2018-Local Density Estimation in High Dimensions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[2018-Local Density Estimation in High Dimensions](http://proceedings.mlr.press/v80/wu18a/wu18a.pdf) By Xian Wu, [Moses Charikar](https://profiles.stanford.edu/moses-charikar), and [Vishnu Natchu](https://dblp.org/pers/hd/n/Natchu:Vishnu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from sklearn import datasets\n",
    "from sklearn.preprocessing import Normalizer\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import euclidean_distances\n",
    "\n",
    "import math\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.spatial import distance\n",
    "\n",
    "mbyte = 1048576\n",
    "norm_l1 = Normalizer(norm='l1')\n",
    "norm_l2 = Normalizer(norm='l2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 545,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys(['title', 'train', 'test', 'K', 'n_train', 'n_test', 'k_near_neighbors', 'nearest_neighbor'])\n"
     ]
    }
   ],
   "source": [
    "%store -r Datasets\n",
    "data = Datasets['SIFT-10K']\n",
    "train = data['train']\n",
    "test = data['test']\n",
    "n_train = data['n_train']\n",
    "n_test = data['n_test']\n",
    "print(data.keys())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "metadata": {},
   "outputs": [],
   "source": [
    "def unit_vector(vector):\n",
    "    \"\"\" Returns the unit vector of the vector.  \"\"\"\n",
    "    return vector / np.linalg.norm(vector)\n",
    "\n",
    "def angle_between(v1, v2):\n",
    "    v1_u = unit_vector(v1)\n",
    "    v2_u = unit_vector(v2)\n",
    "    return np.arccos(np.clip(np.dot(v1_u, v2_u), -1.0, 1.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_k_combinations(k):\n",
    "    kwargs = np.repeat([0, 1], k).reshape(2, -1).T\n",
    "    return np.array(np.meshgrid(*kwargs)).T.reshape(-1, k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 387 µs, sys: 93 µs, total: 480 µs\n",
      "Wall time: 436 µs\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 1, 0, ..., 0, 0, 0],\n",
       "       [1, 0, 0, ..., 0, 0, 0],\n",
       "       ...,\n",
       "       [0, 1, 1, ..., 1, 1, 1],\n",
       "       [1, 0, 1, ..., 1, 1, 1],\n",
       "       [1, 1, 1, ..., 1, 1, 1]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "build_k_combinations(9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def str_to_list(s):\n",
    "    return np.array(s[1:-1].split(' ')).astype(np.int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test Normalized"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fae8e198f28>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "P = datasets.make_blobs(centers=1, n_features=2, n_samples=1000, random_state=1)[0]\n",
    "plt.scatter(P[:, 0], P[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**center the mean**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fae8e0b3e80>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "P = P - P.mean(axis=0)\n",
    "plt.scatter(P[:, 0], P[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**test angle function**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = P[1]\n",
    "p2 = P[4]\n",
    "plt.scatter(P[:, 0], P[:, 1])\n",
    "plt.plot([0, p1[0]], [0, p1[1]], c='b')\n",
    "plt.plot([0, p2[0]], [0, p2[1]], c='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "169.02810957690866"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "angle_between(p1, p2) / np.pi * 180"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**normlize**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.1098521966751331,\n",
       " 1.1098548391224843,\n",
       " -1.1151663754265546,\n",
       " 1.115175498699267)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "norm_P = norm_l2.fit_transform(P)\n",
    "plt.scatter(norm_P[:, 0], norm_P[:, 1])\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## train test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "train, test = train_test_split(norm_P, test_size=100, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(train[:, 0], train[:, 1])\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**target**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. preprocessing the dataset\n",
    "1. given query q, and a range of angles of interest A\n",
    "2. estimate the number of elements that the angles are within range A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = P[0]\n",
    "A = np.pi / 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "metadata": {},
   "outputs": [],
   "source": [
    "idxs = np.argwhere(np.array([angle_between(q, p) for p in P]) <= A).reshape(1, -1)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 414,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(P[:, 0], P[:, 1])\n",
    "plt.scatter(P[idxs, 0], P[idxs, 1])\n",
    "plt.scatter(q[0], q[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "201"
      ]
     },
     "execution_count": 415,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(idxs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LSH Count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import comb, perm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "p(x) = \\Bbb{P}(d_{qx} = i | \\theta_{qx}) = {k \\choose i} \\\n",
    "(1 - {\\theta_{qx} \\over \\pi})^{k-i} \\\n",
    "({\\theta_{qx} \\over \\pi})^i\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 5 # length of hash code\n",
    "pi = 180\n",
    "theta = np.linspace(start=0, stop=180, num=10)\n",
    "for i in range(k + 1):\n",
    "    pr = comb(k, i) * (( 1 - theta / pi) ** (k - i)) * ((theta / pi) ** i)\n",
    "    plt.plot(theta, pr, 'o-', label='hamming distance = {}'.format(i))\n",
    "\n",
    "plt.xticks(theta)\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.xlabel('degree(angle)')\n",
    "plt.ylabel('probability')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hashing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = np.random.normal(0, 1, (2))\n",
    "H = train.dot(v)\n",
    "H[H >= 0] = 1\n",
    "H[H < 0] = 0\n",
