284 lines
216 KiB
Plaintext
284 lines
216 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Zadanie 1\n",
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"Zapoznaj się z teorią algorytmu klastrowania K-means (klasyczny alogorytm w dziedzinie eksploracji danych (ang. <a href=\"https://en.wikipedia.org/wiki/Data_mining\">data mining))</a>) np. przez stronę <a href=\"https://www.statystyka.eu/analiza-skupien/metoda-k-srednich.php\">metoda-k-średnich</a>. Przestestuj jedną wybraną metrykę, inną niż euklidesowa - wykonaj obrazy pokazujące efekty jej działania."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Do zwizualizowania działania klastrowania K-means potrzebne jest zdefiniowanie punktów reprezentujacych dane, punkty są tak losowane by widoczne było ich pogrupowane rozmieszczenie"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 94,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 800x600 with 1 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"# Generowanie losowych punktów danych\n",
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"np.random.seed(23)\n",
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"data = np.vstack([\n",
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" np.random.normal(loc=(2, 2), scale=0.6, size=(25, 2)),\n",
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" np.random.normal(loc=(5, 3), scale=0.8, size=(25, 2)),\n",
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" np.random.normal(loc=(5, 5), scale=0.7, size=(25, 2))\n",
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"])\n",
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"plt.figure(figsize=(8, 6))\n",
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"plt.scatter(data[:, 0], data[:, 1], c='b', label=f'dane')\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Następnie trzeba zdefiniować centroidy od jakich zaczyna się algorytm klastrowania, wybieram 3 losowe punkty spośród danych:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 95,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"k = 4\n",
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"startCentroids = data[np.random.choice(data.shape[0], k, replace=False)]\n",
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"\n",
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"plt.scatter(data[:, 0], data[:, 1], c='b', label=f'dane')\n",
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"plt.scatter(startCentroids[:, 0], startCentroids[:, 1], c='black', marker='X', s=100, label='Centroids')\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Mając wybrane centroidy należy zdefiniować funkcję odległości, zastosuję odległość Manhattan lub euklidesową"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 96,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Funkcja obliczająca odległość euklidesową\n",
