【机器学习】AGNES层次聚类算法
算法思想：
- 初始每个数据都是一个簇；
- 寻找每个簇之间的距离，获取距离列表；
- 合并距离最近的两个簇Ci，Cj，并删除Cj，更新距离列表，使簇个数减1；
- 重复第3步，直到簇个数等于所需个数k。
数据集来源：周志华西瓜书数据集4.0
1.读取文件：
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
data = pd.read_csv("./西瓜数据集4.0.csv", index_col='number')
data = data.values.tolist()
2.使用matplotlib.pyplot绘出原始数据
# 画出原始图像
fig, ax = plt.subplots()
plt.scatter([i[0] for i in data], [i[1] for i in data])
plt.show()
3.计算欧氏距离
'''
计算欧氏距离
'''
def calDist(a, b):
a = np.array(a)
b = np.array(b)
dist = np.sqrt(np.dot((a - b), (a - b).T))
return dist
4.使用最小距离法计算簇之间的最小距离
'''
计算簇之间的最小距离
'''
def calClusterMinDist(c1, c2):
minDist = 1e5
for vec1 in c1:
for vec2 in c2:
dist = calDist(vec1, vec2)
if dist < minDist:
minDist = dist
return minDist
5.使用平均距离法计算簇之间的平均距离
'''
计算簇之间的平均距离
'''
def calClusterAvgDist(c1, c2):
num = len(c1) * len(c2)
sum_dist = 0
for vec1 in c1:
for vec2 in c2:
dist = calDist(vec1, vec2)
sum_dist += dist
return sum_dist
6.获取簇之间的距离列表
'''
获取最小距离列表
'''
def getMinDistList(data, method):
cluster_num = len(data)
# print("cluster_num",cluster_num)
minDistList = [[0 for i in range(cluster_num)] for j in range(cluster_num)]
for i in range(cluster_num):
j = i + 1
while j < cluster_num:
# print("data[i]:",data[i])
# print("data[j]:",data[j])
if method == "minDist": # 使用最小距离计算
minDistList[i][j] = calClusterMinDist(data[i], data[j])
minDistList[j][i] = minDistList[i][j]
elif method == "avgDist": # 使用平均距离计算
minDistList[i][j] = calClusterAvgDist(data[i], data[j])
minDistList[j][i] = minDistList[i][j]
j += 1
return minDistList
7.寻找最小值
'''
寻找距离列表中的最小值，用于合并簇以及删除
'''
def findMin(minDistList):
row = len(minDistList)
minDist = 1e5
min_i = 0
min_j = 0
for i in range(row):
for j in range(row):
dist = minDistList[i][j]
if dist < minDist and dist != 0:
minDist = minDistList[i][j]
min_i = i
min_j = j
return min_i, min_j, minDist
8.实现
'''
AGNES算法实现
'''
def AGNES(data, k, method):
cluster_num = len(data)
C = []
for i in data: # 添加数据
tmp = [i]
C.append(tmp)
minDistList = getMinDistList(C, method)
while cluster_num > k:
i, j, minDist = findMin(minDistList)
# print(len(minDistList))
# print(i,j,minDist)
C[i].extend(C[j]) # 合并
del C[j] # 删除
minDistList = getMinDistList(C, method)
cluster_num -= 1
return C
9.程序入口
'''
程序入口
'''
if __name__ == "__main__":
C_min = AGNES(data, 3, 'minDist')
C_avg = AGNES(data, 3, 'avgDist')
fig, ax = plt.subplots(nrows=2, ncols=1)
ax[0].scatter([i[0] for i in C_min[0]], [i[1] for i in C_min[0]], c='r')
ax[0].scatter([i[0] for i in C_min[1]], [i[1] for i in C_min[1]], c='g')
ax[0].scatter([i[0] for i in C_min[2]], [i[1] for i in C_min[2]], c='b')
ax[0].set_title("使用最小距离进行聚类")
ax[1].scatter([i[0] for i in C_avg[0]], [i[1] for i in C_avg[0]], c='r')
ax[1].scatter([i[0] for i in C_avg[1]], [i[1] for i in C_avg[1]], c='g')
