用Python实现Kmeans算法(未用numpy)

kemans算法

K-means算法是硬聚类算法，是典型的基于原型的目标函数聚类方法的代表，它是数据点到原型的某种距离作为优化的目标函数，利用函数求极值的方法得到迭代运算的调整规则。K-means算法以欧式距离作为相似度测度，它是求对应某一初始聚类中心向量V最优分类，使得评价指标J最小。算法采用误差平方和准则函数作为聚类准则函数。

要求随机取1000个点，其中随机5个为中心点，.求其余995个点与每个中心点的距离距离最小的，将此点和对应的中心点归为一类.类中求平均值作为新的中心点如果新中心点和旧中心点的误差小于某个阈值，停止，否则重复以上操作。

代码实现:

import random
import matplotlib.pyplot as plt
import numpy



class KMeans():

    def __init__(self, k=1):
        '''
        :param k: k代表分类数
        '''
        self.__k = k
        self.__data = []  # 存放原始数据
        self.__pointCenter = []  # 存放中心点，第一次获得的中心点通过随机方式在__data里随机出来
        self.__result = []
        for i in range(k):
            self.__result.append([])  # [[],[],[],[],[]]
            pass
        pass

    def fit(self, data, threshold, times=50000):
        '''
        进行模型训练
        :param data: 训练数据
        :param threshold: 阈值，退出条件
        :return:
        '''
        self.__data = data
        self.randomCenter()
        print(self.__pointCenter)
        centerDistance = self.calPointCenterDistance(self.__pointCenter, self.__data)

        # 对原始数据进行分类，将每个点分到离它最近的中心点
        i = 0
        for temp in centerDistance:
            index = temp.index(min(temp))
            self.__result[index].append(self.__data[i])
            i += 1
            pass
        # 打印分类结果
        # print(self.__result)
        oldCenterPoint = self.__pointCenter
        newCenterPoint = self.calNewPointCenter(self.__result)

        while self.calCenterToCenterDistance(oldCenterPoint, newCenterPoint) > threshold:
            times -= 1
            result = []
            for i in range(self.__k):
                result.append([])
                pass
            # 保存上次的中心点
            oldCenterPoint = newCenterPoint
            centerDistance = self.calPointCenterDistance(newCenterPoint, self.__data)

            # 对原始数据进行分类，将每个点分到离它最近的中心点
            i = 0
            for temp in centerDistance:
                index = temp.index(min(temp))
                result[index].append(self.__data[i])  # result = [[[10,20]]]
                i += 1
                pass

            newCenterPoint = self.calNewPointCenter(result)
            print(self.calCenterToCenterDistance(oldCenterPoint, newCenterPoint))
            self.__result = result
            pass
        self.__pointCenter = newCenterPoint
        return newCenterPoint, self.__result
        pass

    def calCenterToCenterDistance(self, old, new):
        '''
        计算两次中心点之间的距离，求和求均值
        :param old: 上次的中心点
        :param new: 新计算的中心点
        :return:
        '''
        total = 0
        for point1, point2 in zip(old, new):
            total += self.distance(point1, point2)
            pass
        return total / len(old)
        pass

    def calPointCenterDistance(self, center, data):
        '''
        计算每个点和每个中心点之间的距离
        :return:
        '''
        centerDistance = []
        for temp in data:
            centerDistance.append([self.distance(temp, point) for point in center])
            pass
        print(centerDistance)
        return centerDistance
        pass

    def calNewPointCenter(self, result):
        '''
        计算新的中心点
        :param result:
        :return:
        '''
        newCenterPoint = []
        for temp in result:
            # 转置
            temps = [[temp[x][i] for x in range(len(temp))] for i in range(len(temp[0]))]
            point = []
            for t in temps:
                # 对每个维度求和，去平均
                point.append(sum(t) / len(t))  # mean
                pass
            newCenterPoint.append(point)
            pass
        print(newCenterPoint)
        return newCenterPoint
        pass

    def distance(self, pointer1, pointer2):
        '''
        计算两个点之间的距离，支持任意维度，欧式距离
        :param pointer1:
        :param pointer2:
        :return:
        '''
        distance = (sum([(x1 - x2) ** 2 for x1, x2 in zip(pointer1, pointer2)])) ** 0.5
        return distance
        pass

    def randomCenter(self):
        '''
        从原始的__data里随机出最开始进行计算的k个中心点
        :return:
        '''
        while len(self.__pointCenter) < self.__k:
            # 随机一个索引
            index = random.randint(0, len(self.__data) - 1)
            # 判断中心点是否重复，如果不重复，加入中心点列表
            if self.__data[index] not in self.__pointCenter:
                self.__pointCenter.append(self.__data[index])
                pass
            pass
        pass

    pass


if __name__ == "__main__":
    data = [[random.randint(1, 100), random.randint(1, 100)] for i in range(1000)]
    for i in range(10):
        kmeans = KMeans(k=5)
        centerPoint, result = kmeans.fit(data, 0.0001)
        print(centerPoint)
        plt.plot()
        plt.title("KMeans Classification")
        i = 0
        tempx = []
        tempy = []
        color = []
        for temp in result:
            temps = [[temp[x][i] for x in range(len(temp))] for i in range(len(temp[0]))]
            color += [i] * len(temps[0])
            tempx += temps[0]
            tempy += temps[1]

            i += 2
            pass
        plt.scatter(tempx, tempy, c=color, s=30)
        plt.show()

运行结果