如何让Mean Shift自适应带宽的代码实现

以下是使用 Python 实现自适应带宽 Mean Shift 算法的示例代码：

import numpy as np

def adaptive_bandwidth(X, c):
    """
    计算自适应带宽
    :param X: 样本数据，numpy array，shape为(n_samples, n_features)
    :param c: 常数，用于调整带宽大小
    :return: 自适应带宽，numpy array，shape为(n_samples,)
    """
    n_samples, n_features = X.shape
    
    # 计算每个样本点之间的欧式距离矩阵
    dist_matrix = np.zeros((n_samples, n_samples))
    for i in range(n_samples):
        for j in range(i+1, n_samples):
            dist_matrix[i][j] = np.sqrt(np.sum((X[i]-X[j])**2))
            dist_matrix[j][i] = dist_matrix[i][j]
    
    # 计算每个样本点的密度
    density = np.zeros(n_samples)
    for i in range(n_samples):
        density[i] = np.sum(np.exp(-dist_matrix[i]**2/2))
    
    # 计算每个样本点的自适应带宽
    bandwidth = np.zeros(n_samples)
    for i in range(n_samples):
        bandwidth[i] = c / np.sqrt(density[i])
    
    return bandwidth

def mean_shift(X, bandwidth, threshold):
    """
    计算均值漂移后的样本点
    :param X: 样本数据，numpy array，shape为(n_samples, n_features)
    :param bandwidth: 带宽，numpy array，shape为(n_samples,)
    :param threshold: 阈值，用于判断两个样本点是否属于同一类
    :return: 漂移后的样本点，numpy array，shape为(n_samples, n_features)
    """
    n_samples, n_features = X.shape
    
    # 迭代计算每个样本点的均值漂移
    for i in range(n_samples):
        x = X[i]
        b = bandwidth[i]
        while True:
            # 计算每个样本点与当前点的距离
            dist = np.sqrt(np.sum((X-x)**2, axis=1))
            # 计算每个样本点的权重
            weight = np.exp(-dist**2/(2*b**2))
            # 计算每个样本点的均值
            mean = np.sum(X*weight.reshape(-1, 1), axis=0) / np.sum(weight)
            # 判断均值是否收敛
            if np.sum((mean-x)**2) < threshold:
                X[i] = mean
                break
            x = mean
    
    return X

def cluster(X, bandwidth, threshold):
    """
    对均值漂移后的样本点进行聚类
    :param X: 均值漂移后的样本点，numpy array，shape为(n_samples, n_features)
    :param bandwidth: 带宽，numpy array，shape为(n_samples,)
    :param threshold: 阈值，用于判断两个样本点是否属于同一类
    :return: 聚类结果，list，每个元素为一个类别，其中每个元素为一个样本点的索引
    """
    n_samples, n_features = X.shape
    visited = np.zeros(n_samples)
    clusters = []
    
    # 对每个样本点进行聚类
    for i in range(n_samples):
        if visited[i] == 0:
            cluster_i = [i]
            visited[i] = 1
            for j in range(i+1, n_samples):
                if visited[j] == 0 and np.sum((X[i]-X[j])**2 / bandwidth[i]**2) < threshold:
                    cluster_i.append(j)
                    visited[j] = 1
            clusters.append(cluster_i)
    
    return clusters

# 示例代码
X = np.random.rand(100, 2)
bandwidth = adaptive_bandwidth(X, 1)
X_shifted = mean_shift(X, bandwidth, 1e-5)
clusters = cluster(X_shifted, bandwidth, 0.1)
print(clusters)

上述代码中，`adaptive_bandwidth` 函数用于计算自适应带宽，`mean_shift` 函数用于计算均值漂移后的样本点，`cluster` 函数用于对均值漂移后的样本点进行聚类。

需要注意的是，上述代码中的阈值参数 `threshold` 可以根据具体的数据集和应用场景进行调整。