k-Nearest_Neighbors.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Winner of raw_majority_vote(['a','b','c','b']) is  b\n"
     ]
    }
   ],
   "source": [
    "from typing import List\n",
    "from collections import Counter\n",
    "\n",
    "def raw_majority_vote(labels: List[str]) -> str:\n",
    "    votes = Counter(labels)\n",
    "    winner, _ = votes.most_common(1)[0]\n",
    "    return winner\n",
    "\n",
    "\n",
    "print(\"Winner of raw_majority_vote(['a','b','c','b']) is \", raw_majority_vote(['a','b','c','b']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Winner of majority_vote(['a','b','c','b','a']) is  b\n"
     ]
    }
   ],
   "source": [
    "def majority_vote(labels: List[str]) -> str:\n",
    "    # Assume labels are ordered from nearest to farthest\n",
    "    vote_counts = Counter(labels)\n",
    "    winner, winner_count =  vote_counts.most_common(1)[0]\n",
    "    \n",
    "    num_winners = len([count\n",
    "                       for count in vote_counts.values()\n",
    "                       if count == winner_count])\n",
    "    if num_winners == 1:\n",
    "        return winner  #if unique winner then return\n",
    "    else:\n",
    "        return majority_vote(labels[:-1]) #try again without the farthest\n",
    "    \n",
    "\n",
    "print(\"Winner of majority_vote(['a','b','c','b','a']) is \", majority_vote(['a','b','c','b','a']))    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import NamedTuple\n",
    "from Vector_operations_on_data import Vector, distance\n",
    "\n",
    "class LabeledPoint (NamedTuple):\n",
    "    point: Vector\n",
    "    label: str\n",
    "      \n",
    "def knn_classify(k: int,\n",
    "                 labeled_points: List[Vector],\n",
    "                 new_point: Vector) -> str:\n",
    "    \n",
    "    # Order the labeled points from nearest to farthest    \n",
    "    by_distance = sorted(labeled_points,\n",
    "                         key=lambda lp: distance(lp.point, new_point))\n",
    "    \n",
    "    # Find the labels for the k closest\n",
    "    k_nearest_labels = [lp.label for lp in by_distance[:k]]\n",
    "    \n",
    "    # Let them vote\n",
    "    return majority_vote(k_nearest_labels)\n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'5.1,3.5,1.4,0.2,Iris-setosa\\n4.9,3.0,1.4,0.2,Iris-setosa\\n4.7,3.2,1.3,0.2,Iris-setosa\\n4.6,3.1,1.5,0.2,Iris-setosa\\n5.0,3.6,1.4,0.2,Iris-setosa\\n5.4,3.9,1.7,0.4,Iris-setosa\\n4.6,3.4,1.4,0.3,Iris-setosa\\n5.0,3.4,1.5,0.2,Iris-setosa\\n4.4,2.9,1.4,0.2,Iris-setosa\\n4.9,3.1,1.5,0.1,Iris-setosa\\n5.4,3.7,1.5,0.2,Iris-setosa\\n4.8,3.4,1.6,0.2,Iris-setosa\\n4.8,3.0,1.4,0.1,Iris-setosa\\n4.3,3.0,1.1,0.1,Iris-setosa\\n5.8,4.0,1.2,0.2,Iris-setosa\\n5.7,4.4,1.5,0.4,Iris-setosa\\n5.4,3.9,1.3,0.4,Iris-setosa\\n5.1,3.5,1.4,0.3,Iris-setosa\\n5.7,3.8,1.7,0.3,Iris-setosa\\n5.1,3.8,1.5,0.3,Iris-setosa\\n5.4,3.4,1.7,0.2,Iris-setosa\\n5.1,3.7,1.5,0.4,Iris-setosa\\n4.6,3.6,1.0,0.2,Iris-setosa\\n5.1,3.3,1.7,0.5,Iris-setosa\\n4.8,3.4,1.9,0.2,Iris-setosa\\n5.0,3.0,1.6,0.2,Iris-setosa\\n5.0,3.4,1.6,0.4,Iris-setosa\\n5.2,3.5,1.5,0.2,Iris-