吴恩达《机器学习》——第七次作业：k-means算法

偏执的太偏执、 2022-01-27 06:37 261阅读 0赞

1.  2D-kmeans算法

import numpy as np
    import pandas as pd
    import matplotlib.pyplot as plt
    
    import seaborn as sb
    from scipy.io import loadmat
    
    def find_closet_centroids(X, centroids):
        '''将每个特征计算属于那个特征'''
        m = X.shape[0]
        k = centroids.shape[0]
        idx = np.zeros(m)
    
        for i in range(m):
    
            min_dist = 1000000
            for j in range(k):
    
                dist = np.sum((X[i, :] - centroids[j, :]) ** 2)
                if dist < min_dist:
                    min_dist = dist
                    idx[i] = j
    
        return idx
    
    
    
    def compute_centroids(X, idx, k):
        '''更新聚类中心'''
        m, n = X.shape
        centroids = np.zeros((k, n))
    
        for i in range(k):
    
            indices = np.where(idx == i)
            centroids[i, :] = (np.sum(X[indices, :], axis=1) / len(indices[0])).ravel()
    
        return centroids
    
    def run_one_kmeans(X, initial_centroids, max_iters):
        '''运行k-means均值算法进行聚类'''
        m, n = X.shape
        k = initial_centroids.shape[0]
        idx = np.zeros(m)
        centroids = initial_centroids
    
        for i in range(max_iters):
            idx = find_closet_centroids(X, centroids)
            centroids = compute_centroids(X, idx, k)
    
        return idx, centroids
    
    def init_centroids(X, k):
        '''随机初始化聚类中心'''
        m, n = X.shape
        centroids = np.zeros((k, n))
        idx = np.random.randint(0, m, k)
    
        for i in range(k):
            centroids[i, :] = X[idx[i], :]
        return centroids
    
    
    
    def run_all_kmeans(X, k, n_init, max_iter):
        '''kmeans算法'''
        min_dist = 1000000
        m, n = X.shape
        result_centroids = np.zeros((k, n))
        result_idx = np.zeros(m)
        cnt = 0
        for i in range(n_init):
            initial_centroids = init_centroids(X, k)        #
            #print(initial_centroids)
            idx, centroids = run_one_kmeans(X, initial_centroids, max_iter)
            dist = 0
            for j in range(m):
                dist += np.sum((X[j, :] - centroids[int(idx[j]), :]) ** 2) / len(X)
            if dist < min_dist:
                min_dist = dist
                result_idx = idx
                result_centroids = centroids
                cnt = i
        #print(cnt)
    
        return result_idx, result_centroids
    
    
    
    
    data = loadmat('data/ex7data2.mat')
    X = data['X']
    
    
    idx, centroids = run_all_kmeans(X, 3, 30, 10)
    
    cluster1 = X[np.where(idx == 0)[0], :]
    cluster2 = X[np.where(idx == 1)[0], :]
    cluster3 = X[np.where(idx == 2)[0], :]
    
    fig, ax = plt.subplots(figsize=(12, 8))
    ax.scatter(cluster1[:, 0], cluster1[:, 1], s=30, color='r', label='Cluster 1')
    ax.scatter(cluster2[:, 0], cluster2[:, 1], s=30, color='g', label='Cluster 2')
    ax.scatter(cluster3[:, 0], cluster3[:, 1], s=30, color='b', label='Cluster 3')
    ax.legend()
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0NoZXJpc2hfeA_size_16_color_FFFFFF_t_70]

1.  k-means应用：图像压缩  
    图像压缩前：  
    ![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0NoZXJpc2hfeA_size_16_color_FFFFFF_t_70 1]

from IPython.display import Image
    import numpy as np
    import pandas as pd
    import matplotlib.pyplot as plt
    
    import seaborn as sb
    
    from k_means_and_PCA.kmeans_2D import run_all_kmeans
    
    from scipy.io import loadmat
    
    Image(filename='data/bird_small.png')
    
    image_data = loadmat('data/bird_small.mat')
    
    A = image_data['A'] / 255
    
    
    X = np.reshape(A, (A.shape[0] * A.shape[1], A.shape[2]))
    
    idx, centroids = run_all_kmeans(X, 16, 10, 10)
    
    X_recovered = centroids[idx.astype(int), :]
    X_recovered = np.reshape(X_recovered, (A.shape[0], A.shape[1], A.shape[2]))
    X_recovered *= 255
    plt.imshow(X_recovered.astype(int))
    plt.show()

图像压缩处理后 ：  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0NoZXJpc2hfeA_size_16_color_FFFFFF_t_70 2]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0NoZXJpc2hfeA_size_16_color_FFFFFF_t_70]: /images/20220127/af8f1ec03b7d4bfc9f273ca7544a22ac.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0NoZXJpc2hfeA_size_16_color_FFFFFF_t_70 1]: /images/20220127/c9cdad0402764ad9a16d3fe9eb10e4ff.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0NoZXJpc2hfeA_size_16_color_FFFFFF_t_70 2]: /images/20220127/c10213490c3f4320b19b293d4cd2f99d.png