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‎charpter17_kmeans/kmeans.ipynb‎

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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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"### kmeans"
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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": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"from sklearn.cluster import KMeans"
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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": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[0, 2],\n",
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" [0, 0],\n",
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" [1, 0],\n",
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" [5, 0],\n",
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" [5, 2]])"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"X = np.array([[0,2],[0,0],[1,0],[5,0],[5,2]])\n",
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"X"
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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": 14,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[1 1 1 0 0]\n"
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]
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}
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],
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"source": [
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"from sklearn.cluster import KMeans\n",
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"kmeans = KMeans(n_clusters=2, random_state=0).fit(X)\n",
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"print(kmeans.labels_)"
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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": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([1, 0])"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"kmeans.predict([[0, 0], [12, 3]])"
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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": 5,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[5. , 1. ],\n",
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" [0.33333333, 0.66666667]])"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"kmeans.cluster_centers_"
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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": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"5.0\n"
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]
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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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"# 定义欧式距离\n",
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"def euclidean_distance(x1, x2):\n",
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" distance = 0\n",
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" # 距离的平方项再开根号\n",
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" for i in range(len(x1)):\n",
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" distance += pow((x1[i] - x2[i]), 2)\n",
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" return np.sqrt(distance)\n",
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"\n",
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"print(euclidean_distance(X[0], X[4]))"
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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": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 定义中心初始化函数\n",
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"def centroids_init(k, X):\n",
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" m, n = X.shape\n",
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" centroids = np.zeros((k, n))\n",
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" for i in range(k):\n",
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" # 每一次循环随机选择一个类别中心\n",
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" centroid = X[np.random.choice(range(m))]\n",
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" centroids[i] = centroid\n",
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" return centroids"
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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": 8,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 定义样本的最近质心点所属的类别索引\n",
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"def closest_centroid(sample, centroids):\n",
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" closest_i = 0\n",
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" closest_dist = float('inf')\n",
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" for i, centroid in enumerate(centroids):\n",
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" # 根据欧式距离判断，选择最小距离的中心点所属类别\n",
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" distance = euclidean_distance(sample, centroid)\n",
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" if distance < closest_dist:\n",
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" closest_i = i\n",
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" closest_dist = distance\n",
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" return closest_i"
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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": 9,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 定义构建类别过程\n",
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"def build_clusters(centroids, k, X):\n",
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" clusters = [[] for _ in range(k)]\n",
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" for x_i, x in enumerate(X):\n",
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" # 将样本划分到最近的类别区域\n",
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" centroid_i = closest_centroid(x, centroids)\n",
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" clusters[centroid_i].append(x_i)\n",
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" return clusters"
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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": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 根据上一步聚类结果计算新的中心点\n",
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"def calculate_centroids(clusters, k, X):\n",
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" n = X.shape[1]\n",
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" centroids = np.zeros((k, n))\n",
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" # 以当前每个类样本的均值为新的中心点\n",
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" for i, cluster in enumerate(clusters):\n",
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" centroid = np.mean(X[cluster], axis=0)\n",
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" centroids[i] = centroid\n",
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" return centroids"
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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": 11,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 获取每个样本所属的聚类类别\n",
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"def get_cluster_labels(clusters, X):\n",
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" y_pred = np.zeros(X.shape[0])\n",
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" for cluster_i, cluster in enumerate(clusters):\n",
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" for X_i in cluster:\n",
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" y_pred[X_i] = cluster_i\n",
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" return y_pred"
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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": 12,
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"metadata": {},
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"outputs": [],
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"source": [
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"# 根据上述各流程定义kmeans算法流程\n",
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"def kmeans(X, k, max_iterations):\n",
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" # 1.初始化中心点\n",
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" centroids = centroids_init(k, X)\n",
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" # 遍历迭代求解\n",
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" for _ in range(max_iterations):\n",
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" # 2.根据当前中心点进行聚类\n",
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" clusters = build_clusters(centroids, k, X)\n",
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" # 保存当前中心点\n",
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" prev_centroids = centroids\n",
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" # 3.根据聚类结果计算新的中心点\n",
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" centroids = calculate_centroids(clusters, k, X)\n",
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" # 4.设定收敛条件为中心点是否发生变化\n",
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" diff = centroids - prev_centroids\n",
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" if not diff.any():\n",
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" break\n",
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" # 返回最终的聚类标签\n",
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" return get_cluster_labels(clusters, X)"
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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": 13,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[0. 0. 0. 1. 1.]\n"
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]
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}
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],
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"source": [
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"# 测试数据\n",
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"X = np.array([[0,2],[0,0],[1,0],[5,0],[5,2]])\n",
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"# 设定聚类类别为2个，最大迭代次数为10次\n",
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"labels = kmeans(X, 2, 10)\n",
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"# 打印每个样本所属的类别标签\n",
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"print(labels)"
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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": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.3"
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},
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"toc": {
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"base_numbering": 1,
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"nav_menu": {},
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"number_sections": true,
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"sideBar": true,
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"skip_h1_title": false,
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"title_cell": "Table of Contents",
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"title_sidebar": "Contents",
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"toc_cell": false,
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"toc_position": {},
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"toc_section_display": true,
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"toc_window_display": false
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}

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