{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 235,
   "id": "4750c48d",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from io import StringIO\n",
    "import geopy.distance # https://geopy.readthedocs.io/en/stable/#module-geopy.distance\n",
    "import seaborn as sns\n",
    "from scipy.spatial.distance import cdist\n",
    "from scipy.optimize import minimize\n",
    "from scipy.ndimage.interpolation import rotate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "id": "d5bbd3ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Place Name</th>\n",
       "      <th>Latitude</th>\n",
       "      <th>Longitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Ra'anana, Israel</td>\n",
       "      <td>32.184448</td>\n",
       "      <td>34.870766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Bethlehem, Israel</td>\n",
       "      <td>31.705791</td>\n",
       "      <td>35.200657</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Ashdod, Israel</td>\n",
       "      <td>31.801447</td>\n",
       "      <td>34.643497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Nazareth, Israel</td>\n",
       "      <td>32.699635</td>\n",
       "      <td>35.303547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Bat Yam, Tel-Aviv, Israel</td>\n",
       "      <td>32.017136</td>\n",
       "      <td>34.745441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Tel Aviv-Yafo, Israel</td>\n",
       "      <td>32.109333</td>\n",
       "      <td>34.855499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Haifa, Israel</td>\n",
       "      <td>32.794044</td>\n",
       "      <td>34.989571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Karmiel, Israel</td>\n",
       "      <td>32.919945</td>\n",
       "      <td>35.290146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Herzliya, Tel-Aviv, Israel</td>\n",
       "      <td>32.166313</td>\n",
       "      <td>34.843311</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Rehovot, Israel</td>\n",
       "      <td>31.894756</td>\n",
       "      <td>34.809322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Jerusalem, Israel</td>\n",
       "      <td>31.771959</td>\n",
       "      <td>35.217018</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    Place Name   Latitude  Longitude\n",
       "0             Ra'anana, Israel  32.184448  34.870766\n",
       "1            Bethlehem, Israel  31.705791  35.200657\n",
       "2               Ashdod, Israel  31.801447  34.643497\n",
       "3             Nazareth, Israel  32.699635  35.303547\n",
       "4    Bat Yam, Tel-Aviv, Israel  32.017136  34.745441\n",
       "5        Tel Aviv-Yafo, Israel  32.109333  34.855499\n",
       "6                Haifa, Israel  32.794044  34.989571\n",
       "7              Karmiel, Israel  32.919945  35.290146\n",
       "8   Herzliya, Tel-Aviv, Israel  32.166313  34.843311\n",
       "9              Rehovot, Israel  31.894756  34.809322\n",
       "10           Jerusalem, Israel  31.771959  35.217018"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# https://www.latlong.net/category/cities-108-15.html\n",
    "df = pd.read_csv(StringIO(\"\"\"Place Name\tLatitude\tLongitude\n",
    "Ra'anana, Israel\t32.184448\t34.870766\n",
    "Bethlehem, Israel\t31.705791\t35.200657\n",
    "Ashdod, Israel\t31.801447\t34.643497\n",
    "Nazareth, Israel\t32.699635\t35.303547\n",
    "Bat Yam, Tel-Aviv, Israel\t32.017136\t34.745441\n",
    "Tel Aviv-Yafo, Israel\t32.109333\t34.855499\n",
    "Haifa, Israel\t32.794044\t34.989571\n",
    "Karmiel, Israel\t32.919945\t35.290146\n",
    "Herzliya, Tel-Aviv, Israel\t32.166313\t34.843311\n",
    "Rehovot, Israel\t31.894756\t34.809322\n",
    "Jerusalem, Israel\t31.771959\t35.217018\"\"\"), sep='\\t')\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "id": "1919c099",
   "metadata": {},
   "outputs": [],
   "source": [
    "cities = [x.partition(',')[0] for x in df['Place Name']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "id": "7636d729",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.         61.5626296  47.59132622]\n",
      " [61.5626296   0.         53.84305935]\n",
      " [47.59132622 53.84305935  0.        ]]\n"
     ]
    }
   ],
   "source": [
    "# https://stackoverflow.com/questions/57294120/calculating-distance-between-latitude-and-longitude-in-python\n",
    "lat_lon = df[['Latitude', 'Longitude']].values\n",
    "\n",
    "D = cdist(\n",
    "    lat_lon,\n",
    "    lat_lon,\n",
    "    lambda lat_lon1, lat_lon2: geopy.distance.distance(lat_lon1, lat_lon2).km\n",
    ")\n",
    "print(D[:3, :3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "id": "ecbc9533",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 489,
       "width": 485
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(D, cmap='autumn_r')\n",
    "plt.xticks(np.arange(11), cities, rotation=90)\n",
    "plt.yticks(np.arange(11), cities);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "856f53aa",
   "metadata": {},
   "source": [
    "## Classical MDS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "id": "6405709a",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = D.shape[0]\n",
    "m = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "id": "6a022ecd",
   "metadata": {},
   "outputs": [],
   "source": [
    "D2 = D**2\n",
    "\n",
    "I = np.eye(n)\n",
    "J = np.ones(n)\n",
    "C = I - J/n\n",
    "B = -0.5 * C @ D2 @ C # Gram matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "id": "8f97526b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0]\n"
     ]
    }
   ],
   "source": [
    "λ, E = np.linalg.eig(B)\n",
    "idx = λ.argsort()[-m:]\n",
    "print(idx)\n",
    "λ = λ[idx]\n",
    "E = E[idx].T\n",
    "Λ = np.diag(λ)\n",
    "X = E @ Λ**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "id": "e8b04b19",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LOOKS BAD\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 597
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for city, (x, y) in zip(cities, X):\n",
    "    plt.scatter(x, y, marker='.', color='k')\n",
    "    plt.text(x, y, city)\n",
    "print(\"LOOKS BAD\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7892a4bf",
   "metadata": {},
   "source": [
    "## Metric MDS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "id": "13bb8277",
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss(X, D, p=1):\n",
    "    X = X.reshape((n, 2))\n",
    "    S = (D**p - scipy.spatial.distance.cdist(X, X))\n",
    "    assert (S == S.T).all(), S\n",
    "    assert (np.diag(S)==0).all(), np.diag(S)\n",
    "    return np.sqrt((S*S).sum()/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "id": "58ad576e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 592
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sol = minimize(loss, np.zeros(2*n), args=(D, 1.4))\n",
    "assert sol.success\n",
    "X = sol.x\n",
    "X = X.reshape((n, 2))\n",
    "\n",
    "for city, (x, y) in zip(cities, X):\n",
    "    plt.scatter(-x, y, marker='.', color='k')\n",
    "    plt.text(-x, y, city)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5d30b0a",
   "metadata": {},
   "source": [
    "## Scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "id": "9335e2ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.manifold import MDS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "id": "5e3e4c71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 414,
       "width": 612
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mds = MDS(random_state=12)\n",
    "X = mds.fit_transform(lat_lon)\n",
    "\n",
    "for city, (x, y) in zip(cities, X):\n",
    "    plt.scatter(x, y, marker='.', color='k')\n",
    "    plt.text(x, y, city)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "c1f209b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 608
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mds = MDS(dissimilarity='precomputed', random_state=12)\n",
    "X = mds.fit_transform(D)\n",
    "\n",
    "for city, (x, y) in zip(cities, X):\n",
    "    plt.scatter(x, y, marker='.', color='k')\n",
    "    plt.text(x, y, city)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee2c0623",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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