setosa\\n5.2,3.4,1.4,0.2,Iris-setosa\\n4.7,3.2,1.6,0.2,Iris-setosa\\n4.8,3.1,1.6,0.2,Iris-setosa\\n5.4,3.4,1.5,0.4,Iris-setosa\\n5.2,4.1,1.5,0.1,Iris-setosa\\n5.5,4.2,1.4,0.2,Iris-setosa\\n4.9,3.1,1.5,0.1,Iris-setosa\\n5.0,3.2,1.2,0.2,Iris-setosa\\n5.5,3.5,1.3,0.2,Iris-setosa\\n4.9,3.1,1.5,0.1,Iris-setosa\\n4.4,3.0,1.3,0.2,Iris-setosa\\n5.1,3.4,1.5,0.2,Iris-setosa\\n5.0,3.5,1.3,0.3,Iris-setosa\\n4.5,2.3,1.3,0.3,Iris-setosa\\n4.4,3.2,1.3,0.2,Iris-setosa\\n5.0,3.5,1.6,0.6,Iris-setosa\\n5.1,3.8,1.9,0.4,Iris-setosa\\n4.8,3.0,1.4,0.3,Iris-setosa\\n5.1,3.8,1.6,0.2,Iris-setosa\\n4.6,3.2,1.4,0.2,Iris-setosa\\n5.3,3.7,1.5,0.2,Iris-setosa\\n5.0,3.3,1.4,0.2,Iris-setosa\\n7.0,3.2,4.7,1.4,Iris-versicolor\\n6.4,3.2,4.5,1.5,Iris-versicolor\\n6.9,3.1,4.9,1.5,Iris-versicolor\\n5.5,2.3,4.0,1.3,Iris-versicolor\\n6.5,2.8,4.6,1.5,Iris-versicolor\\n5.7,2.8,4.5,1.3,Iris-versicolor\\n6.3,3.3,4.7,1.6,Iris-versicolor\\n4.9,2.4,3.3,1.0,Iris-versicolor\\n6.6,2.9,4.6,1.3,Iris-versicolor\\n5.2,2.7,3.9,1.4,Iris-versicolor\\n5.0,2.0,3.5,1.0,Iris-versicolor\\n5.9,3.0,4.2,1.5,Iris-versicolor\\n6.0,2.2,4.0,1.0,Iris-versicolor\\n6.1,2.9,4.7,1.4,Iris-versicolor\\n5.6,2.9,3.6,1.3,Iris-versicolor\\n6.7,3.1,4.4,1.4,Iris-versicolor\\n5.6,3.0,4.5,1.5,Iris-versicolor\\n5.8,2.7,4.1,1.0,Iris-versicolor\\n6.2,2.2,4.5,1.5,Iris-versicolor\\n5.6,2.5,3.9,1.1,Iris-versicolor\\n5.9,3.2,4.8,1.8,Iris-versicolor\\n6.1,2.8,4.0,1.3,Iris-versicolor\\n6.3,2.5,4.9,1.5,Iris-versicolor\\n6.1,2.8,4.7,1.2,Iris-versicolor\\n6.4,2.9,4.3,1.3,Iris-versicolor\\n6.6,3.0,4.4,1.4,Iris-versicolor\\n6.8,2.8,4.8,1.4,Iris-versicolor\\n6.7,3.0,5.0,1.7,Iris-versicolor\\n6.0,2.9,4.5,1.5,Iris-versicolor\\n5.7,2.6,3.5,1.0,Iris-versicolor\\n5.5,2.4,3.8,1.1,Iris-versicolor\\n5.5,2.4,3.7,1.0,Iris-versicolor\\n5.8,2.7,3.9,1.2,Iris-versicolor\\n6.0,2.7,5.1,1.6,Iris-versicolor\\n5.4,3.0,4.5,1.5,Iris-versicolor\\n6.0,3.4,4.5,1.6,Iris-versicolor\\n6.7,3.1,4.7,1.5,Iris-versicolor\\n6.3,2.3,4.4,1.3,Iris-versicolor\\n5.6,3.0,4.1,1.3,Iris-versicolor\\n5.5,2.5,4.0,1.3,Iris-versicolor\\n5.5,2.6,4.4,1.2,Iris-versicolor\\n6.1,3.0,4.6,1.4,Iris-versicolor\\n5.8,2.6,4.0,1.2,Iris-versicolor\\n5.0,2.3,3.3,1.0,Iris-versicolor\\n5.6,2.7,4.2,1.3,Iris-versicolor\\n5.7,3.0,4.2,1.2,Iris-versicolor\\n5.7,2.9,4.2,1.3,Iris-versicolor\\n6.2,2.9,4.3,1.3,Iris-versicolor\\n5.1,2.5,3.0,1.1,Iris-versicolor\\n5.7,2.8,4.1,1.3,Iris-versicolor\\n6.3,3.3,6.0,2.5,Iris-virginica\\n5.8,2.7,5.1,1.9,Iris-virginica\\n7.1,3.0,5.9,2.1,Iris-virginica\\n6.3,2.9,5.6,1.8,Iris-virginica\\n6.5,3.0,5.8,2.2,Iris-virginica\\n7.6,3.0,6.6,2.1,Iris-virginica\\n4.9,2.5,4.5,1.7,Iris-virginica\\n7.3,2.9,6.3,1.8,Iris-virginica\\n6.7,2.5,5.8,1.8,Iris-virginica\\n7.2,3.6,6.1,2.5,Iris-virginica\\n6.5,3.2,5.1,2.0,Iris-virginica\\n6.4,2.7,5.3,1.9,Iris-virginica\\n6.8,3.0,5.5,2.1,Iris-virginica\\n5.7,2.5,5.0,2.0,Iris-virginica\\n5.8,2.8,5.1,2.4,Iris-virginica\\n6.4,3.2,5.3,2.3,Iris-virginica\\n6.5,3.0,5.5,1.8,Iris-virginica\\n7.7,3.8,6.7,2.2,Iris-virginica\\n7.7,2.6,6.9,2.3,Iris-virginica\\n6.0,2.2,5.0,1.5,Iris-virginica\\n6.9,3.2,5.7,2.3,Iris-virginica\\n5.6,2.8,4.9,2.0,Iris-virginica\\n7.7,2.8,6.7,2.0,Iris-virginica\\n6.3,2.7,4.9,1.