主函数
# -*- coding: utf-8 -*-
"""
参考： https://gist.github.com/iandanforth/5862470
"""
import random
from kmeans_tools import Cluster, get_distance, gen_random_sample
import matplotlib.pyplot as plt
from matplotlib import colors as mcolors
def kmeans(samples, k, cutoff):
"""
kmeans函数
"""
# 随机选k个样本点作为初始聚类中心
init_samples = random.sample(samples, k)
# 创建k个聚类，聚类的中心分别为随机初始的样本点
clusters = [Cluster([sample]) for sample in init_samples]
# 迭代循环直到聚类划分稳定
n_loop = 0
while True:
# 初始化一组空列表用于存储每个聚类内的样本点
lists = [[] for _ in clusters]
# 开始迭代
n_loop += 1
# 遍历样本集中的每个样本
for sample in samples:
# 计算样本点sample和第一个聚类中心的距离
smallest_distance = get_distance(sample, clusters[0].centroid)
# 初始化属于聚类 0
cluster_index = 0
# 计算和其他聚类中心的距离
for i in range(k - 1):
# 计算样本点sample和聚类中心的距离
distance = get_distance(sample, clusters[i+1].centroid)
# 如果存在更小的距离，更新距离
if distance < smallest_distance:
smallest_distance = distance
cluster_index = i + 1
# 找到最近的聚类中心，更新所属聚类
lists[cluster_index].append(sample)
# 初始化最大移动距离
biggest_shift = 0.0
# 计算本次迭代中，聚类中心移动的距离
for i in range(k):
shift = clusters[i].update(lists[i])
# 记录最大移动距离
biggest_shift = max(biggest_shift, shift)
# 如果聚类中心移动的距离小于收敛阈值，即：聚类稳定
if biggest_shift < cutoff:
print("第{}次迭代后，聚类稳定。".format(n_loop))
break
# 返回聚类结果
return clusters
def run_main():
"""
主函数
"""
# 样本个数
n_samples = 1000
# 特征个数 (特征维度)
n_feat = 2
# 特征数值范围
lower = 0
upper = 200
# 聚类个数
n_cluster = 3
# 生成随机样本
samples = [gen_random_sample(n_feat, lower, upper) for _ in range(n_samples)]
# 收敛阈值
cutoff = 0.2
clusters = kmeans(samples, n_cluster, cutoff)
# 输出结果
for i, c in enumerate(clusters):
for sample in c.samples:
print('聚类--{}，样本点--{}'.format(i, sample))
# 可视化结果
plt.subplot()
color_names = list(mcolors.cnames)
for i, c in enumerate(clusters):
x = []
y = []
random.choice
color = [color_names[i]] * len(c.samples)
for sample in c.samples:
x.append(sample.coords[0])
y.append(sample.coords[1])
plt.scatter(x, y, c=color)
plt.show()
if __name__ == '__main__':
run_main()
k-means_tools
# -*- coding: utf-8 -*-
"""
参考： https://gist.github.com/iandanforth/5862470
"""
import math
import random
class Cluster(object):
"""
聚类
"""
def __init__(self, samples):
if len(samples) == 0:
# 如果聚类中无样本点
raise Exception("错误：一个空的聚类！")
# 属于该聚类的样本点
self.samples = samples
# 该聚类中样本点的维度
self.n_dim = samples[0].n_dim
# 判断该聚类中所有样本点的维度是否相同
for sample in samples:
if sample.n_dim != self.n_dim:
raise Exception("错误： 聚类中样本点的维度不一致！")
# 设置初始化的聚类中心
self.centroid = self.cal_centroid()
def __repr__(self):
"""
输出对象信息
"""
return str(self.samples)
def update(self, samples):
"""
计算之前的聚类中心和更新后聚类中心的距离
"""
old_centroid = self.centroid
self.samples = samples
self.centroid = self.cal_centroid()
shift = get_distance(old_centroid, self.centroid)
return shift
def cal_centroid(self):
"""
对于一组样本点计算其中心点
"""
n_samples = len(self.samples)
# 获取所有样本点的坐标（特征）
coords = [sample.coords for sample in self.samples]
unzipped = zip(*coords)
# 计算每个维度的均值
centroid_coords = [math.fsum(d_list)/n_samples for d_list in unzipped]
return Sample(centroid_coords)
class Sample(object):
"""
样本点类
"""
def __init__(self, coords):
self.coords = coords # 样本点包含的坐标
self.n_dim = len(coords) # 样本点维度
def __repr__(self):
"""
输出对象信息
"""
return str(self.coords)
def get_distance(a, b):
"""
返回样本点a, b的欧式距离
参考：https://en.wikipedia.org/wiki/Euclidean_distance#n_dimensions
"""
if a.n_dim != b.n_dim:
# 如果样本点维度不同
raise Exception("错误: 样本点维度不同，无法计算距离！")
acc_diff = 0.0
for i in range(a.n_dim):
square_diff = pow((a.coords[i]-b.coords[i]), 2)
acc_diff += square_diff
distance = math.sqrt(acc_diff)
return distance
def gen_random_sample(n_dim, lower, upper):
"""
生成随机样本
"""
sample = Sample([random.uniform(lower, upper) for _ in range(n_dim)])
return sample