    "H = H.astype(np.int8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 428,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oPe7uK8OfbwJPAcMSiKk2fbI29zmNRpIqs23Etp/SeUm8sy8Ag81skJl1B04G2gx9MbNhwG8IksJ7Gcd3MLMe4fW+wCHAKwnEJO1pNJJUmV/E2PZTOqfgxODum4GJwKPAq8Bsd3/ZzC43s9YhMtcAnwPubjcs9ctAk5m9CDwJXOXuSgwiEimqn+G06c+VKJLqk0QfA+7+EPBQu2MXZ1w/Msf9/gDsl0QMNS9qNVWRGvPsG3maViUvNdJVC23KIzWof++eaYdQlZQYqkW+TXm0zLZUqfOO2ivtEKqSEkMt0DLbUqWi+hmkc5QYaoEmtkmNuqhxSdohVCQlhmqgjmeRrO6Y/3baIVQkJYZqsPC2tCMQkSqixFANvCXtCESkiigxiEhFO/2gAWmHUHWUGKpd/fi0IxApqisaNEc2aUoM1e7YqWlHICIVRolBRETaUGIQEZE2lBhERKQNJQYREWlDiUFERNpIJDGY2Ugze93MlpnZ5Czne5jZrPD8AjMbmHHugvD462Z2VBLxiIhI5xWcGMysDrgROBrYBzjFzPZpV2w88L67fwm4Frg6vO8+BFuB7guMBH4dPp6IiKQkiRrDgcAyd3/T3TcCdwGj25UZDcwIr98DHGFmFh6/y903uPtbwLLw8UQqjzvcdhts3Jh2JCIFSSIx9Afeybi9PDyWtUy4R/Q64Asx7wuAmU0wsyYza1q9enUCYYsk6MMP4cQT4cwzYebMtKMRKUgSicGyHPOYZeLcNzjoPs3d6929vl+/fh0MUaSI/vQnOOgguO8++NWv4Iwz0o5IpCBdE3iM5cDuGbd3A1bmKLPczLoC2wNrY95XpHzNnQunnQbdu8O8eXD44WlHJFKwJGoMLwCDzWyQmXUn6Eye067MHGBceP0E4Al39/D4yeGopUHAYOD5BGISKa4tW+Cyy+C44+BLX4KmJiUFqRoF1xjcfbOZTQQeBeqAW939ZTO7HGhy9znALcDvzGwZQU3h5PC+L5vZbOAVYDNwtrs2F5Ayt24d/NM/wQMPwHe/CzfdBD17ph2VSGKSaErC3R8CHmp37OKM658CJ+a47xRgShJxiBTdK6/A8cfDm2/Cv/87nH02WLauMpHKlUhiEKkJ994L48bBttvCE0/AN76RdkQiRaElMUSitLTAz34G3/kO7Lsv/PGPSgpS1VRjEMln7Vo49VR49FE466yg+ahHj7SjEikqJQaRXJqbg/6Ed96B3/wGJkxIOyKRklBTkkg2d90FBx8Mn34KTz+tpCA1RYmh2jXPTjuCyrJ5M5x7LpxyCnzta7BwYZAgRGqIEkO1e/zytCOoHGvWwFFHBctanH02PP447Lxz2lFJhIsal6QdQtVRH0O1W7c87Qgqwx//GPQnrFoFv/2t1juqIDPnv512CFVHNYZqZ/oVR7r9djjkkGDZ7GeeUVKoMFlX3ZSC6FOjGtSPz31OK4zktmkT/OQnwaS1gw4K+hPq69OOShLUs5s+4jpD71o1OHZq2hFUnlWr4IgjgnkJkyYFK6NqOfeqc+WYIWmHUJHUxyC1Z8GCYBbz2rXBpjqnnpp2RFIkDcOy7vslEVRjqAUasvp3N98M3/xmsH/Cc88pKYhkocRQLawu97mHzy9dHOVqwwb4wQ+CZS0OOyzYP+GrX007KilQ46IVaYdQlZQYqsX+Z+Q+98nakoVRllauDJLBtGkweTI89BD06ZN2VJKAC+/LPYehd89uJYykuhSUGMysj5nNM7Ol4c8dspQZambPmdnLZtZsZidlnLvNzN4ys8XhZWgh8dQ0dUBn98wzwQzmJUvg7rvhyiuhLk/tSirKxxtzj7q7dNS+JYykuhRaY5gMPO7ug4HHw9vtrQe+6+77AiOB68ysd8b589x9aHhZXGA8kkut9TO4w69/Dd/6Fmy3XdDhfMIJaUclJaSO584rNDGMBmaE12cADe0LuPuf3H1peH0l8B6gcYHF0DNP80gt9TN8+il873vBshZHHQXPPx/soyBVRUthFE+hiWEnd38XIPy5Y77CZnYg0B14I+PwlLCJ6Voz00L3hTj66tznaqWf4e23g010brsNLr4Y5syB3r0j7yaV5448S2Fsq4ltBYl898zsMTN7KctldEeeyMx2AX4HnOnuW8LDFwB7AwcAfYCcX2vNbIKZNZlZ0+rVqzvy1LVjyNj856u9OenJJ2H//eH11+H+++Gyy6CLPiBq0S80sa0gkf817n6ku38ly+V+YFX4gd/6wf9etscws+2AB4GL3H1+xmO/64ENwG+BA/PEMc3d6929vp9mqOaWb22kam1Ocodrr4URI6BvX3jhBRg1Ku2oJEXqXyhMoV+n5gDjwuvjgPvbFzCz7sB9wO3ufne7c61JxQj6J14qMB75rDKWRTU2J61fD6efHixrMWpU0Mm8115pRyVFNnzKvLRDqGqFJoargBFmthQYEd7GzOrN7OawzFjgm8AZWYalzjSzJcASoC9wRYHxyPa7px1B6bz1Fnz963DnnTBlCtxzTzACSareqg835jynhfMKV9BaSe7+V+CILMebgO+H1+8A7shx/8MLeX7J4oiL4d6zcp9vnh3dF1EJfv/7YJe1LVvgwQfh6KPTjkhKJGq2sxbOK5xSa7WJ+tB/4JzSxFEs7nD11UEi6N8/WNpCSaGmXPPo63nPq3+hcEoMtWbTx5U7Oumjj2Ds2GBZixNPDBbB23PPtKOSElvxwSc5z1kJ46hmSgzVKN/GPVCZo5OWLg0207n3XrjmmqBfoVevtKOSEotqRrr2JK2qkwQlhmoUtW5SpY1OevBBOOAA+J//gUcfhXPPBdN3w1p0wb3NOc/16l6nZqSEKDHUqrmT0o4g2pYtcPnlcNxxsMceQX/CkUemHZWk6JNNuYdjr8+zoJ50jBJDtRp0aP7zC28rSRidtm4dHH88XHJJME/h2Wdh4MC0o5IURa2NtGvvniWKpPopMVSrcXPyn/cy/nb16qswfHjQhHT99TBjBvTUP32ty7c2EsB5R2liY1K053Otyrd0Rpruuw+++13Ydlt4/HE4NKLmIwIcsmcf9S8kqEw/HSQR+UYn+Zby6mdoaYGLLoIxY2CffWDhQiUF+UxUM9LMsw4uUSS1QYmhmh07NX9yaLqlPOY0vP9+0ME8ZQqMHw9PPw277ZZ2VFImGhetiGxGkmQpMVS7qKGrac+EXrIkGIr62GNw000wfTpss026MUlZyTdEFWDwjprPkjQlhlqX5kzo2bODSWvr1we1hB/8QPMTpI3GRSvyDlEFmDfpsNIEU0OUGGpBvi0/ARp/VJo4Wm3eDP/6r3DSSTB0aNCfcLDaiGVr5////LUFfY0oDiWGWpBvy0+ALZtL1xG9Zg2MHBksa/HjHwe7ru2yS2meWyrOhs35awunHTSgRJHUFiWGWjBkLHSLaIdturX4cSxaBPX18MwzcOutcOON0L178Z9XKtKIqU/lPd+tC1zRsF9pgqkxBSUGM+tjZvPMbGn4c4cc5VoyNumZk3F8kJktCO8/K9ztTYrhuOsiCnhx+xp+97tgU52WFvjv/4Yzzyzec0nFa1y0gqXvfZy3zDUnasG8Yim0xjAZeNzdBwOPh7ez+cTdh4aXzM14rwauDe//PhCxLKh02pCx0ctk5Nvgp7M2bYJ//udg0trw4UF/wgEHJP88UlWiRiJ17WKa0FZEhSaG0cCM8PoMgn2bYwn3eT4cuKcz95dOiFomA+DKBNtsV60KFr27/no45xyYNw923DG5x5eqFGck0i9P/GqJoqlNhSaGndz9XYDwZ67/+m3MrMnM5ptZ64f/F4AP3H1zeHs5oK8AxRY1QmnDumSe5/nnYf/94YUX4I474NproVu3ZB5bqto5sxZHllFtobgiE4OZPWZmL2W5jO7A8wxw93rgVOA6M9uT7CPNPE8cE8Lk0rR69eoOPLW0ETVCCeCG4YU9xy23wDe+ESSCP/wBTjutsMeTmnHa9Ociy5yukUhFF5kY3P1Id/9Klsv9wCoz2wUg/PlejsdYGf58E3gKGAasAXqbWetCfrsBK/PEMc3d6929vl+/fh14idJGnL6GNa91bvjqxo3wox/B978P3/xmsH/CUHUQSjyNi1bw7Bv5N5E6ZM8+GolUAoU2Jc0BxoXXxwH3ty9gZjuYWY/wel/gEOAVd3fgSeCEfPeXIojT19DR/RrefRe+9a1gWYvzz4dHHoEvfKFT4UltmhSjCUmL5ZVGoYnhKmCEmS0FRoS3MbN6M7s5LPNloMnMXiRIBFe5+yvhufOBSWa2jKDP4ZYC45G4ovaF9pb4w1f/8IegP+HFF2HWLLjqKqirKzxGqRkjpj5F/u5m2OnzGs1eKhZ8ca8s9fX13tTUlHYYle+G4UGzUT5jpgfNT7k88giMGgUDBkBjI3zlK8nGKFXvtOnPRTYhAfz5qn8sQTTVzcwWhv29eWnmcy2buAD67p2/TNTqq1//Opx1VjD6SElBOiFOUrjuJPVVlZISQ62buCD/+U0f5++I3m67YGmLHbJOehfJK2oDHoA60/DUUlNiELCI/oCmW+CXETULkQ66qHFJrA14fjVWtYVSU2IQ2P+M6DIfvQszRkWXE4kpTlLQXs7pUGKQYJe3qL4GgLeeLn4sUhOGXPJIZJnTDxqg4akpUWKQwMQF0UNYofBZ0VLzvnTBg/xtQ0veMv1799REthQpMcjfHTs1OjmseU1NStJpQy55hM0xRsifd9RexQ9GclJikLaOnRpd5q2n09snWipW46IVkTUFCCayqV8hXUoMsrU4TUqNP1ZykNgaF62ItWrqNnXGggtHlCAiyUeJQbZ27NTohfa2bIqe/CZCMCw1TlLYrkcdr005pgQRSRQlBskuzkJ7mz5WZ7Tk1bhoRaxhqQDNl40scjQSlxKD5BanSWnNa8nu+iZV5by7o2sKoCUvyo0Sg+QWZ5QSBLu+qeYg7Qy55BEidugENImtHCkxSH7HTg1WWI2y5jX4+Y7qkBYgSApxRiAN3rGXJrGVISUGiTZkbLyaQ8sGuPcs1R5q3IipT8VOCvMmHVb8gKTDCkoMZtbHzOaZ2dLw51ZLbJrZt8xsccblUzNrCM/dZmZvZZxTQ2O5irtsBgS1ByWHmjTkkkdY+t7HkeUO2bOPkkIZK7TGMBl43N0HA4+Ht9tw9yfdfai7DwUOB9YDv88ocl7reXeP11Ml6Zi4AHpsH69sZ/eNloq194UPxaopHLJnHzUflblCE8NoYEZ4fQbQEFH+BOBhd19f4PNKWi54O37NoekWLZ9RAy5qXMLAyQ/yaUv0Whfb9ahTUqgAhSaGndz9XYDw544R5U8G7mx3bIqZNZvZtWbWo8B4pBQmLoieANfqrae1l0MVO236c7HnKWzXo05zFSpEZGIws8fM7KUsl9EdeSIz2wXYD3g04/AFwN7AAUAf4Pw8959gZk1m1rR69eqOPLUUw7g58Lld4pX96F24tLdGLFWZF+b8hqvfOZ03e5zKM91/wqguz+QsO3jHXkoKFcTcYyx1mOvOZq8Dh7n7u+EH/1PunnVZRDP7Z2Bfd5+Q4/xhwLnufmzU89bX13tTU1On45YEzRjVsX0axkwPRjlJZZs7iS1Nt7T5ZrneuzN50/eZs+Uf2hRVTaF8mNlCd6+PKldoU9IcYFx4fRxwf56yp9CuGSlMJpiZEfRPvFRgPFJq4+bEG8ra6t6zVHOoZM2zYcqu0C4pAGxrG/nXrm1/t9vUmZJCBSo0MVwFjDCzpcCI8DZmVm9mN7cWMrOBwO5A+6+WM81sCbAE6AtcUWA8koa4M6Rb3fcDJYdK1Dwb7j87WCMrh13tr59dH7xjLy2KV6EKakpKi5qSytilvYGYf1M9+8DRV6tpqdzNnQRNtxLn97p8S1/+YeP1nH7QAO3AVoZK1ZQk0taYafHLfrI2aFrSfIfydcPwYNhxjKSwxeHGLqdy3UlDlRQqXNe0A5Aq0/rtv/FHsGVzvPs03QIv3gXHXafaQzn55d7BiLKYuhwwniuP/XkRA5JSUY1BkjdkLFz81/gT4SBot1btIX2tncuXbt+hpED9+HjbwkpFUGKQ4unIRLhWTbfAL3ZV53QaZowKknOezuWt9OwTDEFWUqgqSgxSXOPmBB8cPfup5A3VAAAH60lEQVTEv8/GsPYwRQmiZDo6H6VLXfB7Pf8tNf9VIY1KktJpnh3sE92Rb6QA3Xqp/6EYmmfDw+cHgwA6oktXaPgP/T4qUNxRSUoMUnpzJ4UjXTqh795BE5V0XmcTNATLoJz7WvIxSUlouKqUr47s7dDemte07lJnzZ0UvHcd7UdoNehQJYUaoeGqko6JCzrerv0Zh8YfB1fVnBGteTbc90Pw6L0SslItreaoKUnS19mmjZ59oHsvWLcctt8NjrhYiSJTB2Ys5zTo0GAAgVQF9TFI5Smk7