吴恩达《机器学习》——第七次作业：k-means算法

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  1. 2D-kmeans算法

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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

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

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