experiment.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PureFacts Point Coverage Problem\n",
    "> 2022-11-05\n",
    "\n",
    "Given a set A of points in a 2D space (input.csv - see attached), select an N number of random\n",
    "Representative Points from this set such that they best \"cover\" the shape of the point set (as opposed\n",
    "to its density).\n",
    "Output should be the source code and 5 separate output.csv files where N = 10, 25, 63, 159, 380\n",
    "\n",
    "&copy; 2022 Samm Du   \n",
    "MIT License"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import csv\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "\n",
    "from typing import Optional\n",
    "from itertools import combinations\n",
    "from sklearn.cluster import KMeans, AgglomerativeClustering\n",
    "from sklearn.neighbors import NearestNeighbors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Ingestion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "filename: str = \"./input.csv\"\n",
    "data = []\n",
    "with open(filename, \"r\") as input_file:\n",
    "    csv_reader = csv.reader(input_file, delimiter=',')\n",
    "    for line in csv_reader:\n",
    "        data.append(tuple(int(x) for x in line))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Configuration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# number of representative points to pick from the input data\n",
    "NUM_REPS = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_of_points(points: list) -> tuple[float, float]:\n",
    "    \"\"\"https://stackoverflow.com/a/4355934\"\"\"\n",
    "    return (\n",
    "        sum([p[0] for p in points]) / len(points), \n",
    "        sum([p[1] for p in points]) / len(points)\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def point_distance(a: tuple[int, int], b: tuple[int, int]) -> float:\n",
    "    \"\"\"Return the Euclidean distance between two 2D input points.\"\"\"\n",
    "    return ((b[0] - a[0])**2 + (b[1] - a[1])**2)**(1/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### k-Means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmeans = KMeans(\n",
    "    n_clusters=NUM_REPS,\n",
    "    init='random', \n",
    "    n_init=80,\n",
    "    max_iter=300\n",
    ")\n",
    "kmeans.fit(data)\n",
    "kmeans_centroids = kmeans.cluster_centers_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hierarchical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "hcluster = AgglomerativeClustering(\n",
    "    n_clusters=NUM_REPS,\n",
    "    linkage='complete'\n",
    ")\n",
    "hcluster.fit(data)\n",
    "hcluster_labels = hcluster.labels_\n",
    "\n",
    "hcluster_groups = [[] for i in range(NUM_REPS)]\n",
    "for point, label in zip(data, hcluster_labels):\n",
    "    hcluster_groups[label].append(point)\n",
    "\n",
    "hcluster_centroids = []\n",
    "for group in hcluster_groups:\n",
    "    hcluster_centroids.append(mean_of_points(group))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graph Disconnect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a graph of all points with their position as an attribute\n",
    "G = nx.Graph()\n",
    "for id, pos in enumerate(data):\n",
    "    G.add_node(id, pos=pos)\n",
    "\n",
    "# Add edges between points within a certain radius, and limit the number of neighbors \n",
    "# each point can have\n",
    "# Ref: https://networkx.org/documentation/stable/_modules/networkx/generators/geometric.html#geometric_edges\n",
    "\n",
    "# configure performance optimization parameters\n",
    "radius = 6000\n",
    "num_neighbors = 180\n",
    "# get (node_id, (pos_x, pos_y)) for all nodes\n",
    "nodes_pos = G.nodes(data=\"pos\")\n",
    "# add edges that meet the criteria\n",
    "for (u, pu), (v, pv) in combinations(nodes_pos, 2):\n",
    "    dist_sq = sum(abs(a - b) ** 2 for a, b in zip(pu, pv))\n",
    "    if ((dist_sq <= radius**2) and \n",
    "        (sum(1 for n in G.neighbors(u)) <= num_neighbors) and \n",
    "        (sum(1 for n in G.neighbors(v)) <= num_neighbors)):\n",
    "        G.add_edge(u, v, dist=(dist_sq**(1/2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total edge count: 86050\n",
      "Total connected components: 1\n"
     ]
    }
   ],
   "source": [
    "# sort all edges in the graph from short to long in a list\n",
    "edges_short_to_long = sorted(G.edges(data=True), key=lambda edge: edge[2]['dist'])\n",
    "print(\"Total edge count:\", len(edges_short_to_long))\n",
    "print(\"Total connected components:\", nx.number_connected_components(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Longest edge: (58, 73, {'dist': 1524.7294842036733})\n",
      "Total connected components: 10\n"
     ]
    }
   ],
   "source": [
    "# keep removing the largest edge from the graph, until the graph has NUM_REPS disconnected components\n",
    "while nx.number_connected_components(G) < NUM_REPS:\n",
    "    largest_edge = edges_short_to_long.pop()\n",
    "    G.remove_edge(largest_edge[0], largest_edge[1])\n",
    "\n",
    "print(\"Longest edge:\", edges_short_to_long[-1])\n",