yFTLX+YJfUeUgdjblKirTJxE4OakqR8HDsVBhwULNTWsrHzj/PW08EErVqadJVYQqC2E6sAqjFIuZo7CRbe1vl28WyqKVEk0UyUqZreG8lJTUlSPdqPt+/Zp+Nj79ur6w6jb6ycppLm2fD45bDunWQfVyvc1hQlBqluHVneO5IFq8KWy4djZyeexWZQ/z3VEGqQ+hikutV/L7k2dTwY259tZJR1gf3PLM6HaPNsaDwbthTQn9IRXbpDQwXVkiQ1BSUGMzsRuBT4MnCgu2f9Gm9mI4H/B9QBN7t7605vg4C7gD7AH4F/cvcS/ZdIRWv9oE4sOZB9uKxvCZ4j9vMYdOmW+8PeuoB1LV0yADTCSDqq0JnPLwFjgP/KVcDM6oAbgaOBfYBTzGyf8PTVwLXuPhh4H+jA/pBS846dCpeuCy6dnUmdOM//oe9bSpcUBh0avj9rlRSkQwqqMbj7qwBmlq/YgcAyd38zLHsXMNrMXgUOB04Ny80gqH38RyExSY3KnJlbyFpAlU6zlCUBpehj6A9kDqVYDgwHvgB84O6bM473z/UgZjYBmAAwYMCA4kQq1WHI2L9/Q26eDfdPhJYN6cZULBpVJEUQmRjM7DFg5yynLnT3+2M8R7bqhOc5npW7TwOmQTAqKcbzirRNEpB7fSarS3bORLFYHex/hkYUSVFFJgZ3P7LA51gO7J5xezdgJbAG6G1mXcNaQ+txkeLJNaO36ENEO8i6BP0R2++uNaCk5ErRlPQCMDgcgbQCOBk41d3dzJ4ETiAYmTQOiFMDEUle+5pF82yYe06wm1yHdHBUkhKAlKGCJriZ2fHAvwP9gA+Axe5+lJntSjAs9Ziw3DHAdQTDVW919ynh8T34+3DVRcDp7h7ZGKwJbiIiHaeZzyIi0oZ2cBMRkU5RYhARkTaUGEREpA0lBhERaUOJQURE2lBiEBGRNpQYRESkjYqcx2Bmq4G/FOGh+xIs1VHJKv01VHr8UPmvQfGnr1iv4Yvu3i+qUEUmhmIxs6Y4kz/KWaW/hkqPHyr/NSj+9KX9GtSUJCIibSgxiIhIG0oMbU1LO4AEVPprqPT4ofJfg+JPX6qvQX0MIiLShmoMIiLSRk0nBjM70cxeNrMtZpZzBICZ/dnMlpjZYjMrq/W+O/AaRprZ62a2zMwmlzLGfMysj5nNM7Ol4c8dcpRrCd//xWaWYxu20ol6P82sh5nNCs8vMLOBpY8yvxiv4QwzW53xvn8/jThzMbNbzew9M3spx3kzs+vD19dsZl8rdYz5xIj/MDNbl/H+X1yy4Ny9Zi/Al4G9gKeA+jzl/gz0TTvezr4Ggg2S3gD2ALoDLwL7pB17GNu/AZPD65OBq3OU+yjtWDvyfgI/Bm4Kr58MzEo77k68hjOAG9KONc9r+CbwNeClHOePAR4m2F/+IGBB2jF3MP7DgLlpxFbTNQZ3f9XdX087jkLEfA0HAsvc/U1330iwa97o4kcXy2hgRnh9BtCQYixxxXk/M1/XPcARZmYljDFKOf9NxOLu/wXk26R7NHC7B+YT7DG/S2miixYj/tTUdGLoAAd+b2YLzWxC2sF0Qn/gnYzby8Nj5WAnd38XIPy5Y45y25hZk5nNN7O0k0ec9/OzMu6+GVgHfKEk0cUT92/iO2EzzD1mtntpQktMOf/dx3Wwmb1oZg+b2b6letKupXqitJjZY8DOWU5d6O73x3yYQ9x9pZntCMwzs9fCbF8SCbyGbN9USzYcLV/8HXiYAeHvYA/gCTNb4u5vJBNhh8V5P1N9z2OIE98DwJ3uvsHMfkhQAzq86JElp9x/B1H+SLCExUdmdgzQCAwuxRNXfWJw9yMTeIyV4c/3zOw+gmp4yRJDAq9hOZD5bW83YGWBjxlbvvjNbJWZ7eLu74bV/PdyPEbr7+BNM3sKGEbQRp6GOO9na5nlZtYV2J7yajaIfA3u/teMm9OBq0sQV5JS/bsvlLv/LeP6Q2b2azPr6+5FXwdKTUkRzKyXmX2+9TrwbSDrKIIy9gIw2MwGmVl3gs7Q1Ef2hOYA48Lr44CtakBmtoOZ9Qiv9wUOAV4pWYRbi/N+Zr6uE4AnPOxRLBORr6Fde/wo4NUSxpeEOcB3w9FJBwHrWpstK4GZ7dzaL2VmBxJ8Xv81/70SknbPfJoX4HiCbxUbgFXAo+HxXYGHwut7EIzYeBF4maD5JvXYO/IawtvHAH8i+JZdNq+BoN39cWBp+LNPeLweuDm8/nVgSfg7WAKML4O4t3o/gcuBUeH1bYC7gWXA88AeacfciddwZfg3/yLwJLB32jG3i/9O4F1gU/g/MB74IfDD8LwBN4avbwl5Rh6WafwTM97/+cDXSxWbZj6LiEgbakoSEZE2lBhERKQNJQYREWlDiUFERNpQYhARkTaUGEREpA0lBhERaUOJQURE2vhfe2CKNy8mN9YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(train[H==0, 0], train[H==0, 1])\n",
    "plt.scatter(train[H==1, 0], train[H==1, 1])\n",
    "plt.plot([0, v[0]], [0, v[1]], c='r')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hashing(q, V):\n",
    "    H = np.array([q.dot(v.T) for v in V])\n",
    "    H[H >= 0] = 1\n",
    "    H[H < 0] = 0\n",
    "    H = H.astype(np.int8)\n",
    "    return H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hash Tables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "g(v) = (h_1(v), ..., h_k(v)) \\\\\n",
    "G = g_1, g_2, ..., g_L\n",
    "$$\n",
    "\n",
    "**bit-wise hash**\n",
    "\n",
    "$$\n",
    "h_r(v) = \n",
    "\\begin{cases}\n",
    "0, & \\text{if }r\\cdot v \\le 0 \\\\\n",
    "1, & \\text{otherwise}\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 474,
   "metadata": {},
   "outputs": [],
   "source": [
    "def construct_hash_tables(P, k, L, random_state=None):\n",
    "    \n",
    "    if random_state is None:\n",
    "        rand = np.random.RandomState()\n",
    "    else:\n",
    "        rand = np.random.RandomState(random_state)\n",
    "    \n",
    "    n, d = P.shape\n",
    "    \n",
    "    V = np.array([rand.normal(0, 1, (k, d)) for i in range(L)])\n",
    "    \n",
    "    hash_tables = []\n",
    "    \n",
    "    for i in range(L):\n",
    "        # hashing\n",
    "        H = P.dot(V[i].T)\n",
    "        H[H >= 0] = 1\n",
    "        H[H < 0] = 0\n",
    "        H = H.astype(np.int8)\n",
    "        \n",
    "        # get unique key\n",
    "        keys = np.unique(H, axis=0)\n",
    "\n",
    "        # buckets\n",
    "        buckets = dict()\n",
    "        \n",
    "        for key in keys:\n",
    "            buckets[str(key)] = []\n",
    "            \n",
    "        for j, h in enumerate(H):\n",
    "            buckets[str(h)].append(j)\n",
    "\n",
    "        hash_tables.append(buckets)\n",
    "    \n",
    "    return hash_tables, V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 475,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 400 ms, sys: 3.32 ms, total: 404 ms\n",
      "Wall time: 402 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "k = 7\n",
    "L = 10\n",
    "random_state = 1\n",
    "\n",
    "hash_tables, V = construct_hash_tables(train, k, L, random_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# str_list -> array\n",
    "# np.array(list(map(str_to_list, list(hash_tables[0].keys()))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Counts Vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### normal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "metadata": {},
   "outputs": [],
   "source": [
    "def construct_count_tables(hash_tables):\n",
    "    \n",
    "    count_tables = []\n",
    "    \n",
    "    for hash_table in hash_tables: # L hash table\n",
    "        count_table = dict()\n",
    "        \n",
    "        str_keys = list(hash_table.keys()) # keys of hash table is string eg. '[0 0 0]'\n",
    "        arr_keys = np.array(list(map(str_to_list, str_keys))) # string to array \n",
    "                                                              # eg. '[0 0 0]' -> [0, 0, 0]\n",
    "        \n",
    "        for key in str_keys:\n",
    "            count_table[key] = dict() # indexing\n",
    "        \n",
    "        for i, str_key in enumerate(str_keys):\n",
    "            arr_key = arr_keys[i] # array  eg. [0, 0, 0]\n",
    "            \n",
    "            # self count\n",
    "            count_table[str_key][0] = [(str_key, len(hash_table[str_key]))]\n",
    "            \n",
    "            for j in range(i + 1, len(str_keys)): # hamming distance starts from 1 \n",
    "                arr_candidate_key = arr_keys[j]\n",
    "                str_candidate_key = str_keys[j]\n",
    "                \n",
