kmeans++聚类聚成这样合理吗

Question

kmeans++聚类聚成这样合理吗
聚类的算法代码如下

class Kmeans:
    def __init__(self, k, threshold=1e-5):
        self.k = k
        self.threshold = threshold
    
    def centroid_init(self,X):
        centroids = []
        centroids.append(X[np.random.choice(X.shape[0])])
        for i in range(self.k-1):
            D = []
            for x in X:
                D.append(np.min([np.linalg.norm(x - c) for c in centroids]))
            centroids.append(X[np.argmax(D)])
        return np.array(centroids)
                              
    def train(self, X):
        # 初始化聚类中心
        self.centroids = self.centroid_init(X)
        y_pred = np.zeros(shape=(X.shape[0],))
        while True:
            # 涂色
            for i, x in enumerate(X):
                y_pred[i] = self.predict(x)
            
            # 计算新的聚类中心
            new_centroids = self.centroids.copy()
            for i in range(self.k):
                new_centroids[i] = X[y_pred==i].mean()
            
            # 如果聚类中心位置基本没有变化，那么终止
            if np.max(np.abs(new_centroids - self.centroids)) < self.threshold:
                break
            
            # 否则更新聚类中心，重复上述步骤
            self.centroids = new_centroids
        return y_pred

    def predict(self, x):
        dis = []
        # 计算每个样本与中心的距离
        for c in self.centroids:
            dis.append(np.linalg.norm(x - c))
        # 将样本索引添加到距离最小的中心对应的分类中
        return np.argmin(dis)

下图左边是原数据分布，右边是上面的算法生成的聚类分布

Answer 1

唉，终究是解决了，求均值的时候X[y_pred==i].mean()没加axis=0
顺便把新实现的代码贴一下吧

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs

class Kmeans:
    def __init__(self, k, init='pp-soft', max_iter=300, thresh=1e-5):
        self.k = k
        self.thresh = thresh
        self.max_iter = max_iter
        self.init = init

    def random_centroid_init(self,X):
        # 随机选取K个样本作为聚类中心
        return X[np.random.choice(X.shape[0], size=self.k)]
    
    def max_centroid_init(self,X):
        centroids = []
        centroids.append(X[np.random.choice(X.shape[0])])
        for i in range(self.k-1):
            index = np.argmax([np.min(self.dist(x)) for x in X])
            centroids.append(X[index])
        return np.array(centroids)

    def soft_centroid_init(self,X):
        centroids = []
        centroids.append(X[np.random.choice(X.shape[0])])
        for i in range(self.k-1):
            D = [np.min(self.dist(x)) for x in X]
            number = np.random.choice(int(np.sum(D)))
            for i,d in enumerate(D):
                number -= d
                if number<0:
                    centroids.append(X[i])
                    break
        return np.array(centroids)

    def dist(self, x):
        return [np.linalg.norm(x - c) for c in self.centroids]

    def fit_predict(self, X):
        # 初始化聚类中心
        if self.init == 'random':
            self.centroids = self.random_centroid_init(X)
        elif self.init == 'pp-max':
            self.centroids = self.max_centroid_init(X)
        else:
            self.centroids = self.soft_centroid_init(X)
        for _ in range(self.max_iter):
            # 涂色
            y_pred = np.array([np.argmin(self.dist(x)) for x in X])
            
            # 计算新的聚类中心
            new_centroids = self.centroids.copy()
            for i in range(self.k):
                new_centroids[i] = np.mean(X[y_pred==i],axis=0)
            
            # 如果聚类中心位置基本没有变化，那么终止
            if np.max(np.abs(new_centroids - self.centroids)) < self.thresh:
                break
            
            # 否则更新聚类中心，重复上述步骤
            self.centroids = new_centroids
        return y_pred
    
X, y = make_blobs(n_samples=1000, n_features=2, centers=3)

model = Kmeans(3)
y_pred = model.fit_predict(X)

plt.figure()
plt.subplot(121)
plt.scatter(X[:, 0], X[:, 1], c=y)
plt.subplot(122)
plt.scatter(X[:, 0], X[:, 1], c=y_pred)
plt.show()