjgXtbxcP20Pz9NNPV9n2yvvjH/+o8iWXXJKYgRVP2s8Fa926dSrbHkfz58/3fX48NUi25nDQoEEqP/HEE0U+VglI6fqkeNn60quvvlpl20PTj60vmjNnjsrnn3++ypUrVy7ysVNAqbsmxGL/vTh27FiRn9umTRuVY10v5s6dq/J5552ncqNGjYp87iQo1dcEFFnGXRNQKGoWAQAAAABFx2IRAAAAAOCRsrehothK3S0FO3bsUHn8+PEqjxo1yvf5I0eOVNnvtuKaNWuqfMcddxRliKmq1M0F6/jx4yovWbJEZXsL4YIFC1T+4osv8rd79Oih9tmWB+3atVPZ3q6e4rjlDCIZcE1AkXFNgAjXBJzEbagAAAAAgKJjsQgAAAAA8GCxCAAAAADwoGax9OH+c+RhLiAP9UkQ4ZqAk7gmQIRrAk6iZhEAAAAAUHQsFgEAAAAAHiwWAQAAAAAeLBYBAAAAAB4sFgEAAAAAHiwWAQAAAAAeLBYBAAAAAB4sFgEAAAAAHiwWAQAAAAAeLBYBAAAAAB4sFgEAAAAAHi4SiZT0GAAAAAAAKYZ3FgEAAAAAHiwWAQAAAAAeLBYBAAAAAB4sFgEAAAAAHiwWAQAAAAAeLBYBAAAAAB7/D+Qt7nZ5sx4VAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1152x288 with 7 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x288 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x288 with 7 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for k in res.keys():\n",
    "    for k2 in res[k].keys():\n",
    "        plot_digits(res[k][k2], '-'.join(map(str, [k, k2])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "899237be",
   "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": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}