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"def euclidean_distance(point1, point2):\n",
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" return np.sqrt(np.sum((point1 - point2) ** 2))\n",
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"\n",
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"# Funkcja obliczająca odległość Manhattan\n",
|
||
|
|
"def manhattan_distance(point1, point2):\n",
|
||
|
|
" return np.sum(np.abs((point1 - point2)))\n",
|
||
|
|
"\n",
|
||
|
|
"# Funkcja obliczająca odległość euklidesową do kwadratu\n",
|
||
|
|
"def euclidean2_distance(point1, point2):\n",
|
||
|
|
" return np.sum((point1 - point2) ** 2)\n",
|
||
|
|
"\n",
|
||
|
|
"# Funkcja obliczająca odległość Minkowskiego dla m = 2\n",
|
||
|
|
"def minkowski_distance(point1, point2):\n",
|
||
|
|
" m = 2\n",
|
||
|
|
" return np.sum(np.abs(point1 - point2) ** m) ** (1/m)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Kolejnym etapem jest zdefiniowanie funkcji klastryzującej"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 97,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# Funkcja algorytmu K-means\n",
|
||
|
|
"def k_means(data, k, distance, centroids, max_iters=100):\n",
|
||
|
|
" \n",
|
||
|
|
" for _ in range(max_iters):\n",
|
||
|
|
" clusters = [[] for _ in range(k)]\n",
|
||
|
|
" \n",
|
||
|
|
" for point in data:\n",
|
||
|
|
" distances = [distance(point, centroid) for centroid in centroids]\n",
|
||
|
|
" cluster_index = np.argmin(distances)\n",
|
||
|
|
" clusters[cluster_index].append(point)\n",
|
||
|
|
" \n",
|
||
|
|
" new_centroids = np.array([np.mean(cluster, axis=0) if cluster else centroids[i]\n",
|
||
|
|
" for i, cluster in enumerate(clusters)])\n",
|
||
|
|
" \n",
|
||
|
|
" if np.all(centroids == new_centroids):\n",
|
||
|
|
" break\n",
|
||
|
|
" \n",
|
||
|
|
" centroids = new_centroids\n",
|
||
|
|
"\n",
|
||
|
|
" return clusters, centroids\n",
|
||
|
|
"\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 98,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAqcAAAIjCAYAAAA+xLLKAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAACB8UlEQVR4nO3de1xT9f8H8NcB3EDkmlOJTQEBRVIzzVIDIfWrXZQC1MxKy+6kYFpf61uppWmlJZVZ+e2rdtE0JLuYt0wuWqRmmnlJMBAkTEoBUQEZ5/fHfluMbbDBLmfj9Xw89qCdc7bz2Yb02ud8Pu+PIIqiCCIiIiIiCXBzdAOIiIiIiLQYTomIiIhIMhhOiYiIiEgyGE6JiIiISDIYTomIiIhIMhhOiYiIiEgyGE6JiIiISDIYTomIiIhIMhhOiYiIiEgyGE6JqEVxcXGIi4tzdDNaJSsrC4IgICsry9FNadbq1ashCAKKiook1w5Hff7O/HtnTSEhIZg6daruviW/03wPyRkxnJJL0P4Pdf/+/XrbKysrMXjwYHh6emLr1q0Oap10/fnnn5g9ezZ69+6Njh07wtvbGwMHDsSCBQtQUVFht3a8/PLL2LRpk93OZw/jxo1Dx44dceHCBZPHTJ48GTKZDH///bcdWyYtR48exbx58xweys0REhICQRCM3saMGePo5