    "                dis = np.sum(np.abs(arr_key - arr_candidate_key))\n",
    "                \n",
    "                if dis not in count_table[str_key]:\n",
    "                    count_table[str_key][dis] = [(str_candidate_key, \n",
    "                                                  len(hash_table[str_candidate_key]))] \n",
    "                                                # (hashing, number)\n",
    "                else:\n",
    "                    count_table[str_key][dis].append((str_candidate_key, \n",
    "                                                      len(hash_table[str_candidate_key])))\n",
    "                    \n",
    "                if dis not in count_table[str_candidate_key]:\n",
    "                    count_table[str_candidate_key][dis] = [(str_key, len(hash_table[str_key]))]\n",
    "                else:\n",
    "                    count_table[str_candidate_key][dis].append((str_key, len(hash_table[str_key])))\n",
    "        \n",
    "        count_tables.append(count_table)\n",
    "        \n",
    "    return count_tables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 433,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 11.1 ms, sys: 3.3 ms, total: 14.4 ms\n",
      "Wall time: 27.6 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "count_tables = construct_count_tables(hash_tables)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 434,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 0 0]\n",
      "{0: [('[0 0 0 0 0 0 0]', 178)], 1: [('[0 0 0 0 0 0 1]', 41), ('[1 0 0 0 0 0 0]', 8)], 2: [('[0 1 0 0 0 0 1]', 113), ('[1 0 0 1 0 0 0]', 32)], 3: [('[0 1 1 0 0 0 1]', 39), ('[1 0 0 1 1 0 0]', 37)], 4: [('[0 1 1 0 0 1 1]', 46), ('[1 0 0 1 1 1 0]', 30)], 5: [('[0 1 1 0 1 1 1]', 29), ('[1 0 1 1 1 1 0]', 119)], 6: [('[0 1 1 1 1 1 1]', 5), ('[1 1 1 1 1 1 0]', 51)], 7: [('[1 1 1 1 1 1 1]', 172)]}\n"
     ]
    }
   ],
   "source": [
    "for key, value in count_tables[0].items():\n",
    "    print(key)\n",
    "    print(value)\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### aggregate-counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [],
   "source": [
    "def aggregate_counts(hash_tables, k):\n",
    "    count_tables = []\n",
    "    \n",
    "    N = dict()\n",
    "    combinations = build_k_combinations(k)\n",
    "    for key in combinations:\n",
    "        N[str(key)] = []\n",
    "        n_keys = combinations[np.sum(np.abs(combinations - key), axis=1) == 1]\n",
    "        for n_key in n_keys:\n",
    "            N[str(key)].append(str(n_key))\n",
    "        \n",
    "    for hash_table in hash_tables:\n",
    "        \n",
    "        count_table = dict()\n",
    "\n",
    "        for key in combinations:\n",
    "            count_table[str(key)] = dict()\n",
    "\n",
    "        for r in range(k + 1):\n",
    "            for key in combinations:\n",
    "                str_key = str(key)\n",
    "                if r == 0:\n",
    "                    if str_key in hash_table:\n",
    "                        count_table[str_key][r] = len(hash_table[str_key])\n",
    "                    else:\n",
    "                        count_table[str_key][r] = 0\n",
    "            \n",
    "                else:\n",
    "                    for n_key in N[str_key]:\n",
    "                        if r not in count_table[str_key]:\n",
    "                            count_table[str_key][r] = count_table[n_key][r - 1]\n",
    "                        else:\n",
    "                            count_table[str_key][r] += count_table[n_key][r - 1]\n",
    "                    \n",
    "                    if r != 1:\n",
    "                        count_table[str_key][r] -= ((k - r + 2) * count_table[str_key][r - 2])\n",
    "                        count_table[str_key][r] /= r\n",
    "        \n",
    "        str_keys = list(hash_table.keys())\n",
    "        temp = dict()\n",
    "        for key in str_keys:\n",
    "            temp[key] = count_table[key]\n",
    "        \n",
    "        count_tables.append(temp)\n",
    "    \n",
    "    return count_tables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### normal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "metadata": {},
   "outputs": [],
   "source": [
    "def construct_sample_table(H, hash_tables, count_tables, I, n_samples):\n",
    "    sample_table = dict()   \n",
    "\n",
    "    candidates = []\n",
    "    count = 0\n",
    "    \n",
    "    for l, h in enumerate(H):\n",
    "        if str(h) in count_tables[l]: # hash code in tables\n",
    "            for i in I:\n",
    "                if i in count_tables[l][str(h)]:\n",
    "                    for key, number in count_tables[l][str(h)][i]:\n",
    "                        candidates.append(hash_tables[l][key])\n",
    "                        count += number\n",
    "    \n",
    "    count /= len(hash_tables)\n",
    "    candidates = np.concatenate(np.array(candidates))\n",
    "    \n",
    "#     idx_samples = np.random.choice(candidates, size=n_samples, replace=False)\n",
    "    samples = np.random.choice(candidates, size=n_samples, replace=True)\n",
    "    \n",
    "    sample_table['count'] = count\n",
    "    sample_table['candidates'] = candidates\n",
    "    sample_table['samples'] = samples\n",
    "    sample_table['n_samples'] = n_samples\n",
    "    sample_table['I'] = I\n",
    "    \n",
    "    return sample_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = test[0]\n",
    "H = hashing(q, V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 463,
   "metadata": {},
   "outputs": [],
   "source": [
    "I = [0, 1]\n",
    "n_samples = 200\n",
    "\n",
    "sample_table = construct_sample_table(H, hash_tables, count_tables, I, n_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 464,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'count': 208.3,\n",
       " 'candidates': array([ 30,  33,  35, ..., 889, 891, 895]),\n",
       " 'samples': array([457, 602, 353, 268, 231, 545, 607, 457, 423, 502, 575, 513,   1,\n",
       "        720, 746, 448, 230, 418, 834,  47, 472, 229, 142, 134,   9, 641,\n",
       "        359, 747, 466, 116, 453, 497,  47, 233,  51,  70, 528, 240, 899,\n",