8,Iris-virginica\\n6.7,3.3,5.7,2.1,Iris-virginica\\n7.2,3.2,6.0,1.8,Iris-virginica\\n6.2,2.8,4.8,1.8,Iris-virginica\\n6.1,3.0,4.9,1.8,Iris-virginica\\n6.4,2.8,5.6,2.1,Iris-virginica\\n7.2,3.0,5.8,1.6,Iris-virginica\\n7.4,2.8,6.1,1.9,Iris-virginica\\n7.9,3.8,6.4,2.0,Iris-virginica\\n6.4,2.8,5.6,2.2,Iris-virginica\\n6.3,2.8,5.1,1.5,Iris-virginica\\n6.1,2.6,5.6,1.4,Iris-virginica\\n7.7,3.0,6.1,2.3,Iris-virginica\\n6.3,3.4,5.6,2.4,Iris-virginica\\n6.4,3.1,5.5,1.8,Iris-virginica\\n6.0,3.0,4.8,1.8,Iris-virginica\\n6.9,3.1,5.4,2.1,Iris-virginica\\n6.7,3.1,5.6,2.4,Iris-virginica\\n6.9,3.1,5.1,2.3,Iris-virginica\\n5.8,2.7,5.1,1.9,Iris-virginica\\n6.8,3.2,5.9,2.3,Iris-virginica\\n6.7,3.3,5.7,2.5,Iris-virginica\\n6.7,3.0,5.2,2.3,Iris-virginica\\n6.3,2.5,5.0,1.9,Iris-virginica\\n6.5,3.0,5.2,2.0,Iris-virginica\\n6.2,3.4,5.4,2.3,Iris-virginica\\n5.9,3.0,5.1,1.8,Iris-virginica\\n\\n'"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Download Iris dataset\n",
    "import requests\n",
    "data = requests.get(\n",
    "    \"https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data\")\n",
    "\n",
    "with open('iris.csv','w') as f:\n",
    "    f.write(data.text)\n",
    "data.text"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processed 0 lines.\n"
     ]
    }
   ],
   "source": [
    "from typing import Dict\n",
    "import csv\n",
    "from collections import defaultdict\n",
    "\n",
    "def parse_iris_row(row: List[str]) -> LabeledPoint:\n",
    "    \"sepal_length, sepal_width, petal_length, petal_width, class\"\n",
    "    measurements = [float(value) for value in row[:-1]]\n",
    "    \n",
    "    #Let's assume e.g. class \"Iris-virginica\" and we just want \"virginica\"\n",
    "    label = row[-1].split(\"-\")[-1]\n",
    "    \n",
    "    return LabeledPoint(measurements, label)\n",
    "\n",
    "with open('iris.csv') as csv_file:\n",
    "    csv_reader = csv.reader(csv_file, delimiter=',')\n",
    "    line_count = 0\n",
    "    iris_data = []\n",
    "    for row in csv_reader:\n",
    "        iris_data.append(row)\n",
    "    print(f'Processed {line_count} lines.')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['5.1', '3.5', '1.4', '0.2', 'Iris-setosa'],\n",
       " ['4.9', '3.0', '1.4', '0.2', 'Iris-setosa'],\n",
       " ['4.7', '3.2', '1.3', '0.2', 'Iris-setosa'],\n",
       " ['4.6', '3.1', '1.5', '0.2', 'Iris-setosa'],\n",
       " ['5.0', '3.6', '1.4', '0.2', 'Iris-setosa'],\n",
       " ['5.4', '3.9', '1.7', '0.4', 'Iris-setosa'],\n",
       " ['4.6', '3.4', '1.4', '0.3', 'Iris-setosa'],\n",
       " ['5.0', '3.4', '1.5', '0.2', 'Iris-setosa'],\n",
       " ['4.4', '2.9', '1.4', '0.2', 'Iris-setosa'],\n",
       " ['4.9', '3.1', '1.5', '0.1', 'Iris-setosa'],\n",
       " ['5.4', '3.7', '1.5', '0.2', 'Iris-setosa'],\n",
       " ['4.8', '3.4', '1.6', '0.2', 'Iris-setosa'],\n",
       " ['4.8', '3.0', '1.4', '0.1', 'Iris-setosa'],\n",
       " ['4.3', '3.0', '1.1', '0.1', 'Iris-setosa'],\n",
       " ['5.8', '4.0', '1.2', '0.2', 'Iris-setosa'],\n",
       " ['5.7', '4.4', '1.5', '0.4', 'Iris-setosa'],\n",
       " .............................................,\n",