ax[1].scatter([i[0] for i in C_avg[2]], [i[1] for i in C_avg[2]], c='b')
ax[1].set_title("使用平均距离进行聚类")
fig.tight_layout()
plt.show()
完整代码如下：
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
data = pd.read_csv("./西瓜数据集4.0.csv", index_col='number')
data = data.values.tolist()
# 画出原始图像
fig, ax = plt.subplots()
plt.scatter([i[0] for i in data], [i[1] for i in data])
plt.show()
'''
计算欧氏距离
'''
def calDist(a, b):
a = np.array(a)
b = np.array(b)
dist = np.sqrt(np.dot((a - b), (a - b).T))
return dist
'''
计算簇之间的最小距离
'''
def calClusterMinDist(c1, c2):
minDist = 1e5
for vec1 in c1:
for vec2 in c2:
dist = calDist(vec1, vec2)
if dist < minDist:
minDist = dist
return minDist
'''
计算簇之间的平均距离
'''
def calClusterAvgDist(c1, c2):
num = len(c1) * len(c2)
sum_dist = 0
for vec1 in c1:
for vec2 in c2:
dist = calDist(vec1, vec2)
sum_dist += dist
return sum_dist
'''
获取最小距离列表
'''
def getMinDistList(data, method):
cluster_num = len(data)
# print("cluster_num",cluster_num)
minDistList = [[0 for i in range(cluster_num)] for j in range(cluster_num)]
for i in range(cluster_num):
j = i + 1
while j < cluster_num:
# print("data[i]:",data[i])
# print("data[j]:",data[j])
if method == "minDist": # 使用最小距离计算
minDistList[i][j] = calClusterMinDist(data[i], data[j])
minDistList[j][i] = minDistList[i][j]
elif method == "avgDist": # 使用平均距离计算
minDistList[i][j] = calClusterAvgDist(data[i], data[j])
minDistList[j][i] = minDistList[i][j]
j += 1
return minDistList
'''
寻找距离列表中的最小值，用于合并簇以及删除
'''
def findMin(minDistList):
row = len(minDistList)
minDist = 1e5
min_i = 0
min_j = 0
for i in range(row):
for j in range(row):
dist = minDistList[i][j]
if dist < minDist and dist != 0:
minDist = minDistList[i][j]
min_i = i
min_j = j
return min_i, min_j, minDist
'''
AGNES算法实现
'''
def AGNES(data, k, method):
cluster_num = len(data)
C = []
for i in data: # 添加数据
tmp = [i]
C.append(tmp)
minDistList = getMinDistList(C, method)
while cluster_num > k:
i, j, minDist = findMin(minDistList)
# print(len(minDistList))
# print(i,j,minDist)
C[i].extend(C[j]) # 合并
del C[j] # 删除
minDistList = getMinDistList(C, method)
cluster_num -= 1
return C
'''
程序入口
'''
if __name__ == "__main__":
C_min = AGNES(data, 3, 'minDist')
C_avg = AGNES(data, 3, 'avgDist')
fig, ax = plt.subplots(nrows=2, ncols=1)
ax[0].scatter([i[0] for i in C_min[0]], [i[1] for i in C_min[0]], c='r')
ax[0].scatter([i[0] for i in C_min[1]], [i[1] for i in C_min[1]], c='g')
ax[0].scatter([i[0] for i in C_min[2]], [i[1] for i in C_min[2]], c='b')
ax[0].set_title("使用最小距离进行聚类")
ax[1].scatter([i[0] for i in C_avg[0]], [i[1] for i in C_avg[0]], c='r')
ax[1].scatter([i[0] for i in C_avg[1]], [i[1] for i in C_avg[1]], c='g')
ax[1].scatter([i[0] for i in C_avg[2]], [i[1] for i in C_avg[2]], c='b')
ax[1].set_title("使用平均距离进行聚类")
fig.tight_layout()
plt.show()