       "        784, 522, 719, 211, 392, 484, 665, 449,  82, 876, 403, 201, 325,\n",
       "        517, 692, 280, 812, 373, 387, 569,  97, 261, 734, 395, 784, 197,\n",
       "        375, 607, 621, 493, 713, 406,  74, 474, 542, 538, 513, 761, 375,\n",
       "         69,  68,  30, 474, 150, 300, 625, 658, 108, 168, 538, 192, 814,\n",
       "        847, 471,  78, 247, 395, 208, 192, 513, 221, 805, 476, 230, 545,\n",
       "        286, 831, 598, 794, 293,  78, 769, 450, 412, 471, 768, 693, 118,\n",
       "         88, 784, 835, 545, 118, 397, 871, 449, 714, 128, 538, 533, 345,\n",
       "        630, 774, 812, 387, 661, 659,  93,  26,  93,  52, 211, 734, 784,\n",
       "         54, 395,  12, 208, 661, 693, 720,  47,  72, 510, 794, 470, 590,\n",
       "        362,  89, 550,  88,   9, 535, 300, 507, 757, 496, 575, 802, 462,\n",
       "        429, 567, 164, 863, 403, 410, 244,   2, 151, 134, 802,  22, 598,\n",
       "        151,  93, 579, 294, 145, 598, 439,  33, 107, 827, 484, 687, 344,\n",
       "        158, 156, 566, 472, 300]),\n",
       " 'n_samples': 200,\n",
       " 'I': [0, 1]}"
      ]
     },
     "execution_count": 464,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### hamming-distance-sampler (ERROR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [],
   "source": [
    "a = np.array([0, 0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [],
   "source": [
    "mask = np.array([1, 0, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [],
   "source": [
    "mask ^ a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [],
   "source": [
    "def counts_matrix(count_tables, k):\n",
    "    Ms = []\n",
    "    for count_table in count_tables:\n",
    "        M = dict()\n",
    "        for key, items in count_table.items():\n",
    "            M[key] = np.zeros((k + 1, k + 1))\n",
    "            M[key][0][k] = items[0][0][1]\n",
    "            \n",
    "            arr_key = str_to_list(key)\n",
    "            \n",
    "            for hamming_distance, keys_counts in items.items():\n",
    "                if hamming_distance == 0:\n",
    "                    continue\n",
    "                for key_count in keys_counts:\n",
    "                    arr_candidate_key = str_to_list(key_count[0])\n",
    "                    a = np.argwhere(arr_key != arr_candidate_key)[0][0]\n",
    "                    M[key][hamming_distance][a] += key_count[1]\n",
    "            \n",
    "        Ms.append(M)\n",
    "    \n",
    "    return Ms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [],
   "source": [
    "M = counts_matrix(count_tables, k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [],
   "source": [
    "def hamming_distance_sampler(H, hash_tables, k, i, M):\n",
    "    mask = np.zeros(k).astype(np.int8)\n",
    "    g = 0\n",
    "    for j, hash_table in enumerate(hash_tables):\n",
    "        h = H[j]\n",
    "        for r in range(k):\n",
    "            if g < i:\n",
    "                h1 = h ^ mask\n",
    "                h2 = h1 ^ np.append(np.append(np.repeat(0, r), 1), np.repeat(0, k-r-1))\n",
    "                str_h1 = str(h1)\n",
    "                str_h2 = str(h2)\n",
    "                \n",
    "                if str_h2 in M[j]:\n",
    "                    if str_h1 in M[j]:\n",
    "                        pr = M[j][str_h2][i - g - 1, r + 1] / (M[j][str_h2][i - g - 1, r + 1] + \n",
    "                                                               M[j][str_h1][i - g, r + 1])\n",
    "                    else:\n",
    "                        pr = 1\n",
    "                else:\n",
    "                    continue\n",
    "                \n",
    "                f = np.random.choice([1, 0], p=[pr, 1 - pr])\n",
    "                if f == 1:\n",
    "                    g += 1\n",
    "                    mask = mask ^ np.append(np.append(np.repeat(0, r), 1), np.repeat(0, k-r-1))\n",
    "        \n",
    "        print(h ^ mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [],
   "source": [
    "q = test[0]\n",
    "H = hashing(q, V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "outputs": [],
   "source": [
    "hamming_distance_sampler(H, hash_tables, k, 1, M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Z = \n",
    "\\begin{cases}\n",
    "\\frac{\\sum_{l=1}^{L}C_q^l(\\cal{I})}{L\\cdot p(x)} &, \\text{if } \\theta_{qx} \\in \\cal{A} \\\\\n",
    "0 &, \\text{otherwise}\n",
    "\\end{cases} \\\\\n",
    "\\text{where }p(x) = \\Bbb{P}(d_{qx}\\in \\cal{I} |\\theta_{qx}) \\ \n",
    "= \\sum_{i \\in I}\\Bbb{P}(d_qx = i|\\theta_{qx}) \\\\\n",
    "$$\n",
    "$$\n",
    "\\text{Estimator} = \\frac{\\sum_{i=1}^S Z_i}{S}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 449,
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate(P, q, k, A, sample_table):\n",
    "    Z = 0\n",
    "    for idx in sample_table['samples']:\n",
    "        theta_qx = angle_between(q, P[idx])\n",
    "        if theta_qx <= A:\n",
    "            px = 0\n",
    "            for i in sample_table['I']:\n",
    "                px += comb(k, i) * (( 1 - theta_qx / np.pi) ** (k - i)) * ((theta_qx / np.pi) ** i)\n",
    "            Z += (sample_table['count'] / px)\n",
    "\n",
    "    return Z / sample_table['n_samples']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 476,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 428 ms, sys: 6.66 ms, total: 434 ms\n",
      "Wall time: 422 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "k = 7\n",
    "L = 10\n",
    "A = np.pi / 4\n",
    "random_state = 1\n",
    "\n",
    "hash_tables, V = construct_hash_tables(train, k, L, random_state)\n",
    "count_tables = construct_count_tables(hash_tables)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 478,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.79 s, sys: 93.2 ms, total: 1.89 s\n",
      "Wall time: 1.81 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "real_density = []\n",
    "for q in test:\n",
    "    real_density.append(sum(np.array([angle_between(q, p) for p in train]) <= (A)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 481,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.11 s, sys: 6.62 ms, total: 1.12 s\n",
      "Wall time: 1.12 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "n_samples = 200\n",
