Kmeans算法 python实现

K-Means算法简介：事先确定常数K，常数K意味着最终的聚类类别数，首先随机选定初始点为质心，并通过计算每一个样本与质心之间的相似度(这里为欧式距离)，将样本点归到最相似的类中，接着，重新计算每个类的质心(即为类中心)，重复这样的过程，知道质心不再改变，最终就确定了每个样本所属的类别以及每个类的质心。   总的来说，算法很简单，下面是python的简单实现：

import numpy as np

from matplotlib.pyplot import *
import numpy as np
class Classifier:
def __init__(self, max_k=9):
self.__dots = []
self.__max_k = max_k

def fit(self, data):
centerd, radius = [], np.zeros(self.__max_k, np.float32)
for k in range(1, self.__max_k):
_, distance_group, data_type = self.__fit_k_means(data, k)
type_distance = np.min(distance_group, axis=0)
centerd.append(_)
for idx in range(k):
type_data_idx = np.where(data_type == idx)
radius[k] += np.max(type_distance[type_data_idx])
radius[k] = np.sqrt(radius[k]) * k
best_k = np.argmax(radius[:self.__max_k-1] - radius[1:])
self.__dots = centerd[best_k]

def predict(self, data):
distance_group = []
for dot in self.__dots:
distance_group.append(self.__calc_distance(dot, data))
return np.argmin(distance_group, axis=0)

# 该函数用于计算当k指定时的k均值中心点
def __fit_k_means(self, data, k):
data_size, distance_group = len(data), []# 随机选取第一个中心点
centerd = [data[np.random.randint(0, data_size, dtype=np.int)]]
distance_group.append(self.__calc_distance(centerd[0], data))
for counter in range(k):
farpoint= np.argmax(np.min(distance_group, axis=0))
distance_group.append(self.__calc_distance(data[farpoint], data))
centerd.append(data[farpoint])
data_type = np.argmin(distance_group, axis=0)
# 标准k均值算法步骤，迭代更新各中心点坐标，最大迭代次数50
for repeat_times in range(50):
updated= np.copy(centerd)
for idx in range(len(centerd)):
updated[idx] = np.average(data[np.where(data_type == idx)], axis=0)
# 如果更新以后和更新之前的差距小于临界值，则停止迭代
if np.max(np.linalg.norm(updated - centerd, axis=0) < 0.1):
break
distance_group=[]
centerd =updated
for dot in centerd:
# 按照新的中心点坐标更新各点到中心点距离
distance_group.append(self.__calc_distance(dot, data))
data_type = np.argmin(distance_group, axis=0)
return centerd, distance_group, data_type

@staticmethod
# 计算各点到中心点的欧氏距离
def __calc_distance(central_dot, data):
distance = []
for this_dot in data:
distance.append(np.linalg.norm(central_dot - this_dot))
return distance

if __name__ == '__main__':
print('正在初始化聚类器')
data_file = open('melon.txt')
color_list = ['pink', 'green', 'gray', 'purple',  'orange','red', 'blue', 'black','white']
data_lines, data = data_file.readlines(), []
data_type_count = np.zeros(4, np.int)
for line in data_lines:
raw_data = line.split('\t')
data_type_count[int(raw_data[0]) - 1] += 1
data.append(np.array(raw_data[1:], np.float32))
classifier = Classifier(max_k=9)
for n in range(3):#2,3,4
data_n_types = np.array(data[:np.sum(data_type_count[:n+2])], np.float32)
print('正在对 %d 类的数据进行聚类...' % (n + 2), end='')
np.random.shuffle(data_n_types)
classifier.fit(data_n_types)
label_n_types = classifier.predict(data_n_types)
for i in range(9):
# 最大的可能种类为9种
type_i_in_n = data_n_types[np.where(label_n_types == i)]
#print(data.length)
scatter(type_i_in_n[:, 0], type_i_in_n[:, 1], c = color_list[i], s=20)
show()
data_file.close()