DIANA算法案例含代码

DIANA算法是一种基于距离的层次聚类算法，它的核心思想是将数据集中的每个数据点都视为一个单独的簇，然后不断地合并簇，直到所有的数据点都被合并为一个簇。

下面是一个使用Python实现DIANA算法的示例代码：

import numpy as np

def euclidean_distance(x1, x2):
    """
    计算两个向量之间的欧几里得距离
    """
    return np.sqrt(np.sum((x1 - x2)**2))

class DIANA:
    def __init__(self, k):
        self.k = k
    
    def fit(self, X):
        n_samples, n_features = X.shape
        
        # 初始化簇列表，每个数据点对应一个簇
        clusters = [{"id": i, "centroid": X[i], "elements": [i]} for i in range(n_samples)]
        
        # 不断合并簇，直到只剩下k个簇
        while len(clusters) > self.k:
            # 计算每个簇之间的距离
            distances = np.zeros((len(clusters), len(clusters)))
            for i in range(len(clusters)):
                for j in range(i+1, len(clusters)):
                    distances[i][j] = euclidean_distance(clusters[i]["centroid"], clusters[j]["centroid"])
                    distances[j][i] = distances[i][j]
            
            # 找到距离最近的两个簇
            min_dist = np.min(distances[np.nonzero(distances)])
            cluster_indexes = np.where(distances == min_dist)
            cluster1_index = cluster_indexes[0][0]
            cluster2_index = cluster_indexes[1][0]
            
            # 合并两个簇
            new_cluster = {"id": len(clusters), "centroid": (clusters[cluster1_index]["centroid"] + clusters[cluster2_index]["centroid"])/2, "elements": clusters[cluster1_index]["elements"] + clusters[cluster2_index]["elements"]}
            del clusters[cluster2_index]
            del clusters[cluster1_index]
            clusters.append(new_cluster)
        
        # 为每个数据点分配簇标签
        labels = np.zeros(n_samples)
        for i in range(len(clusters)):
            for j in clusters[i]["elements"]:
                labels[j] = i
        
        self.clusters = clusters
        self.labels = labels

下面是一个使用DIANA算法对Iris数据集进行聚类的示例：

from sklearn.datasets import load_iris

iris = load_iris()
X = iris.data

diana = DIANA(k=3)
diana.fit(X)

print(diana.labels)

输出结果为：

[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.
 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 2. 2. 2. 2. 2. 2. 2. 2. 2.
 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2.
 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2.
 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]

其中，簇标签0表示第一类，簇标签1表示第二类，簇标签2表示第三类。