       " ['6.9', '3.1', '5.4', '2.1', 'Iris-virginica'],\n",
       " ['6.7', '3.1', '5.6', '2.4', 'Iris-virginica'],\n",
       " ['6.9', '3.1', '5.1', '2.3', 'Iris-virginica'],\n",
       " ['5.8', '2.7', '5.1', '1.9', 'Iris-virginica'],\n",
       " ['6.8', '3.2', '5.9', '2.3', 'Iris-virginica'],\n",
       " ['6.7', '3.3', '5.7', '2.5', 'Iris-virginica'],\n",
       " ['6.7', '3.0', '5.2', '2.3', 'Iris-virginica'],\n",
       " ['6.3', '2.5', '5.0', '1.9', 'Iris-virginica'],\n",
       " ['6.5', '3.0', '5.2', '2.0', 'Iris-virginica'],\n",
       " ['6.2', '3.4', '5.4', '2.3', 'Iris-virginica'],\n",
       " ['5.9', '3.0', '5.1', '1.8', 'Iris-virginica'],\n",
       " []]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[LabeledPoint(point=[5.1, 3.5, 1.4, 0.2], label='setosa'),\n",
       " LabeledPoint(point=[4.9, 3.0, 1.4, 0.2], label='setosa'),\n",
       " LabeledPoint(point=[4.7, 3.2, 1.3, 0.2], label='setosa'),\n",
       " LabeledPoint(point=[4.6, 3.1, 1.5, 0.2], label='setosa'),\n",
       " LabeledPoint(point=[5.0, 3.6, 1.4, 0.2], label='setosa'),\n",
       " LabeledPoint(point=[5.4, 3.9, 1.7, 0.4], label='setosa'),\n",
       " LabeledPoint(point=[4.6, 3.4, 1.4, 0.3], label='setosa'),\n",
       " LabeledPoint(point=[5.0, 3.4, 1.5, 0.2], label='setosa'),\n",
       " LabeledPoint(point=[4.4, 2.9, 1.4, 0.2], label='setosa'),\n",
       " LabeledPoint(point=[4.9, 3.1, 1.5, 0.1], label='setosa'),\n",
       " LabeledPoint(point=[5.4, 3.7, 1.5, 0.2], label='setosa'),\n",
       " LabeledPoint(point=[4.8, 3.4, 1.6, 0.2], label='setosa'),\n",
       " LabeledPoint(point=[4.8, 3.0, 1.4, 0.1], label='setosa'),\n",
       " LabeledPoint(point=[4.3, 3.0, 1.1, 0.1], label='setosa'),\n",
       " LabeledPoint(point=[5.8, 4.0, 1.2, 0.2], label='setosa'),\n",
       " LabeledPoint(point=[5.7, 4.4, 1.5, 0.4], label='setosa'),\n",
        " .............................................,\n",
       " LabeledPoint(point=[6.3, 2.5, 5.0, 1.9], label='virginica'),\n",
       " LabeledPoint(point=[6.5, 3.0, 5.2, 2.0], label='virginica'),\n",
       " LabeledPoint(point=[6.2, 3.4, 5.4, 2.3], label='virginica')]"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris_data = iris_data[:-2]\n",
    "\n",
    "iris_data = [parse_iris_row(row) for row in iris_data]\n",
    "iris_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# group the points by species for plotting\n",
    "points_by_species: Dict[str, List[Vector]] = defaultdict(list)\n",
    "for iris in iris_data:\n",
    "    points_by_species[iris.label].append(iris.point)\n",
    "    \n",
    "from matplotlib import pyplot as plt\n",
    "metrics = ['sepal_length', 'sepal_width', 'petal_length', 'petal_width']\n",
    "pairs = [(i,j) for i in range(4) for j in range(4) if i<j]\n",
    "marks = ['+','.','x'] # 3 markers for 3 classes\n",
    "\n",
    "fig, ax = plt.subplots(2,3)\n",
    "\n",
    "for row in range(2):\n",
    "    for col in range(3):\n",
    "        i,j = pairs [3*row+col]\n",
    "        ax[row][col].set_title(f\"{metrics[i]} vs {metrics[j]}\", fontsize = 8)\n",
    "        ax[row][col].set_xticks([])\n",