    "\n",
    "I = [0, 1, 2]\n",
    "\n",
    "estimate_density = []\n",
    "\n",
    "for q in test:\n",
    "    H = hashing(q, V)\n",
    "    sample_table = construct_sample_table(H, hash_tables, count_tables, I, n_samples)\n",
    "    estimate_density.append(estimate(train, q, k, A, sample_table))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 482,
   "metadata": {},
   "outputs": [],
   "source": [
    "estimate_density = np.array(estimate_density).astype(np.int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 483,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0568522652854725"
      ]
     },
     "execution_count": 483,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.abs(estimate_density - real_density) / real_density).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## W"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "W = {1 \\over L}\\sum_{l=1}^L\\sum_{x\\in\\cal A_q} \\\n",
    "\\frac{\\Bbb1(x\\in \\cal B^l_q(\\cal I))}{p(x)} \\\\\n",
    "\\text{where }p(x) = \\Bbb P(d_{qx}\\in \\cal I |\\theta_{qx}) \\ \n",
    "= \\sum_{i \\in I}\\Bbb P(d_qx = i|\\theta_{qx})\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{align}\n",
    "E(W) &= {1\\over L}\\sum_{l=1}^L\\sum_{x\\in \\cal A_q} \\\n",
    "\\frac{E(\\Bbb1(x\\in\\cal B^l_q(\\cal I)))}{p(x)} \\\\\n",
    "&= |\\cal A_q|\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 495,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_W(P, q, k, A, sample_table):\n",
    "    W = 0\n",
    "    for idx in sample_table['candidates']:\n",
    "        theta_qx = angle_between(q, P[idx])\n",
    "        if theta_qx <= A:\n",
    "            px = 0\n",
    "            for i in sample_table['I']:\n",
    "                px += comb(k, i) * (( 1 - theta_qx / np.pi) ** (k - i)) * ((theta_qx / np.pi) ** i)\n",
    "            W += (1 / px)\n",
    "    return W / L\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 498,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 12.9 s, sys: 93.4 ms, total: 13 s\n",
      "Wall time: 12.9 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "I = [0, 1, 2]\n",
    "estimate_W = []\n",
    "for q in test:\n",
    "    H = hashing(q, V)\n",
    "    sample_table = construct_sample_table(H, hash_tables, count_tables, I, n_samples)\n",
    "    estimate_W.append(calculate_W(train, q, k, A, sample_table))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 499,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03734922534322747"
      ]
     },
     "execution_count": 499,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimate_W = np.array(estimate_W).astype(np.int)\n",
    "(np.abs(estimate_W - real_density) / real_density).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 536,
   "metadata": {
    "code_folding": [
     25,
     67
    ]
   },
   "outputs": [],
   "source": [
    "class LSHEstimateDensity(object):\n",
    "    \"\"\"\n",
    "    Given a dataset P and a query q, \n",
    "    Estimate the number of points within a specified angular distance.\n",
    "    \"\"\"\n",
    "    def __init__(self, P, k, L, random_state=None):\n",
    "        \"\"\"\n",
    "        Desc:\n",
    "            init function\n",
    "        Param:\n",
    "            P: set of vectors\n",
    "            k: length of hash code\n",
    "            L: number of hash tables\n",
    "            random_state\n",
    "        \"\"\"\n",
    "        self._P = P\n",
    "        self._k = k\n",
    "        self._L = L\n",
    "        self._n, self._d = P.shape\n",
    "        \n",
    "        if random_state is not None:\n",
    "            self._rand = np.random.RandomState(random_state)\n",
    "        else:\n",
    "            self._rand = np.random.RandomState(random_state)\n",
    "        \n",
    "    def _hashing(self, q, V):\n",
    "        H = np.array([q.dot(v.T) for v in V])\n",
    "        H[H >= 0] = 1\n",
    "        H[H < 0] = 0\n",
    "        H = H.astype(np.int8)\n",
    "        return H\n",
    "    \n",
    "    def _construct_hash_tables(self):\n",
    "        rand = self._rand\n",
    "        k = self._k\n",
    "        L = self._L\n",
    "        n = self._n\n",
    "        d = self._d\n",
    "        P = self._P\n",
    "\n",
    "        V = np.array([rand.normal(0, 1, (k, d)) for i in range(L)])\n",
    "\n",
    "        hash_tables = []\n",
    "\n",
    "        for i in range(L):\n",
    "            # hashing\n",
    "            H = P.dot(V[i].T)\n",
    "            H[H >= 0] = 1\n",
    "            H[H < 0] = 0\n",
    "            H = H.astype(np.int8)\n",
    "\n",
    "            # get unique key\n",
    "            keys = np.unique(H, axis=0)\n",
    "\n",
    "            # buckets\n",
    "            buckets = dict()\n",
    "\n",
    "            for key in keys:\n",
    "                buckets[str(key)] = []\n",
    "\n",
    "            for j, h in enumerate(H):\n",
    "                buckets[str(h)].append(j)\n",
    "\n",
    "            hash_tables.append(buckets)\n",
    "\n",
    "        return hash_tables, V\n",
    "\n",
    "    def _construct_count_tables(self, hash_tables):\n",
    "        \n",
    "        count_tables = []\n",
    "\n",
    "        for hash_table in hash_tables: # L hash table\n",
    "            count_table = dict()\n",
    "\n",
    "            str_keys = list(hash_table.keys()) # keys of hash table is string eg. '[0 0 0]'\n",
    "            arr_keys = np.array(list(map(str_to_list, str_keys))) # string to array \n",
    "                                                                  # eg. '[0 0 0]' -> [0, 0, 0]\n",
    "\n",
    "            for key in str_keys:\n",
    "                count_table[key] = dict() # indexing\n",
    "\n",
    "            for i, str_key in enumerate(str_keys):\n",
    "                arr_key = arr_keys[i] # array  eg. [0, 0, 0]\n",
    "\n",
    "                # self count\n",
    "                count_table[str_key][0] = [(str_key, len(hash_table[str_key]))]\n",
    "\n",
    "                for j in range(i + 1, len(str_keys)): # hamming distance starts from 1 \n",
    "                    arr_candidate_key = arr_keys[j]\n",
    "                    str_candidate_key = str_keys[j]\n",
