吴恩达-机器学习2022版 k-means聚类算法实现整理

1.核心函数四个：

import numpy as np
import matplotlib.pyplot as plt

1.find_closest_centroids ：寻找最近的质心

#寻找最近的质心
def find_closest_centroids(X, centroids):

    K = centroids.shape[0]
    idx = np.zeros(X.shape[0], dtype=int)
    
    for i in range(X.shape[0]):
        distance = []        
        for j in range(K):         
            norm_ij = np.linalg.norm(X[i] - centroids[j])
            distance.append(norm_ij)           
        idx[i] = np.argmin(distance)
   
    return idx

2.compute_centroids ：迭代重新计算质心

def compute_centroids(X, idx, K):
    
    m, n = X.shape
    centroids = np.zeros((K, n))   
    
    for k in range(K):
        points = X[idx == k] 
        centroids[k] = np.mean(points, axis = 0)
    
    return centroids

3.kMeans_init_centroids ：随机初始化质心

def kMeans_init_centroids(X, K):
    
    randidx = np.random.permutation(X.shape[0])
    centroids = X[randidx[:K]]
    
    return centroids

4.run_kMeans ：执行k-means算法

def run_kMeans(X, initial_centroids, max_iters=10, plot_progress=False):
    
    m, n = X.shape
    K = initial_centroids.shape[0]
    centroids = initial_centroids
    previous_centroids = centroids    
    idx = np.zeros(m)
    
    for i in range(max_iters):     
        print("K-Means iteration %d/%d" % (i, max_iters-1))       
        idx = find_closest_centroids(X, centroids)      
        if plot_progress:
            plot_progress_kMeans(X, centroids, previous_centroids, idx, K, i)
            previous_centroids = centroids
            
        centroids = compute_centroids(X, idx, K)
    plt.show() 
    return centroids, idx

2.实例：使用k-means算法对图片像素进行压缩 255色压缩到1色

1.代码

#进行图片压缩
#读取图片
original_img = plt.imread('bird_small.png')
#数据标准化 使像素值全部落在0-1之间
original_img = original_img / 255

X_img = np.reshape(original_img, (original_img.shape[0] * original_img.shape[1], 3))
K = 16                       
max_iters = 10               

initial_centroids = kMeans_init_centroids(X_img, K) 
centroids, idx = run_kMeans(X_img, initial_centroids, max_iters) 
X_recovered = centroids[idx, :] 
X_recovered = np.reshape(X_recovered, original_img.shape) 

fig, ax = plt.subplots(1,2, figsize=(8,8))
plt.axis('off')

#展示原图片
ax[0].imshow(original_img*255)
ax[0].set_title('Original')
ax[0].set_axis_off()

#展示压缩后图片
ax[1].imshow(X_recovered*255)
ax[1].set_title('Compressed with %d colours'%K)
ax[1].set_axis_off()