MMJ-K-means with single One-SCOM point.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d8c341f4-72ec-41d9-8094-82d124d0d245",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "exec(open(\"./funcs/mmj_functions.py\").read())\n",
    "exec(open(\"./funcs/algo_4_funcs.py\").read()) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "efa57ad3",
   "metadata": {},
   "outputs": [],
   "source": [
    "exec(open(\"./funcs/mmj_kmeans_single_one_scom.py\").read())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ad2ac2d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "import kmedoids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2b698a2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(12647)\n",
    "np.random.seed(12647)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2baeabee-a859-49f8-a070-cf2135ae5563",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_data_145 = pickle.load(  open( \"./data/test_data_145.p\", \"rb\" ) ) \n",
    "true_K_145 =  pickle.load(  open( \"./data/true_num_of_145.p\", \"rb\" ) ) \n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0cc457f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def MMJ_K_means_using_PAM_algo_testing(X, num_clusters, mmj_matrix): \n",
    "    import kmedoids\n",
    "    km_model = kmedoids.fasterpam(mmj_matrix, num_clusters)\n",
    "    label = km_model.labels\n",
    "    \n",
    "    print(\"Loss is:\", np.round(km_model.loss/len(X), 8) )\n",
    "\n",
    "    centers_idx = [[ii] for ii in km_model.medoids]\n",
    "    dis_to_medoids = np.array([[mmj_matrix[i,j] for j in km_model.medoids] for i in range(len(X))])\n",
    "    min_dis_to_medoids = np.min(dis_to_medoids, axis = 1)\n",
    "\n",
    "    strong_ambi_p_idx, weak_ambi_p_idx = [], []\n",
    "    for i, _ in enumerate(dis_to_medoids):   \n",
    "        ppp = np.sum(dis_to_medoids[i] == min_dis_to_medoids[i])\n",
    "        if  ppp == 1:\n",
    "            pass      \n",
    "        elif ppp == num_clusters:\n",
    "            strong_ambi_p_idx.append(i)      \n",
    "        else:\n",
    "            weak_ambi_p_idx.append(i)\n",
    "     \n",
    "    if strong_ambi_p_idx or weak_ambi_p_idx:\n",
    "        plot_2D_or_3D_data_empty_circles_weak_strong_multi_one_scom(X, label,centers_idx, strong_ambi_p_idx, weak_ambi_p_idx)        \n",
    "    else:\n",
    "        plot_2D_or_3D_data(X, label, centers_idx = centers_idx, plot_center = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ba21bd90",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c54d88f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_id  = 106\n",
    "\n",
    "\n",
    "X = test_data_145[data_id] \n",
    " \n",
    "num_clusters =  true_K_145[data_id] \n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "34cfb0cd",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ec80ca51",
   "metadata": {},
   "outputs": [],
   "source": [
    "mmj_matrix =  cal_mmj_matrix_by_algo_4_Calculation_and_Copy(X) \n",
    " \n",
    "mmj_matrix_squared = mmj_matrix**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c4a9419a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a04f0b6a",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss is: 0.48530449\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MMJ_K_means_using_PAM_algo_testing(X, num_clusters, mmj_matrix_squared)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ca02b84b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Got a better one! Loss is:  4.84650641\n",
      "Got a better one! Loss is:  0.48530449\n",
      "The single One-SCOM  of each cluster:  [[203], [103], [304]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    " \n",
    "attempts = 20\n",
    "\n",
    "label, centroids_idx, loss, strong_ambi_p_idx, weak_ambi_p_idx = \\\n",
    "KMeans_several_times_ambi_points_single_one_scom(X, num_clusters, attempts, mmj_matrix)\n",
    "\n",
    "print(\"The single One-SCOM  of each cluster: \", centroids_idx)\n",
    "\n",
    "if strong_ambi_p_idx or weak_ambi_p_idx:\n",
    "    plot_2D_or_3D_data_empty_circles_weak_strong_multi_one_scom(X, label,centroids_idx, strong_ambi_p_idx, weak_ambi_p_idx)        \n",
    "else:\n",
    "    plot_2D_or_3D_data(X, label, centers_idx = centroids_idx, plot_center = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8f36a98a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7b3ee26e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Note the two calculated losses are equal.\n",
    "# The One-SCOM for each cluster can have multiple points, we can arbitrarily choose one or keep them all."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "efabf2ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "# One-SCOM means SCOM-of-length-one. SCOM stands for Semantic Center of Mass.  \n",
    "# One-SCOM is the counterpart of center of mass or centroid on graph. See:\n",
    "# https://arxiv.org/abs/2110.06043\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c6aca8a5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec9dcbcb-2144-4fc6-90c8-b2e54f2af64f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}