hG5DA9HN4DIVqqqqvCvf/0Lv/zyCz7//HP+z6OJffv24dZbb0V1dTXuueceDBw4EACwf/9+LF68GDk5Odi+fbtd2vLyyy8jOTkZd9xxh9WfOzY2FpcvX4ZMJrP6czdn8uTJ+Oqrr/D555/jvvvuM9h/6dIlfPHFFxgzZgyuuuoq3Hvvvbjrrrsgl8vt2k5z2PL34OjRo5g/fz7i4uIQEhJit/O21rXXXotZs2YZbL/66qvt1gZH/U4T2QvDKbmkCxcuYPTo0Th48CAyMzNxyy23OLpJklJRUYE777wT7u7u+Pnnn9G7d2+9/QsXLsTKlSsd1DrrqKmpgUwmg5ubGzw9Pe1+/nHjxsHHxwdr1641Gk6/+OILXLx4EZMnTwYAuLu7w93d3d7NNIujQpAUw1dwcDDuueceh7bBUb/TRPbCy/rkcqqrqzFmzBgcOHAAGzduxG233dbs8fPmzYMgCDhx4gTuuece+Pn5QaFQ4Pnnn4coiigpKUFCQgJ8fX3RrVs3LF261OA5amtrMXfuXISHh0Mul0OlUuHpp59GbW2t3nGrVq3CzTffjC5dukAul6NPnz5YsWKFwfOFhITg9ttvx+7du3XDEsLCwvDhhx/qHXflyhXMnz8fERER8PT0xFVXXYWbbroJO3bsaPY1v/feeygtLcXrr79uEEwBoGvXrnjuuedMPt7U+EhjY+Hy8/ORlJSEbt26wdPTE0qlEnfddRcqKysBAIIg4OLFi1izZo3uEmnj8XWlpaV44IEH0LVrV8jlckRHR+N///uf0fN++umneO655xAcHIyOHTuiqqrKaJvi4uJwzTXX4OjRo4iPj0fHjh0RHByMV1991eC1njp1CuPGjYO3tze6dOmCmTNnYtu2bS2O+fPy8kJiYiJ27tyJs2fPGuxfu3YtfHx8MG7cOJPv6f79+zF69Gh07twZXl5eCA0NxQMPPNDs+w0ARUVFEAQBq1ev1m375ZdfMHXqVISFhcHT0xPdunXDAw88YNaQgqbjFpu7vK1ty6lTp/D444+jV69e8PLywlVXXYXx48frvb7Vq1dj/PjxAID4+HiD5zA2XvLs2bOYNm0aunbtCk9PT/Tv3x9r1qwx+vqXLFmC999/Hz179oRcLsf111+Pffv2tfh628rUOM+pU6ca9A43NDQgPT0dffv2haenJxQKBcaMGWMwRKkxU5+79rV6eXlh8ODByM3NNfp4R/29IjIXe07JpVy8eBG33HIL9u3bh4yMDNx+++1mP3bixImIiorC4sWLsXnzZixYsACBgYF47733cPPNN+OVV17BJ598gtmzZ+P6669HbGwsAM3/XMaNG4fdu3fj4YcfRlRUFA4fPow33ngDJ06c0BtLuWLFCkRHR2PcuHHw8PDAV199hccffxwNDQ1ISUnRa09BQQGSk5Mxbdo0TJkyBf/73/8wdepUDBw4ENHR0QA0wXrRokV48MEHMXjwYFRVVWH//v04cOAARo0aZfK1fvnll/Dy8kJycrIF767l6urqMHr0aNTW1mL69Ono1q0bSktL8fXXX6OiogJ+fn746KOPdO1/+OGHAQA9e/YEoBkTe+ONN0IQBDzxxBNQKBTYsmULpk2bhqqqKqSlpemd76WXXoJMJsPs2bNRW1vbbM/b+fPnMWbMGCQmJmLChAnIyMjAv//9b/Tt21fX037x4kXcfPPNKCsrQ2pqKrp164a1a9di165dZr3+yZMnY82aNdiwYQOeeOIJ3fZz585h27ZtmDRpEry8vIw+9uzZs/jXv/4FhUKBOXPmwN/fH0VFRcjMzDTr3E3t2LEDv//+O+6//35069YNR44cwfvvv48jR44gLy8PgiCY/VzLli1DdXW13rY33ngDBw8exFVXXQVAM2zk+++/x1133QWlUomioiKsWLECcXFxOHr0KDp27IjY2FjMmDEDb775Jp599llERUUBgO5nU5cvX0ZcXBwKCgrwxBNPIDQ0FJ999hmmTp2KiooKpKam6h2/du1aXLhwAY888ggEQcCrr76KxMRE/P777+jQoYMlb5/OlStX8Ndffxls9/b2NvlZNmfatGlYvXo1brnlFjz44IOor69Hbm4u8vLyMGjQILOf54MPPsAjjzyCoUOHIi0tDb///jvGjRuHwMBAqFQq3XGO/HtFZDaRyAWsWrVKBCD26NFD7NChg7hp0yazHzt37lwRgPjwww/rttXX14tKpVIUBEFcvHixbvv58+dFLy8vccqUKbptH330kejm5ibm5ubqPe+7774rAhD37Nmj23bp0iWD848ePVoMCwvT29ajRw8RgJiTk6PbdvbsWVEul4uzZs3Sbevfv7942223mf1atQICAsT+/fubffzw4cPF4cOH6+5r3+/CwkK943bt2iUCEHft2iWKoij+/PPPIgDxs88+a/b5vb299d5TrWnTpolBQUHiX3/9pbf9rrvuEv38/HTvp/a8YWFhBu9x0zZpXw8A8cMPP9Rtq62tFbt16yYmJSXpti1dulQEoPf7dPnyZbF3794Gz2lMfX29GBQUJA4ZMkRvu/Z3Y9u2bbptTd/Tzz//XAQg7tu3z+TzG3ttoiiKhYWFIgBx1apVum3GfvfWrVtn8Htm7LNt+vk3tWHDBhGA+OKLLzZ7vh9++MHgff/ss89MvpdNz7ts2TIRgPjxxx/rttXV1YlDhgwRO3XqJFZVVem9/quuuko8d+6c7tgvvvhCBCB+9dVXJl9Lc7T/Lo3dFi1aZLLdWlOmTBF79Oihu//dd9+JAMQZM2YYHNvQ0KB33sb/Ppp+7nV1dWKXLl3Ea6+9VqytrdUd9/7774sA9NriyL9XRObiZX1yKX/++Sc8PT31egrM9eCDD+r+293dHYMGDYIoipg2bZpuu7+/P3r16oXff/9dt+2zzz5DVFQUevfujb/++kt3u/nmmwFAr5etcc9KZWUl/vrrLwwfPhy///677jK3Vp8+fRATE6O7r1AoDM7t7++PI0eOID8/36LXWlVVBR8fH4se0xp+fn4AgG3btuHSpUsWPVYURWzcuBFjx46FKIp67+3o0aNRWVmJAwcO6D1mypQpZvdederUSW/soEwmw+DBg/Xe361btyI4OFh36R0APD098dBDD5l1Dnd3d9x111344Ycf9C5nr127Fl27dsWIESNMPtbf3x8A8PXXX+PKlStmna85jd+Xmpoa/PXXX7jxxhsBwOB9tMTRo0fxwAMPICEhQW8oSOPzXblyBX///TfCw8Ph7+/f6vN988036NatGyZNmqTb1qFDB8yYMQPV1dXIzs7WO37ixIkICAjQ3df+e2r8GVvqhhtuwI4dOwxujdtkro0bN0IQBMydO9dgnyU92fv378fZs2fx6KOP6l0tmDp1qu7foJY
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 800x600 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 800x600 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 800x600 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAqcAAAIjCAYAAAA+xLLKAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAACE/0lEQVR4nO3deVhUZf8G8PsAMiCy6qjEjAICirhkmqUGQmpavUoBamalZYtpCi6V9VZqaVpmSWVW1mu2uIVoi7kni5apuVSiCQaChEkp4AbIcH5/zG8mhpmBGZjlzHB/rouL5pwzc545Y3rPc57n+wiiKIogIiIiIpIAF3s3gIiIiIhIg+GUiIiIiCSD4ZSIiIiIJIPhlIiIiIgkg+GUiIiIiCSD4ZSIiIiIJIPhlIiIiIgkg+GUiIiIiCSD4ZSIiIiIJIPhlIiMio2NRWxsrL2b0SQZGRkQBAEZGRn2bkqDPvnkEwiCgIKCAsm1w16fvyP/uatr3rx5EAShWc/9+++/LdwqywoODsZ//vOfRo8TBAHz5s2zfoPIKTCckkPT/IN66NAhne3l5eXo378/PDw8sG3bNju1Trr++usvzJ49G926dUPr1q3h5eWFvn37YsGCBSgrK7NZO1599VVs3rzZZuezhVGjRqF169a4dOmS0WPGjx8Pd3d3/PPPPzZsmbTk5ORg3rx5dg/lpggODoYgCBg6dKjB/StXroQgCAb/LiIi8zGcktOpqKjAHXfcgV9++QWbNm3CiBEj7N0kSTl48CB69OiB5cuXIzo6Gm+++SaWLl2KPn36YPHixRgzZozN2mLNcBoTE4Nr164hJibGKq9vzPjx43Ht2jVs2rTJ4P6rV6/iq6++wogRI9C2bVs8+OCDuHbtGjp37mzTdppix44d2LFjh1VeOycnB/PnzzcYTq153qby8PDAnj17cO7cOb19X3zxBTw8PPS2v/DCC7h27Zotmid5165dwwsvvGDvZpCDYDglp3Lp0iUMHz4cR48excaNG3HnnXfau0mSUlZWhnvvvReurq44cuQIVq5cicmTJ2Py5Mn46KOPcPr0aZuHOUurrKxEbW0tXFxc4OHhARcX2/41N2rUKHh7e2PNmjUG93/11Ve4cuUKxo8fDwBwdXWFh4dHk2//WpO7uzvc3d1bzHkbMmjQILRp0wbr16/X2X727FlkZ2fj7rvv1nuOm5ubwdDaEnl4eMDNzc3ezSAHwXBKTuPy5csYMWIEDh8+jI0bNxr8x6IuzZiuU6dO4YEHHoCvry/kcjlefPFFiKKIoqIixMfHw8fHBx07dsTSpUv1XqOqqgpz585FWFgYZDIZlEolnnnmGVRVVekct2rVKtx+++1o3749ZDIZunfvjhUrVui9nmb81t69e7XDEkJDQ/Hpp5/qHHf9+nXMnz8f4eHh8PDwQNu2bXHbbbdh586dDb7nDz74AMXFxXjzzTfRrVs3vf0dOnRosHfD2PhIQ+M7c3NzkZiYiI4dO8LDwwMKhQL33XcfysvLAajHoF25cgWrV6/W3hKdOHGi9vnFxcV45JFH0KFDB8hkMkRFReF///ufwfOuW7cOL7zwAoKCgtC6dWtUVFQYbFNsbCx69OiBnJwcxMXFoXXr1ggKCsLrr7+u917PnDmDUaNGwcvLC+3bt8eMGTOwffv2Rsexenp6IiEhAbt378b58+f19q9Zswbe3t4YNWqU0Wt66NAhDB8+HO3atYOnpydCQkLwyCOPNHi9AaCgoACCIOCTTz7Rbvvll18wceJEhIaGwsPDAx07dsQjjzxi0pCC+mM/Nbe3Df1o2nLmzBlMmTIFXbt2haenJ9q2bYvRo0frvL9PPvkEo0ePBgDExcXpvYahMafnz5/HpEmT0KFDB3h4eKB3795YvXq1wff/xhtv4MMPP0SXLl0gk8lw88034+DBg42+34Z4eHggISFB70vH2rVr4e/vj+HDh+s9x9CYU0EQ8NRTT2Hz5s3o0aOH9s+2KcOPzpw5g7CwMPTo0QN//fUXAOCPP/7A6NGjERAQgNatW+PWW2/Fli1btM8RRRHt2rXDzJkztdtqa2vh5+cHV1dXnWE8r732Gtzc3HD58mUAwLlz5/Dwww9DoVBAJpMhMDAQ8fHxjQ7FWL16Ndzc3PD000/rvG+OOSVT8WsMOYUrV67gzjvvxMGDB5GWlmbSAH2NsWPHIjIyEosXL8aWLVuwYMECBAQE4IMPPsDtt9+O1157DV988QVmz56Nm2++WduzWFtbi1GjRmHv3r14/PHHERkZiV9//RVvvfUWTp06pXO7esWKFYiKisKoUaPg5uaGb775BlOmTEFtbS2mTp2q0568vDwkJSVh0qRJmDBhAv73v/9h4sSJ6Nu3L6KiogCo/9FbtGgRHn30UfTv3x8VFRU4dOgQDh8+jGHDhhl9r19//TU8PT2RlJRkxtU1X3V1NYYPH46qqipMmzYNHTt2RHFxMb799luUlZXB19cXn332mbb9jz/+OACgS5cuANRjYm+99VbtP+RyuRxbt27FpEmTUFFRgZSUFJ3zvfLKK3B3d8fs2bNRVVXVYK/bxYsXMWLECCQkJGDMmDFIS0vDs88+i549e2p72q9cuYLbb78dJSUlSE5ORseOHbFmzRrs2bPHpPc/fvx4rF69Ghs2bMBTTz2l3X7hwgVs374d48aNg6enp8Hnnj9/HnfccQfkcjnmzJkDPz8/FBQUID093aRz17dz50788ccfePjhh9GxY0ccP34cH374IY4fP479+/eb1WO7bNkybXDReOutt3D06FG0bdsWgHrYyA8//ID77rsPCoUCBQUFWLFiBWJjY5GTk4PWrVsjJiYG06dPx9tvv43nn38ekZGRAKD9Xd+1a9cQGxuLvLw8PPXUUwgJCcGXX36JiRMnoqysDMnJyTrHr1mzBpcuXcITTzwBQRDw+uuvIyEhAX/88QdatWplzuXTcf/99+OOO+7A6dOntX9W16xZg6SkJLNed+/evUhPT8eUKVPg7e2Nt99+G4mJiSgsLNRex/pOnz6N22+/HQEBAdi5cyfatWuHv/76CwMHDsTVq1cxffp0tG3bFqtXr8aoUaOQlpaGe++9F4IgYNCgQcjKytK+1i+//ILy8nK4uLhg37592i/y2dnZ6NOnD9q0aQMASExMxPHjxzFt2jQEBwfj/Pnz2LlzJwoLCxEcHGywnR9++CEmT56M559/HgsWLDD5mhDpEIkc2KpVq0QAYufOncVWrVqJmzdvNvm5c+fOFQGIjz/+uHZbTU2NqFAoREEQxMWLF2u3X7x4UfT09BQnTJig3fbZZ5+JLi4uYnZ2ts7rvv/++yIAcd++fdptV69e1Tv/8OHDxdDQUJ1tnTt3FgGIWVlZ2m3nz58XZTKZOGvWLO223r17i3fffbfJ71XD399f7N27t8nHDx48WBw8eLD2seZ65+fn6xy3Z88eEYC4Z88eURRF8ciRIyIA8csvv2zw9b28vHSuqcakSZPEwMBA8e+//9bZft9994m+vr7a66k5b2hoqN41rt8mzfsBIH766afabVVVVWLHjh3FxMRE7balS5eKAHT+PF27dk3s1q2b3msaUlNTIwYGBooDBgzQ2a75s7F9+3bttvrXdNOmTSIA8eDBg0Zf39B7E0VRzM/PFwGIq1at0m4z9Gdv7dq1en/ODH229T//+jZs2CACEF9++eUGz/fjjz/qXfcvv/zS6LWsf95ly5aJAMTPP/9cu626ulocMGCA2KZNG7GiokLn/bdt21a8cOGC9tivvvpKBCB+8803Rt9LQzp37izefffdYk1NjdixY0fxlVdeEUVRFHNyckQAYmZmpvb61f3cNH/H1AVAdHd3F/Py8rTbjh07JgIQ33nnHb3nlpaWiidOnBBvuOEG8eabb9Z5XykpKSIAnb+DLl26JIaEhIjBwcGiSqUSRVEUlyxZIrq6umqv09tvvy127txZ7N+/v/jss8+KoiiKKpVK9PPzE2fMmCGKovrvPADikiVLTLo2oiiKqampoiAI2utT/33PnTu3wdci0uBtfXIKf/31Fzw8PKBUKs1+7qOPPqr9b1d
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 800x600 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"\n",
|
||
|
|
"clusters, centroids = k_means(data, k, euclidean_distance, startCentroids)\n",
|
||
|
|
"\n",
|
||
|
|
"# Wizualizacja\n",
|
||
|
|
"plt.figure(figsize=(8, 6))\n",
|
||
|
|
"colors = ['r', 'g', 'b', 'y']\n",
|
||
|
|
"for i, cluster in enumerate(clusters):\n",
|
||
|
|
" cluster = np.array(cluster)\n",
|
||
|
|
" plt.scatter(cluster[:, 0], cluster[:, 1], c=colors[i], label=f'Cluster {i+1}')\n",
|
||
|
|
"plt.scatter(centroids[:, 0], centroids[:, 1], c='black', marker='X', s=100, label='Centroids')\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"plt.title(\"K-means Clustering Visualization, Euclidean\")\n",
