ap聚类算法python

以下是用Python实现AP聚类算法的示例代码：

import numpy as np

# 计算相似度矩阵
def cal_similarity(data):
    n = len(data)
    similarity = np.zeros((n, n))
    for i in range(n):
        for j in range(n):
            similarity[i][j] = -np.linalg.norm(data[i] - data[j])
    return similarity

# 计算responsibility
def cal_responsibility(similarity, damping):
    n = similarity.shape[0]
    a = np.zeros((n, n))
    for i in range(n):
        max_s = -np.inf
        max_j = -1
        for j in range(n):
            if j != i:
                if similarity[i][j] > max_s:
                    max_s = similarity[i][j]
                    max_j = j
        for j in range(n):
            if j == max_j:
                a[i][j] = (1 - damping) * (similarity[i][j] - max_s)
            else:
                a[i][j] = (1 - damping) * similarity[i][j]
    return a

# 计算availability
def cal_availability(responsibility, damping):
    n = responsibility.shape[0]
    r_new = np.zeros((n, n))
    for j in range(n):
        r_new[:, j] = responsibility[:, j] + np.maximum(0, np.diag(responsibility) - responsibility[j, j])
        r_new[j, j] = np.sum(np.maximum(0, responsibility[j, :] + np.diag(responsibility)[:j] + np.diag(responsibility)[j+1:]))
    a_new = damping * r_new + (1 - damping) * responsibility
    return a_new, r_new

# AP聚类算法
def ap_clustering(data, max_iter=1000, damping=0.9, convergence_iter=10, convergence_tol=1e-6):
    similarity = cal_similarity(data)
    n = similarity.shape[0]
    responsibility = np.zeros((n, n))
    availability = np.zeros((n, n))
    cluster_centers_indices = []
    for i in range(max_iter):
        if i % convergence_iter == 0:
            tmp = responsibility + availability
            if np.allclose(tmp, tmp.diagonal().reshape(n, -1)):
                break
        # 计算responsibility
        responsibility = cal_responsibility(similarity, damping)
        # 计算availability
        availability_new, responsibility_new = cal_availability(responsibility, damping)
        availability = availability_new
        responsibility = responsibility_new
        # 计算clusters
        clusters = np.argmax(responsibility + availability, axis=1)
        # 计算cluster centers
        cluster_centers_indices = []
        for k in range(n):
            if k == clusters[k]:
                cluster_centers_indices.append(k)
        # 检查是否收敛
        if len(cluster_centers_indices) > 0:
            cluster_centers = data[cluster_centers_indices]
            dist = np.zeros((n, len(cluster_centers)))
            for k in range(len(cluster_centers)):
                dist[:, k] = -np.linalg.norm(data - cluster_centers[k], axis=1)
            new_clusters = np.argmax(dist, axis=1)
            if np.all(clusters == new_clusters):
                break
            clusters = new_clusters
    return cluster_centers_indices, clusters

其中，`data`是一个二维数组，表示待聚类的数据。`max_iter`表示最大迭代次数，`damping`表示阻尼系数，`convergence_iter`表示检查收敛的迭代次数，`convergence_tol`表示收敛阈值。函数返回两个数组，`cluster_centers_indices`表示聚类中心的索引，`clusters`表示每个数据点所属的簇的索引。