K-中心点算法也是一种常用的聚类算法，K-中心点聚类的基本思想和K-Means的思想相同，实质上是对K-means算法的优化和改进。
在K-means中，异常数据，比如孤立点对其的算法过程会有较大的影响。在K-means算法执行过程中，可以通过随机的方式选择初始质心，也只有初始时通过随机方式产生的质心才是实际需要聚簇集合的中心点，而后面通过不断迭代产生的新的质心很可能并不是在聚簇中的点。如果某些异常点距离质心相对较大时，很可能导致重新计算得到的质心偏离了聚簇的真实中心。
K-Medoide算法步骤：
（1）确定聚类的个数K。
（2）在所有数据集合中选择K个点作为各个聚簇的中心点。
（3）计算其余所有点到K个中心点的距离，并把每个点到K个中心点最短的聚簇作为自己所属的聚簇。
（4）在每个聚簇中按照顺序依次选取点，计算该点到当前聚簇中所有点距离之和，最终距离之和最小的点，则视为新的中心点。
（5）重复（2），（3）步骤，直到各个聚簇的中心点不再改变。
e.g.
如果以样本数据{A,B,C,D,E,F}为例，期望聚类的K值为2，则步骤如下：
（1）在样本数据中随机选择B、E作为中心点。
（2）如果通过计算得到D,F到B的距离最近，A,C到E的距离最近，则B,D,F为聚簇C1，A,C,E为聚簇C2。
（3）在C1和C2两个聚类集合中，计算一个点到其他点的距离之和的最小值作为新的中心点，假如分别计算出D到C1中其他所有点的距离之和最小，E到C2中其他所有点的距离之和最小。
（4）再以D,E作为聚簇的中心点，重复上述步骤，直到中心点不再改变。
K-中心聚类算法计算的是某点到其它所有点的距离之和最小的点，通过距离之和最短的计算方式可以减少某些孤立数据对聚类过程的影响。从而使得最终效果更接近真实划分，但是由于上述过程的计算量会相对于K-means，大约增加O（n）的计算量，因此一般情况下K-中心算法更加适合小规模数据运算。
from sklearn.datasets import make_blobsfrom matplotlib import pyplotimport numpy as npimport randomclass KMediod():"""实现简单的k-medoid算法"""def __init__(self, n_points, k_num_center):self.n_points = n_pointsself.k_num_center = k_num_centerself.data = Nonedef get_test_data(self):"""产生测试数据, n_samples表示多少个点, n_features表示几维, centers得到的data是n个点各自坐标target是每个坐标的分类比如说我规定好四个分类，target长度为n范围为0-3，主要是画图颜色区别:return: none"""self.data, target = make_blobs(n_samples=self.n_points, n_features=2, centers=self.n_points)np.put(self.data, [self.n_points, 0], 500, mode='clip')np.put(self.data, [self.n_points, 1], 500, mode='clip')pyplot.scatter(self.data[:, 0], self.data[:, 1], c=target)# 画图pyplot.show()def ou_distance(self, x, y):# 定义欧式距离的计算return np.sqrt(sum(np.square(x - y)))def run_k_center(self, func_of_dis):"""选定好距离公式开始进行训练:param func_of_dis::return:"""print('初始化', self.k_num_center, '个中心点')indexs = list(range(len(self.data)))random.shuffle(indexs) # 随机选择质心init_centroids_index = indexs[:self.k_num_center]centroids = self.data[init_centroids_index, :] # 初始中心点print(centroids)# 确定种类编号print('开始迭代')sample_target = []if_stop = Falsewhile not if_stop:if_stop = Trueclassify_points = [[centroid] for centroid in centroids]print("之前：{}".format(classify_points))sample_target = []# 遍历数据for sample in self.data:# 计算距离，由距离该数据最近的核心，确定该点所属类别distances = [func_of_dis(sample, centroid) for centroid in centroids]cur_level = np.argmin(distances) # 最短距离的中心点的下标sample_target.append(cur_level)# 统计，方便迭代完成后重新计算中间点classify_points[cur_level].append(sample)print("之后：{}".format(classify_points))# 重新划分质心for i in range(self.k_num_center): # 几类中分别寻找一个最优点distances = [func_of_dis(point_1, centroids[i]) for point_1 in classify_points[i]]now_distances = sum(distances) # 首先计算中心点和聚簇其他所有点的距离总和for point in classify_points[i]:distances = [func_of_dis(point_1, point) for point_1 in classify_points[i]]new_distance = sum(distances)# 计算出该聚簇中各个点与其他所有点的总和，若是有小于当前中心点的距离总和的，中心点去掉if new_distance < now_distances:now_distances = new_distancecentroids[i] = point # 换成该点if_stop = Falseprint('结束')return sample_targetdef run(self):"""先获得数据，由传入参数得到杂乱的n个点，然后由这n个点，分为m个类:return:"""self.get_test_data()predict = self.run_k_center(self.ou_distance)pyplot.scatter(self.data[:, 0], self.data[:, 1], c=predict)pyplot.show()test_one = KMediod(n_points=1000, k_num_center=3)test_one.run()
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9.06207736]), array([-7.54006177, -2.89420399]), array([-7.02516788, 6.89731606]), array([-9.96934948, -2.07020696]), array([-4.05452763, 3.27993958]), array([-8.19022691, 7.94713695]), array([-5.76432335, 2.31455027]), array([-8.40288778, 3.8658572 ]), array([-4.30509874, 7.96803087]), array([-6.06569119, -1.7464766 ]), array([-1.04711157, 7.41199014]), array([-2.99968563, 7.77404039]), array([-9.24090674, -1.93198188]), array([-7.28251666, 3.88141803]), array([-1.59974042, 2.21349103]), array([-6.52294712, 6.03637385]), array([-8.46418288, -1.18878668]), array([-9.22367441, -0.35117283]), array([-5.7925676 , 3.59973042]), array([-6.59678419, 4.1199655 ]), array([-2.60562837, 2.60525963]), array([0.57891967, 6.73493388]), array([-4.24014184, -0.08655698]), array([-0.69545709, 7.21621855]), array([-8.24879683, 2.83433128]), array([-7.42474349, 6.65711462]), array([-5.76793631, 9.21715346]), array([-5.52828063, -0.65386148]), array([-8.8850612 , 9.54938826]), array([-9.26683763, -4.47459258]), array([-6.930522 , 6.41255247]), array([-5.35365333, 9.15589483]), array([-3.14292292, 3.85160416]), array([-5.41449716, 5.96402458]), array([-6.105284 , 7.40326056]), array([-6.89402389, 9.63871295]), array([-2.25004527, 8.46242981]), array([-7.87082082, 11.74134411]), array([-8.31146218, 6.96978629]), array([-1.4530296 , -0.87072899]), array([-6.3502515 , 1.37743434]), array([-2.34695934, 8.61670539]), array([-0.09293765, 3.11379854]), array([-3.50305505, 3.53996256]), array([-1.84759785, 6.5722515 ]), array([-1.61411255, 0.62580292]), array([-10.14129297, 1.67739458]), array([-0.93699014, 4.59407507]), array([-5.59722922, 6.58751861]), array([-9.62535645, -0.86009761]), array([-8.90338288, -0.27919226])]]结束Process finished with exit code 0
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