|
||
|
|
"plt.xlabel(\"X coordinate\")\n",
|
||
|
|
"plt.ylabel(\"Y coordinate\")\n",
|
||
|
|
"plt.show()\n",
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"clusters, centroids = k_means(data, k, euclidean2_distance, startCentroids)\n",
|
||
|
|
"\n",
|
||
|
|
"# Wizualizacja\n",
|
||
|
|
"plt.figure(figsize=(8, 6))\n",
|
||
|
|
"colors = ['r', 'g', 'b', 'y']\n",
|
||
|
|
"for i, cluster in enumerate(clusters):\n",
|
||
|
|
" cluster = np.array(cluster)\n",
|
||
|
|
" plt.scatter(cluster[:, 0], cluster[:, 1], c=colors[i], label=f'Cluster {i+1}')\n",
|
||
|
|
"plt.scatter(centroids[:, 0], centroids[:, 1], c='black', marker='X', s=100, label='Centroids')\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"plt.title(\"K-means Clustering Visualization, Euclidean^2\")\n",
|
||
|
|
"plt.xlabel(\"X coordinate\")\n",
|
||
|
|
"plt.ylabel(\"Y coordinate\")\n",
|
||
|
|
"plt.show()\n",
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"clusters, centroids = k_means(data, k, manhattan_distance, startCentroids)\n",
|
||
|
|
"\n",
|
||
|
|
"# Wizualizacja\n",
|
||
|
|
"plt.figure(figsize=(8, 6))\n",
|
||
|
|
"colors = ['r', 'g', 'b', 'y']\n",
|
||
|
|
"for i, cluster in enumerate(clusters):\n",
|
||
|
|
" cluster = np.array(cluster)\n",
|
||
|
|
" plt.scatter(cluster[:, 0], cluster[:, 1], c=colors[i], label=f'Cluster {i+1}')\n",
|
||
|
|
"plt.scatter(centroids[:, 0], centroids[:, 1], c='black', marker='X', s=100, label='Centroids')\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"plt.title(\"K-means Clustering Visualization, Manhattan\")\n",
|
||
|
|
"plt.xlabel(\"X coordinate\")\n",
|
||
|
|
"plt.ylabel(\"Y coordinate\")\n",
|
||
|
|
"plt.show()\n",
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"clusters, centroids = k_means(data, k, minkowski_distance, startCentroids)\n",
|
||
|
|
"\n",
|
||
|
|
"# Wizualizacja\n",
|
||
|
|
"plt.figure(figsize=(8, 6))\n",
|
||
|
|
"colors = ['r', 'g', 'b', 'y']\n",
|
||
|
|
"for i, cluster in enumerate(clusters):\n",
|
||
|
|
" cluster = np.array(cluster)\n",
|
||
|
|
" plt.scatter(cluster[:, 0], cluster[:, 1], c=colors[i], label=f'Cluster {i+1}')\n",
|
||
|
|
"plt.scatter(centroids[:, 0], centroids[:, 1], c='black', marker='X', s=100, label='Centroids')\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"plt.title(\"K-means Clustering Visualization, Minkowski\")\n",
|
||
|
|
"plt.xlabel(\"X coordinate\")\n",
|
||
|
|
"plt.ylabel(\"Y coordinate\")\n",
|
||
|
|
"plt.show()\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"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": "3.13.0"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 4
|
||
|
|
}
|