    "print(\"Total connected components:\", nx.number_connected_components(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "g_disconn_centroids = [\n",
    "    mean_of_points([data[i] for i in cluster])\n",
    "    for cluster in nx.connected_components(G)\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1-NN to Centroids from Input Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def points_1nn_to_centroids(input_data: list, centroids: list) -> set:\n",
    "    knn = NearestNeighbors(n_neighbors=1).fit(input_data)\n",
    "    neighbors_idxs = knn.kneighbors(centroids, n_neighbors=1, return_distance=False)\n",
    "    \n",
    "    return set(input_data[x[0]] for x in neighbors_idxs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### k-Means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(2773, 5788), (3827, 6064), (7048, 4554), (6245, 7039), (4291, 3851), (5267, 3372), (1418, 8847), (7347, 6193), (6580, 5556), (2925, 3861)]\n"
     ]
    }
   ],
   "source": [
    "kmeans_closest_points_set = points_1nn_to_centroids(data, kmeans_centroids)\n",
    "kmeans_closest_points = list(kmeans_closest_points_set)\n",
    "print(kmeans_closest_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hierarchical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(6250, 6915), (1199, 8724), (7214, 4256), (5494, 1672), (3920, 8304), (6880, 5627), (3188, 5989), (4769, 3632), (2925, 3861), (9344, 8190)]\n"
     ]
    }
   ],
   "source": [
    "hcluster_closest_points_set = points_1nn_to_centroids(data, hcluster_centroids)\n",
    "hcluster_closest_points = list(hcluster_closest_points_set)\n",
    "print(hcluster_closest_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graph Disconnect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(1199, 8724), (3873, 3866), (5494, 1672), (3920, 8304), (7279, 824), (8271, 3538), (6053, 7097), (3188, 5989), (6330, 5237), (9344, 8190)]\n"
     ]
    }
   ],
   "source": [
    "g_disconn_closest_points_set = points_1nn_to_centroids(data, g_disconn_centroids)\n",
    "g_disconn_closest_points = list(g_disconn_closest_points_set)\n",
    "print(g_disconn_closest_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_coverage_data(\n",
    "    plot_title: str, \n",
    "    input_data: Optional[list] = None, \n",
    "    centroids: Optional[list] = None, \n",
    "    closest_points: Optional[list] = None\n",
    ") -> None:\n",
    "    colors = ['#444444', '#0784f990', '#fc052edd']\n",
    "    point_sizes = [4, 12, 12]\n",
    "    if (input_data is not None) and len(input_data) > 0:\n",
    "        plt.scatter(\n",
    "            [x[0] for x in input_data], \n",
    "            [y[1] for y in input_data], \n",
    "            s=point_sizes[0],\n",
    "            color=colors[0]\n",
    "        )\n",
    "    if (centroids is not None) and len(centroids) > 0:\n",
    "        plt.scatter(\n",
    "            [x[0] for x in centroids], \n",
    "            [y[1] for y in centroids], \n",
    "            s=point_sizes[1],\n",
    "            color=colors[1]\n",
    "        )\n",
    "    if (closest_points is not None) and len(closest_points) > 0:\n",
    "        plt.scatter(\n",
    "            [x[0] for x in closest_points], \n",
    "            [y[1] for y in closest_points], \n",
    "            s=point_sizes[2],\n",
    "            color=colors[2]\n",
    "        )\n",
    "    plt.title(plot_title)\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### k-Means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_coverage_data(\n",
    "    \"k-Means Clustering\", input_data=data, centroids=kmeans_centroids, closest_points=kmeans_closest_points\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hierarchical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_coverage_data(\n",
    "    \"Hierarchical Clustering (complete/max linkage)\", input_data=data, centroids=hcluster_centroids, closest_points=hcluster_closest_points\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graph Disconnect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_coverage_data(\n",
    "    \"Graph Disconnect\", input_data=data, centroids=g_disconn_centroids, closest_points=g_disconn_closest_points\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Naive Total Distance to Reps\n",
    "\n",
    "Take all points in the input data, compute their distance to every selected rep point, and take the total sum. \n",
    "\n",
    "For optimal point coverage, unselected points should be as close to rep points as possible.\n",
    "\n",
    "Small values in this metric are desireable.   \n",
    "However, this metric favors dense input point distributions, since for dense inputs, more points will be closer to reps compared to sparse inputs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k-Means:\t\t 29272141.394927062\n",
      "Hierarchical:\t\t 34850046.227769665\n",
      "Graph disconnect:\t 37936438.93148547\n"
     ]
    }
   ],
   "source": [
    "def data_to_rep_total_dist(input_data: list, reps: list) -> float:\n",
    "    \"\"\"\n",
    "    Return the sum of all distances from a point to all reps.\n",
    "    \"\"\"\n",
