类聚分析可以通过多种编程语言实现,以下是几个不同编程语言的类聚分析编程例题:
MATLAB编程例题
任务:将8个点按欧氏距离分为3个簇,并展示初始簇中心的选择及算法执行过程。
```matlab
% 数据初始化
x1 = [1, 2, 1, 2, 4, 5, 4, 5];
y1 = [1, 1, 2, 2, 3, 3, 4, 4];
data = [x1, y1];
data = data(1:2, :); % 转换为列向量
% 距离函数
distance = @(x1, y1, x2, y2) abs(x1-x2) + abs(y1-y2);
% 初始簇中心
cen1 = [data(1, 1), data(1, 2)];
cen2 = [data(3, 1), data(3, 2)];
% 簇分配
c1 = []; c2 = [];
for i = 1:length(x1)
dis1 = distance(x1(i), y1(i), cen1(1), cen1(2));
dis2 = distance(x1(i), y1(i), cen2(1), cen2(2));
if dis1 == 0 || dis2 == 0
next
else
if dis1 <= dis2
c1 = [c1, i];
else
c2 = [c2, i];
end
end
end
% 迭代更新簇中心
repeat
new_c1 = c1;
new_c2 = c2;
cen1(1) = mean(x1(new_c1));
cen1(2) = mean(y1(new_c1));
cen2(1) = mean(x1(new_c2));
cen2(2) = mean(y1(new_c2));
until cen1 == cen2;
% 显示结果
disp('第一轮迭代后的簇中心坐标:');
disp(cen1);
disp(cen2);
disp('每个簇的点分配:');
disp(c1);
disp(c2);
```
R语言编程例题
任务:使用R语言进行层次聚类分析。
```r
导入数据
data <- data.frame(x = c(1, 2, 1, 2, 4, 5, 4, 5), y = c(1, 1, 2, 2, 3, 3, 4, 4))
计算距离
distance <- function(x1, y1, x2, y2) {
return(abs(x1 - x2) + abs(y1 - y2))
}
随机选择的两个对象作为初始点
cen1 <- c(data[1, 1], data[1, 2])
cen2 <- c(data[3, 1], data[3, 2])
初始两个簇
c1 <- c(1, 2, 4, 5)
c2 <- c(3, 7)
循环迭代
repeat {
new_c1 <- c1
new_c2 <- c2
cen1 <- mean(data$x[new_c1])
cen1 <- mean(data$y[new_c1])
cen2 <- mean(data$x[new_c2])
cen2 <- mean(data$y[new_c2])
}
输出结果
print(paste("第一轮迭代后的簇中心坐标:", cen1, sep = ", "))
print(paste("第一轮迭代后的簇中心坐标:", cen2, sep = ", "))
```
Python编程例题
任务:使用Python进行K-means聚类分析。