python中k-means和k-means++原理及實現

# 定義歐式距離
import numpy as np
def get_distance(x1, x2):
    return np.sqrt(np.sum(np.square(x1-x2)))

import random
# 定義中心初始化函數，中心點選擇的是樣本特征
def center_init(k, X):
    n_samples, n_features = X.shape
    centers = np.zeros((k, n_features))
    selected_centers_index = []
    for i in range(k):
        # 每一次循環隨機選擇一個類別中心,判斷不讓centers重復
        sel_index = random.choice(list(set(range(n_samples))-set(selected_centers_index)))
        centers[i] = X[sel_index]
        selected_centers_index.append(sel_index)
    return centers

# 判斷一個樣本點離哪個中心點近， 返回的是該中心點的索引
## 比如有三個中心點，返回的是0，1，2
def closest_center(sample, centers):
    closest_i = 0
    closest_dist = float('inf')
    for i, c in enumerate(centers):
        # 根據歐式距離判斷，選擇最小距離的中心點所屬類別
        distance = get_distance(sample, c)
        if distance < closest_dist:
            closest_i = i
            closest_dist = distance
    return closest_i

# 定義構建聚類的過程
# 每一個聚類存的內容是樣本的索引，即對樣本索引進行聚類，方便操作
def create_clusters(centers, k, X):
    clusters = [[] for _ in range(k)]
    for sample_i, sample in enumerate(X):
        # 將樣本劃分到最近的類別區域
        center_i = closest_center(sample, centers)
        # 存放樣本的索引
        clusters[center_i].append(sample_i)
    return clusters

# 根據上一步聚類結果計算新的中心點
def calculate_new_centers(clusters, k, X):
    n_samples, n_features = X.shape
    centers = np.zeros((k, n_features))
    # 以當前每個類樣本的均值為新的中心點
    for i, cluster in enumerate(clusters):  # cluster為分類後每一類的索引
        new_center = np.mean(X[cluster], axis=0) # 按列求平均值
        centers[i] = new_center
    return centers

# 獲取每個樣本所屬的聚類類別
def get_cluster_labels(clusters, X):
    y_pred = np.zeros(np.shape(X)[0])
    for cluster_i, cluster in enumerate(clusters):
        for sample_i in cluster:
            y_pred[sample_i] = cluster_i
            #print('把樣本{}歸到{}類'.format(sample_i,cluster_i))
    return y_pred

# 根據上述各流程定義kmeans算法流程
def Mykmeans(X, k, max_iterations,init):
    # 1.初始化中心點
    if init == 'kmeans':
        centers = center_init(k, X)
    else: centers = get_kmeansplus_centers(k, X)
    # 遍歷迭代求解
    for _ in range(max_iterations):
        # 2.根據當前中心點進行聚類
        clusters = create_clusters(centers, k, X)
        # 保存當前中心點
        pre_centers = centers
        # 3.根據聚類結果計算新的中心點
        new_centers = calculate_new_centers(clusters, k, X)
        # 4.設定收斂條件為中心點是否發生變化
        diff = new_centers - pre_centers
        # 說明中心點沒有變化，停止更新
        if diff.sum() == 0:
            break
    # 返回最終的聚類標簽
    return get_cluster_labels(clusters, X)

# 測試執行
X = np.array([[0,2],[0,0],[1,0],[5,0],[5,2]])
# 設定聚類類別為2個，最大迭代次數為10次
labels = Mykmeans(X, k = 2, max_iterations = 10,init = 'kmeans')
# 打印每個樣本所屬的類別標簽
print("最後分類結果",labels)
## 輸出為  [1. 1. 1. 0. 0.]

# 使用sklearn驗證
from sklearn.cluster import KMeans
X = np.array([[0,2],[0,0],[1,0],[5,0],[5,2]])
kmeans = KMeans(n_clusters=2,init = 'random').fit(X)
# 由於center的隨機性，結果可能不一樣
print(kmeans.labels_)

## 得到kmean++中心點
def get_kmeansplus_centers(k, X):
    n_samples, n_features = X.shape
    init_one_center_i = np.random.choice(range(n_samples))
    centers = []
    centers.append(X[init_one_center_i])
    dists = [ 0 for _ in range(n_samples)]

    # 執行
    for _ in range(k-1):
        total = 0
        for sample_i,sample in enumerate(X):
            # 得到最短距離
            closet_i = closest_center(sample,centers)
            d = get_distance(X[closet_i],sample)
            dists[sample_i] = d
            total += d
        total = total * np.random.random()

        for sample_i,d in enumerate(dists): # 輪盤法選出下一個聚類中心
            total -= d
            if total > 0:
                continue
            # 選取新的中心點
            centers.append(X[sample_i])
            break
    return centers

X = np.array([[0,2],[0,0],[1,0],[5,0],[5,2]])
# 設定聚類類別為2個，最大迭代次數為10次
labels = Mykmeans(X, k = 2, max_iterations = 10,init = 'kmeans++')
print("最後分類結果",labels)
## 輸出為  [1. 1. 1. 0. 0.]

# 使用sklearn驗證
X = np.array([[0,2],[0,0],[1,0],[5,0],[5,2]])
kmeans = KMeans(n_clusters=2,init='k-means++').fit(X)
print(kmeans.labels_)