    "    distance_sum = 0\n",
    "    for i in input_data:\n",
    "        for j in reps:\n",
    "            distance_sum += point_distance(i, j)\n",
    "    return distance_sum\n",
    "\n",
    "print(\"k-Means:\\t\\t\", data_to_rep_total_dist(data, kmeans_closest_points))\n",
    "print(\"Hierarchical:\\t\\t\", data_to_rep_total_dist(data, hcluster_closest_points))\n",
    "print(\"Graph disconnect:\\t\", data_to_rep_total_dist(data, g_disconn_closest_points))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distances to Closest Rep Points\n",
    "Take all points not selected as a rep, find their closest rep, compute their distance. Take all these distances to the closest rep, and find the max, min, and average.\n",
    "\n",
    "For optimal point coverage, unselected points should be as close to their rep as possible.\n",
    "\n",
    "Small values in this metric are desireable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distances from input points to closest rep:\n",
      "\t\t\t(min, max, average)\n",
      "Stats k-Means: \t\t(7.211102550927978, 3246.6056120200374, 525.706511627334)\n",
      "Stats Hierarchical: \t(43.840620433565945, 1976.1905272518638, 639.4778736956712)\n",
      "Stats Graph Disconn: \t(59.481089431852205, 2120.628444589009, 895.2549394460437)\n"
     ]
    }
   ],
   "source": [
    "def dists_to_closest_rep(input_data: list, reps) -> tuple[float, float, float]:\n",
    "    \"\"\"\n",
    "    Return min, max, average of distances from all points to a closest rep.\n",
    "    \"\"\"\n",
    "    dists_to_closest_rep = []\n",
    "    for point in input_data:\n",
    "        if point not in reps:\n",
    "            closest_rep = min(reps, key=lambda rep: point_distance(point, rep))\n",
    "            dists_to_closest_rep.append(point_distance(point, closest_rep))\n",
    "    return min(dists_to_closest_rep), max(dists_to_closest_rep), (sum(dists_to_closest_rep)/len(dists_to_closest_rep))\n",
    "\n",
    "stats_kmeans = dists_to_closest_rep(data, kmeans_closest_points_set)\n",
    "stats_hcluster = dists_to_closest_rep(data, hcluster_closest_points_set)\n",
    "stats_gd = dists_to_closest_rep(data, g_disconn_closest_points_set)\n",
    "\n",
    "print(\"Distances from input points to closest rep:\")\n",
    "print(\"\\t\\t\\t(min, max, average)\")\n",
    "\n",
    "print(f\"Stats k-Means: \\t\\t{stats_kmeans}\")\n",
    "print(f\"Stats Hierarchical: \\t{stats_hcluster}\")\n",
    "print(f\"Stats Graph Disconn: \\t{stats_gd}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Closest Distance Between Reps\n",
    "\n",
    "For optimal point coverage, the selected reps should be as far from each other as possible.\n",
    "\n",
    "Large values in this metric are desireable. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Closest distance between reps:\n",
      "k-Means:\t 997.0245734183285\n",
      "Hierarchical:\t 1411.0977995872574\n",
      "Graph Disconn:\t 1880.5129619335253\n"
     ]
    }
   ],
   "source": [
    "def min_dist_between_reps(reps) -> float:\n",
    "    \"\"\"\n",
    "    Return the minimum distance between all rep points.\n",
    "    \"\"\"\n",
    "    dist = float('inf')\n",
    "    for i in reps:\n",
    "        for j in reps:\n",
    "            if i != j and (dist_self := point_distance(i, j)) < dist:\n",
    "                dist = dist_self\n",
    "    return dist\n",
    "\n",
    "\n",
    "kmeans_rr = min_dist_between_reps(kmeans_closest_points_set)\n",
    "hcluster_rr = min_dist_between_reps(hcluster_closest_points_set)\n",
    "g_disconn_rr = min_dist_between_reps(g_disconn_closest_points_set)\n",
    "\n",
    "print(\"Closest distance between reps:\")\n",
    "print(\"k-Means:\\t\", kmeans_rr)\n",
    "print(\"Hierarchical:\\t\", hcluster_rr)\n",
    "print(\"Graph Disconn:\\t\", g_disconn_rr)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Min-Rep-Rep to Point-Rep Ratios\n",
    "The ratio of (the closest distance between reps) and (the max|average distance from a point to a rep), for each of the methods above.\n",
    "\n",
    "The greater this ratio, the farthest apart are reps to each other, and closer the unselected points to a rep.\n",
    "\n",
    "Large values in this ratio are desireable. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min-Rep-Rep (rr) / Point-Rep ratios (max|avg):\n",
      "k-Means:\t rr/max: 0.3070975327976409 \trr/avg: 1.8965421796508113\n",
      "Hierarchical:\t rr/max: 0.7140494704979498 \trr/avg: 2.206640538525969\n",
      "Graph Disconn:\t rr/max: 0.8867715448841771 \trr/avg: 2.1005334671452682\n"
     ]
    }
   ],
   "source": [
    "print(\"Min-Rep-Rep (rr) / Point-Rep ratios (max|avg):\")\n",
    "print(\"k-Means:\\t rr/max:\", kmeans_rr / stats_kmeans[1], \"\\trr/avg:\", kmeans_rr / stats_kmeans[2])\n",
    "print(\"Hierarchical:\\t rr/max:\", hcluster_rr / stats_hcluster[1], \"\\trr/avg:\", hcluster_rr / stats_hcluster[2])\n",
    "print(\"Graph Disconn:\\t rr/max:\", g_disconn_rr / stats_gd[1], \"\\trr/avg:\", g_disconn_rr / stats_gd[2])"
   ]
  }
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