基本原理
python实现KMeans算法
# 导入相应的包
from copy import deepcopy
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt# 导入数据
data = pd.read_csv('data.csv')
print("Input Data and Shape")
print(data.shape)
data.head()Input Data and Shape
(3000, 2)
V1 | V2 | |
0 | 2.072345 | -3.241693 |
1 | 17.936710 | 15.784810 |
2 | 1.083576 | 7.319176 |
3 | 11.120670 | 14.406780 |
4 | 23.711550 | 2.557729 |
# 提取字段并可视化数据，使用scatter plot
f1 = data['V1'].values
f2 = data['V2'].values
X = np.array(list(zip(f1, f2)))
# X = np.random.random((200, 2))*10
plt.scatter(X[:,0], X[:,1], c='black', s=6)
# K-means里的K值
k = 3
# 随机初始化K个中心点，把结果存储在C
C_x = np.random.randint(0, np.max(X), size=k)
C_y = np.random.randint(0, np.max(X), size=k)
C = np.array(list(zip(C_x, C_y)), dtype=np.float32)
print("初始化之后的中心点：")
print(C)
# 把中心点也展示一下
plt.scatter(X[:,0], X[:,1], c='#050505', s=7)
plt.scatter(C[:,0], C[:,1], marker='*', s=300, c='g')初始化之后的中心点：
[[85. 3.]
[70. 22.]
[41. 18.]]
# 存储之前的中心点
C_old = np.zeros(C.shape)
clusters = np.zeros(len(X)) # K=3, clusters = [0,0,1,2,1,0]
def dist(a, b, ax=1):
return np.linalg.norm(a - b, axis=ax)
error = dist(C, C_old, None)
# 循环算法，直到收敛。收敛的条件就是，判断当前的中心点与之前的中心点之间有没有变化，没有变化距离就会变成0，然后抛出异常
while error != 0:
# Assigning each value to its closest cluster
for i in range(len(X)):
distances = dist(X[i], C)
cluster = np.argmin(distances)
clusters[i] = cluster
# 在计算新的中心点之前，先把旧的中心点存下来，以便计算距离
C_old = deepcopy(C)
# 计算新的中心点
for i in range(k):
points = [X[j] for j in range(len(X)) if clusters[j] == i]
C[i] = np.mean(points, axis=0)
error = dist(C, C_old, None)
colors = ['r', 'g', 'b', 'y', 'c', 'm']
fig, ax = plt.subplots()
for i in range(k):
points = np.array([X[j] for j in range(len(X)) if clusters[j] == i])
ax.scatter(points[:, 0], points[:, 1], s=7, c=colors[i])
ax.scatter(C[:, 0], C[:, 1], marker='*', s=200, c='#050505')