    "\n",
    "                    dis = np.sum(np.abs(arr_key - arr_candidate_key))\n",
    "\n",
    "                    if dis not in count_table[str_key]:\n",
    "                        count_table[str_key][dis] = [(str_candidate_key, \n",
    "                                                      len(hash_table[str_candidate_key]))] \n",
    "                                                    # (hashing, number)\n",
    "                    else:\n",
    "                        count_table[str_key][dis].append((str_candidate_key, \n",
    "                                                          len(hash_table[str_candidate_key])))\n",
    "\n",
    "                    if dis not in count_table[str_candidate_key]:\n",
    "                        count_table[str_candidate_key][dis] = [(str_key, len(hash_table[str_key]))]\n",
    "                    else:\n",
    "                        count_table[str_candidate_key][dis].append((str_key, len(hash_table[str_key])))\n",
    "\n",
    "            count_tables.append(count_table)\n",
    "\n",
    "        return count_tables\n",
    "    \n",
    "    def preprocessing(self):\n",
    "        self.hash_tables, self.V = self._construct_hash_tables()\n",
    "        self.count_tables = self._construct_count_tables(self.hash_tables)\n",
    "    \n",
    "    def _construct_sample_table(self, H, hash_tables, count_tables, I, n_samples=1):\n",
    "        rand = self._rand\n",
    "        \n",
    "        sample_table = dict()   \n",
    "\n",
    "        candidates = []\n",
    "        count = 0\n",
    "\n",
    "        for l, h in enumerate(H):\n",
    "            if str(h) in count_tables[l]: # hash code in tables\n",
    "                for i in I:\n",
    "                    if i in count_tables[l][str(h)]:\n",
    "                        for key, number in count_tables[l][str(h)][i]:\n",
    "                            candidates.append(hash_tables[l][key])\n",
    "                            count += number\n",
    "\n",
    "        count /= len(hash_tables)\n",
    "        candidates = np.concatenate(np.array(candidates))\n",
    "\n",
    "    #     idx_samples = np.random.choice(candidates, size=n_samples, replace=False)\n",
    "        samples = rand.choice(candidates, size=n_samples, replace=True)\n",
    "\n",
    "        sample_table['count'] = count\n",
    "        sample_table['candidates'] = candidates\n",
    "        sample_table['samples'] = samples\n",
    "        sample_table['n_samples'] = n_samples\n",
    "        sample_table['I'] = I\n",
    "\n",
    "        return sample_table\n",
    "    \n",
    "    def estimate(self, q, A, I=[0], n_samples=100):\n",
    "        \"\"\"\n",
    "        Desc:\n",
    "            given a query q, \n",
    "            estimate the number of points within Angular distance A of q.\n",
    "        \n",
    "        Param:\n",
    "            q: query\n",
    "            I: set of hamming distance\n",
    "               default: [0]\n",
    "            A: angular distance\n",
    "               default: np.pi / 3\n",
    "            n_samples: number of samples.\n",
    "               default: 100\n",
    "        \n",
    "        Return:\n",
    "            the number of points within Angular distance A of q \n",
    "        \"\"\"\n",
    "        P = self._P\n",
    "        k = self._k\n",
    "        \n",
    "        H = hashing(q, self.V)\n",
    "        \n",
    "        sample_table = self._construct_sample_table(H, self.hash_tables, self.count_tables, I, n_samples)\n",
    "        \n",
    "        Z = 0\n",
    "        for idx in sample_table['samples']:\n",
    "            theta_qx = angle_between(q, P[idx])\n",
    "            if theta_qx <= A:\n",
    "                px = 0\n",
    "                for i in sample_table['I']:\n",
    "                    px += comb(k, i) * (( 1 - theta_qx / np.pi) ** (k - i)) * ((theta_qx / np.pi) ** i)\n",
    "                Z += (sample_table['count'] / px)\n",
    "\n",
    "        return Z / sample_table['n_samples']\n",
    "    \n",
    "    def calculate_W(self, q, A, I):\n",
    "        W = 0\n",
    "        k = self._k\n",
    "        P = self._P\n",
    "        L = self._L\n",
    "        \n",
    "        H = hashing(q, self.V)\n",
    "        sample_table = self._construct_sample_table(H, self.hash_tables, self.count_tables, I)\n",
    "        \n",
    "        for idx in sample_table['candidates']:\n",
    "            theta_qx = angle_between(q, P[idx])\n",
    "            if theta_qx <= A:\n",
    "                px = 0\n",
    "                for i in sample_table['I']:\n",
    "                    px += comb(k, i) * (( 1 - theta_qx / np.pi) ** (k - i)) * ((theta_qx / np.pi) ** i)\n",
    "                W += (1 / px)\n",
    "                \n",
    "        return W / L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### test points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 503,
   "metadata": {},
   "outputs": [],
   "source": [
    "train, test = train_test_split(norm_P, test_size=100, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 504,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.79 s, sys: 63.3 ms, total: 1.86 s\n",
      "Wall time: 1.77 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "A = np.pi / 4\n",
    "real_density = []\n",
    "for q in test:\n",
    "    real_density.append(sum(np.array([angle_between(q, p) for p in train]) <= (A)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 537,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 20 µs, sys: 0 ns, total: 20 µs\n",
      "Wall time: 23.4 µs\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "k = 7\n",
    "L = 10\n",
    "random_state = 1\n",
    "\n",
    "estimator = LSHEstimateDensity(train, k, L, random_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 538,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 459 ms, sys: 1 µs, total: 459 ms\n",
      "Wall time: 455 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "estimator.preprocessing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 542,
   "metadata": {},
   "outputs": [],
   "source": [
    "I = [0, 1]\n",
    "n_samples = 100\n",
    "estimate_density = []\n",
    "\n",
