【K-means算法】{1} —— 使用Python实现K-means算法并处理Iris数据集

此处基于K-means算法处理Iris数据集

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Kmeans.py模块：

import numpy as np


class KMeansClassifier():

	"""初始化KMeansClassifier类"""
    def __init__(self, k=3, initCent='random', max_iter=500):
        # 类的成员数据(变量前用下划线)
        self._k = k # 中心点
        self._initCent = initCent # 生成初始中心点
        self._max_iter = max_iter # 最大迭代次数
        self._clusterAssment = None # 点分配结果
        self._labels = None
        self._sse = None # 误差平方和
        
        
    def _calEDist(self, arrA, arrB):
        """计算欧氏距离，参数为一维数组"""
        return np.math.sqrt(sum(np.power(arrA-arrB, 2)))
    
    
    def _calMDist(self, arrA, arrB):
        """计算曼哈顿距离，参数为一维数组"""
        return sum(np.abs(arrA-arrB))


    def _randCent(self, data_X, k):
        """随机选取k个质心，返回一个k*n的质心矩阵"""
        n = data_X.shape[1] # 特征的维度
        centroids = np.empty((k,n)) # 使用numpy生成一个k*n的矩阵，用于存储质心
        for j in range(n):
            minJ = min(data_X[:, j])
            rangeJ = float(max(data_X[:, j] - minJ))
            centroids[:, j] = (minJ + rangeJ * np.random.rand(k, 1)).flatten() # 使用flatten函数展平嵌套列表(nested list)
        return centroids
    
    
    def fit(self, data_X):
        """训练模型，参数为m*n维的矩阵"""
        if not isinstance(data_X, np.ndarray):
            data_X = np.asarray(data_X)

        m = data_X.shape[0] # 样本的个数
        self._clusterAssment = np.zeros((m,2)) # 一个m*2维矩阵，矩阵第一列存储样本点所属的族的索引值，第二列存储该点与所属族的质心的平方误差
        
        if self._initCent == 'random':
            self._centroids = self._randCent(data_X, self._k)
            
        clusterChanged = True
        for _ in range(self._max_iter):
            clusterChanged = False
            for i in range(m): # 将每个样本点分配到离它最近的质心所属的族
                minDist = np.inf # 首先将minDist置为一个无穷大的数
                minIndex = -1 # 将最近质心的下标置为-1
                for j in range(self._k): # k次迭代用于寻找最近的质心
                    arrA = self._centroids[j,:]
                    arrB = data_X[i,:]
                    distJI = self._calEDist(arrA, arrB) # 计算误差值
                    if distJI < minDist:
                        minDist = distJI
                        minIndex = j
                if self._clusterAssment[i, 0] != minIndex or self._clusterAssment[i, 1] > minDist**2:
                    clusterChanged = True
                    self._clusterAssment[i,:] = minIndex, minDist**2
            if not clusterChanged: # 若所有样本点所属的族都不改变,则已收敛,结束迭代
                break
            # 更新质心，将每个族中的点的均值作为质心
            for i in range(self._k):
                index_all = self._clusterAssment[:,0] # 取出样本所属簇的索引值
                value = np.nonzero(index_all==i) # 取出所有属于第i个簇的索引值
                ptsInClust = data_X[value[0]] # 取出属于第i个簇的所有样本点
                self._centroids[i,:] = np.mean(ptsInClust, axis=0) # 计算均值
        
        self._labels = self._clusterAssment[:,0]
        self._sse = sum(self._clusterAssment[:,1])
    
    
    def predict(self, X):
        """根据聚类结果，预测新输入数据所属的簇"""
        if not isinstance(X,np.ndarray):
            X = np.asarray(X)
        
        m = X.shape[0] # m代表样本数量
        preds = np.empty((m,))
        # 将每个样本点分配到离它最近的质心所属的簇
        for i in range(m):
            minDist = np.inf
            for j in range(self._k):
                distJI = self._calEDist(self._centroids[j,:], X[i,:])
                if distJI < minDist:
                    minDist = distJI
                    preds[i] = j
        return preds

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test.py模块：

此处的Iris数据集也可以通过调用sklearn引入

import pandas as pd
import numpy as np
from Kmeans import KMeansClassifier
import matplotlib.pyplot as plt


if __name__=="__main__":
    data_X = pd.read_csv(r"iris.csv")
    data_X = data_X.drop(data_X.columns[4], axis=1)
    data_X = np.array(data_X)
    # print(data_X)
    
    # k = 2
    k = 3
    clf = KMeansClassifier(k) # 实例化KMeansClassifier类
    clf.fit(data_X) # 训练模型
    cents = clf._centroids
    labels = clf._labels
    sse = clf._sse
    colors = ['r','y','b']
    for i in range(k):
        index = np.nonzero(labels==i)[0]
        # print(index)
        x0 = data_X[index, 0]
        x1 = data_X[index, 1]
        y_i = i
        for j in range(len(x0)):
            plt.scatter(x0[j], x1[j], color=colors[i])
        plt.scatter(cents[i,0], cents[i,1], marker='x', color=colors[i], linewidths=7)
    
    # plt.title("SSE={:.2f}".format(sse))
    print("误差平方和为: ", sse)
    plt.axis([4.2,8.2,1.8,4.6])
    outname = "./Kmeans" + ".png"
    plt.savefig(outname)
    plt.show()

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Output：

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当K选取为2时：

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参考资料：《机器学习实战》