Exercise 11.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "58d80ff7-a157-4847-8cf9-3acc0495dda3",
   "metadata": {},
   "source": [
    "# Assignment 11"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5bec461-b8b1-4f83-bc3a-4f3df81c9cb3",
   "metadata": {},
   "source": [
    "## Assignment 11.1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1fc0aca-c22b-4ebe-befe-4601f4a98bc6",
   "metadata": {},
   "source": [
    "What is the idea behind KD-trees? For which problems can a KD-tree be used to speed up the computation time? Given are the following 13 points $P = {P_1(1; 6), P_2(7; 6), P_3(3; 5), P_4(6; 5), P_5(6; 4), P_6(2; 3), P_7(5; 3), P_8(1; 2), P_9(2; 2), P_{10}(4; 2), P_{11}(6; 2), P_{12}(1; 1), P_{13}(2; 1)}$.\n",
    "\n",
    "a) Build a KD-tree with a minimum leaf size of 3 as the stopping criterion. Choose the widest dimension $ d \\in {x, y}$ for splitting the data (of size $n$) using the following median split position MSP:"
   ]
  },
  {
   "attachments": {
    "050a9e48-255f-4aa0-814c-dcb37dd7121b.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "bcb3a32f-d4f6-4de9-af74-3d698f2d63e3",
   "metadata": {},
   "source": [
    "<div align=center>\n",
    "    <img width=400 src=\"attachment:050a9e48-255f-4aa0-814c-dcb37dd7121b.png\">\n",
    "</div>\n",
    "\n",
    "<!-- ![image.png](attachment:050a9e48-255f-4aa0-814c-dcb37dd7121b.png) -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "id": "3d02fd7a-c9c2-423f-99b7-b6fb8bc4516e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The range along x is 6 and along y is 5, so the root node splits along x.\n",
      "The first splitting point, along the abscissa, is 3.5\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "points = np.array([[1, 6], [7, 6], [3, 5], [6, 4], [6, 5], [2, 3], [5, 3], [1, 2], [2, 2], [4, 2], [6, 2], [1, 1], [2, 1]])\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlim([0, 7.5])\n",
    "ax.set_ylim([0, 6.5])\n",
    "ax.scatter(points[:, 0], points[:, 1])\n",
    "\n",
    "# Choose which dimension is wider \n",
    "print(f\"The range along x is {np.ptp(points[:, 0])} and along y is {np.ptp(points[:, 1])}, so the root node splits along x.\")\n",
    "\n",
    "# Initialise the list of splitting criteria\n",
    "MSP = []\n",
    "\n",
    "# We start with an odd n\n",
    "n = 13\n",
    "points = points[points[:, 0].argsort()]\n",
    "MSP.append((points[n//2, 0] + points[n//2+1, 0])/2)\n",
    "print(f\"The first splitting point, along the abscissa, is {MSP[0]}\")\n",
    "\n",
    "# Find the median along the x-axis, splitting the space along the x axis \n",
    "ax.axvline(MSP[0], color='k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "id": "a811daeb-7b5b-4034-a052-830f36c13019",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 287,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Then we follow up the search in each box, left and right \n",
    "n = len(points[points[:, 0] < MSP[0]])\n",
    "MSP.append((points[points[:, 0] < MSP[0]][n//2, 1] + points[points[:, 0] < MSP[0]][n//2+1, 1])/2)\n",
    "ax.hlines(y = MSP[1], xmin=0, xmax=MSP[0], color=\"black\")\n",
    "\n",
    "n = len(points[points[:, 0] > MSP[0]])\n",
    "MSP.append((points[points[:, 0] > MSP[0]][n//2, 1] + points[points[:, 0] > MSP[0]][n//2+1, 1])/2)\n",
    "ax.hlines(y = MSP[2], xmin=MSP[0], xmax=7.5, color=\"black\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8abc11cb-0265-4756-981b-09a0db19c725",
   "metadata": {},
   "source": [
    "Search the nearest neighbor of the point $S(4; 5)$ with your KD-tree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "id": "4c62a8af-bb1b-43f8-b2b7-7ac7a940618c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 5])"
      ]
     },
     "execution_count": 288,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.neighbors import KDTree\n",
    "rng = np.random.RandomState(0)\n",
    "tree = KDTree(points, leaf_size=2)              \n",
    "dist, ind = tree.query(np.array([[4, 5]]), k=1)                \n",
    "points[ind][0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "id": "d5af542a-1c6d-4262-8384-83c92e08851c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 289,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.scatter(4, 5, color='r')\n",
    "C1 = plt.Circle(points[ind][0][0], 0.2, color='r', fill=0)\n",
    "ax.add_patch(C1)\n",
    "fig"
   ]
  }
 ],
 "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}