    "for q in test:\n",
    "    estimate_density.append(\n",
    "        estimator.estimate(q, A, I, n_samples)\n",
    "#         estimator.calculate_W(q, A, I)\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 544,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07689337668190699"
      ]
     },
     "execution_count": 544,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.abs((np.round(np.array(estimate_density)) - real_density)) / real_density).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### test SIFT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys(['title', 'train', 'test', 'K', 'n_train', 'n_test', 'k_near_neighbors', 'nearest_neighbor'])\n"
     ]
    }
   ],
   "source": [
    "%store -r Datasets\n",
    "data = Datasets['SIFT-10K']\n",
    "train = data['train']\n",
    "test = data['test']\n",
    "n_train = data['n_train']\n",
    "n_test = data['n_test']\n",
    "print(data.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 504,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.79 s, sys: 63.3 ms, total: 1.86 s\n",
      "Wall time: 1.77 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "A = np.pi / 4\n",
    "real_density = []\n",
    "for q in test:\n",
    "    real_density.append(sum(np.array([angle_between(q, p) for p in train]) <= (A)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 537,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 20 µs, sys: 0 ns, total: 20 µs\n",
      "Wall time: 23.4 µs\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "k = int(np.round(np.log(train.shape[0]))\n",
    "L = 20\n",
    "random_state = 1\n",
    "print(A, k, L)\n",
    "\n",
    "estimator = LSHEstimateDensity(train, k, L, random_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 538,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 459 ms, sys: 1 µs, total: 459 ms\n",
      "Wall time: 455 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "estimator.preprocessing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 542,
   "metadata": {},
   "outputs": [],
   "source": [
    "I = [0, 1, 2, 3]\n",
    "n_samples = 1000\n",
    "estimate_density = []\n",
    "\n",
    "for q in test:\n",
    "    estimate_density.append(\n",
    "        estimator.estimate(q, A, I, n_samples)\n",
    "#         estimator.calculate_W(q, A, I)\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11507596153389507"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.abs((np.round(np.array(estimate_density)) - real_density)) / real_density).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- **k** \n",
    "    - fix $k = np.log(n)$\n",
    "- **L**\n",
    "- **n_samples**\n",
    "- **I**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 551,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3h 11min 53s, sys: 41.2 s, total: 3h 12min 35s\n",
      "Wall time: 3h 14min 5s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "k = 7\n",
    "random_state = 1\n",
    "I = [0]\n",
    "\n",
    "error_ratios = [] # (L, n_samples)\n",
    "\n",
    "for i, L in enumerate(range(10, 110, 10)):\n",
    "    estimator = LSHEstimateDensity(train, k, L, random_state)\n",
    "    estimator.preprocessing()\n",
    "    error_ratios.append([])\n",
    "    \n",
    "    for n_samples in range(100, 1050, 50):\n",
    "        temp = []\n",
    "        for j in range(10):\n",
    "            estimate_density = []\n",
    "            for q in test:\n",
    "                estimate_density.append(estimator.estimate(q, A, I, n_samples))\n",
    "            temp.append((np.abs((np.round(np.array(estimate_density)) - real_density)) / real_density).mean())\n",
    "        error_ratios[i].append(np.array(temp).mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 552,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20, 10))\n",
    "sns.heatmap(error_ratios, annot=True, fmt='.3f',\n",
    "            xticklabels=np.arange(100, 1050, 50),\n",
    "            yticklabels=np.arange(10, 110, 10),\n",
    "            cmap='Blues')\n",
    "plt.xlabel('number of samples')\n",
    "plt.ylabel('number of hash tables')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Next Paper"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## train test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {},
   "outputs": [],
   "source": [
    "train, test = train_test_split(norm_P, test_size=100, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(train[:, 0], train[:, 1])\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 381,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = P[0]\n",
    "dis = np.array([distance.euclidean(q, p) for p in P])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 382,
   "metadata": {},
   "outputs": [],
   "source": [
    "idxs_dis = np.argwhere(dis <= 0.5).reshape(1, -1)[0] # threshold = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 383,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36"
      ]
     },
     "execution_count": 383,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(idxs_dis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 386,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.35336670766094497"
      ]
     },
     "execution_count": 386,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([angle_between(q, P[idx]) for idx in idxs_dis]).max() # calc the max angle of B_q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 387,
   "metadata": {},
   "outputs": [],
   "source": [
    "idxs_angles = np.argwhere(np.array([angle_between(norm_P[0], p) for p in norm_P]) <= 0.353366).reshape(1, -1)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "102"
      ]
     },
     "execution_count": 388,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(idxs_angles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(P[:, 0], P[:, 1])\n",
    "plt.scatter(P[idxs_angles, 0], P[idxs_angles, 1], label='angle local density')\n",
    "plt.scatter(P[idxs_dis, 0], P[idxs_dis, 1], label='euclidean local density')\n",
    "plt.scatter(q[0], q[1], label='query')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "hide_input": false,
  "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": "3.6.7"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "328px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}