Python实现K-Means聚类算法

import scipy.io as sio  # 加载mat文件
import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd
import numpy as np
from sklearn.cluster import KMeans

# 生成随机的k个中心,请使用sample(k)
def random_init(data, k):
    # data：数据集 k：聚类中心个数
    # 返回 k 个聚类中心并转换成array数组
    # ********** Begin **********
    return data.sample(k).values
    # ********** End **********

# 单个找寻聚类
def find_cluster(x, centroids):
    # x:待聚类点坐标  centroids:中心坐标
    # ********** Begin **********
    distances = np.apply_along_axis(func1d=np.linalg.norm, axis=1, arr=centroids - x)
    # ********** End **********
    return np.argmin(distances)

# 集体data聚类标签
def assign_cluster(data, centroids):
    return np.apply_along_axis(lambda x: find_cluster(x, centroids), axis=1, arr=data.values)

#  data中增加一列聚类标签C
def combineDataC(data, C):
    dataC = data.copy()
    dataC['C'] = C
    return dataC

# 新中心点，同时去掉C， 再转换成array数组
def newCentroids(data, C):
    dataC = combineDataC(data, C)
    return dataC.groupby('C', as_index=False).mean().sort_values(by='C').drop('C', axis=1).values

# 损失函数
def cost(data, centroids, C):
    # data:数据集 centroids:中心坐标 C:聚类标签
    m = data.shape[0]  # 样本量
    dataCentroids = centroids[C]  # 各行的中心坐标
    # ********** Begin **********
    distances = np.apply_along_axis(func1d=np.linalg.norm, axis=1, arr=data.values - dataCentroids)
    # ********** End **********
    return distances.sum() / m

# kmeans通道，运行一次
def kMeansIter(data, k, epoch=100, tol=0.0001):
    # 生成最初的中心坐标
    centroids = random_init(data, k)

    costProgress = []  # 用来存放递归聚类的每次损失
    # 分配聚类标签
    for i in range(epoch):
        C = assign_cluster(data, centroids)
        centroids = newCentroids(data, C)
        costProgress.append(cost(data, centroids, C))

        if len(costProgress) > 1:
            if np.abs(costProgress[-1] - costProgress[-2]) / costProgress[-1] < tol:
                break

    return C, centroids, costProgress[-1]

# 每个k运行n_init次，套用kmeans通道
def kMeans(data, k, epoch=100, n_init=10):
    tries = np.array([kMeansIter(data, k) for _ in range(n_init)])
    leasrCostIndex = np.argmin(tries[:, -1])
    return tries[leasrCostIndex]