    "        ax[row][col].set_xticks([])\n",
    "        \n",
    "        for mark, (species, points) in zip(marks, points_by_species.items()):\n",
    "            xs = [point[i] for point in points]\n",
    "            ys = [point[j] for point in points]\n",
    "            ax[row][col].scatter(xs,ys, marker = mark, label = species)\n",
    "            \n",
    "ax[-1][-1].legend(loc = 'lower right', prop = {'size':6})\n",
    "plt.show()\n",
    "pairs\n",
    "       "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0 defaultdict(<class 'int'>, {('versicolor', 'versicolor'): 16, ('setosa', 'setosa'): 13, ('virginica', 'virginica'): 16})\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "from machine_learning import split_data\n",
    "import math\n",
    "\n",
    "random.seed(12)\n",
    "iris_train,iris_test = split_data(iris_data, 0.70)\n",
    "\n",
    "from typing import Tuple\n",
    "\n",
    "# Track how many times we see (predicted, actual)\n",
    "confusion_matrix: Dict[Tuple[str, str], int] = defaultdict(int)\n",
    "num_correct = 0\n",
    "\n",
    "k = 5\n",
    "for iris in iris_test:\n",
    "    predicted = knn_classify(k, iris_train, iris.point)\n",
    "    actual = iris.label\n",
    "    \n",
    "    if predicted == actual:\n",
    "        num_correct += 1\n",
    "        \n",
    "    confusion_matrix[(predicted, actual)]+=1\n",
    "    \n",
    "pct_correct = num_correct/len(iris_test)\n",
    "print(pct_correct, confusion_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Curse of Dimensionality: 100%|███████████████████████████████████████████████████████| 100/100 [00:17<00:00,  3.13it/s]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x19bc36c5a20>]"
      ]
     },
     "execution_count": 64,
     "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": [
    "# curse of dimensionality\n",
    "def random_point(dim: int) -> Vector:\n",
    "    return [random.random() for _ in range(dim)]\n",
    "\n",
    "def random_distance(dim: int, num_pairs: int) -> List[float]:\n",
    "    return [distance(random_point(dim), random_point(dim)) \n",
    "            for _ in range(num_pairs)]\n",
    "import tqdm\n",
    "dimensions = range(1,101)\n",
    "avg_distances = []\n",
    "min_distances = []\n",
    "random.seed(0)\n",
    "for dim in tqdm.tqdm(dimensions, desc = \"Curse of Dimensionality\"):\n",
    "    distances = random_distance(dim, 10000) # 10,000 random pairs\n",
    "    avg_distances.append(sum(distances) / 10000) # track averages\n",
    "    min_distances.append(min(distances)) # track minimums\n",
    "    \n",
    "plt.plot(dimensions, avg_distances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x19bc2e34cf8>]"
      ]
     },
     "execution_count": 65,
     "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": [
    "min_avg_ratio = [min_dist / avg_dist \n",
    "                for min_dist, avg_dist in zip(min_distances, avg_distances)]\n",
    "plt.plot(dimensions, avg_distances)\n",
    "plt.plot(dimensions, min_avg_ratio)"
   ]
  }
 ],
 "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}