代码实现用PSO算法对Kmeans聚类中心的优化

下面是Python代码实现用PSO算法对Kmeans聚类中心的优化：

import numpy as np
from sklearn.cluster import KMeans

class PSO_Kmeans:
    def __init__(self, n_clusters, n_particles, max_iter):
        self.n_clusters = n_clusters # 聚类个数
        self.n_particles = n_particles # 粒子数
        self.max_iter = max_iter # 最大迭代次数

    # 适应度函数，计算SSE
    def fitness(self, X, centers):
        labels = KMeans(n_clusters=self.n_clusters, init=centers, n_init=1).fit(X).labels_
        sse = 0
        for i in range(self.n_clusters):
            sse += np.sum((X[labels == i] - centers[i]) ** 2)
        return sse

    # 初始化粒子群
    def init_particles(self, X):
        particles = np.zeros((self.n_particles, X.shape[1], self.n_clusters))
        for i in range(self.n_particles):
            particles[i] = np.random.uniform(X.min(axis=0), X.max(axis=0), (X.shape[1], self.n_clusters))
        return particles

    # 更新全局最优粒子和个体最优粒子
    def update_best(self, X, particles, fitness_particles, best_particle, best_fitness):
        for i in range(self.n_particles):
            if fitness_particles[i] < best_fitness[i]:
                best_particle[i] = particles[i].copy()
                best_fitness[i] = fitness_particles[i]
        gbest = particles[fitness_particles.argmin()].copy()
        gbest_fitness = fitness_particles.min()
        return best_particle, best_fitness, gbest, gbest_fitness

    # 更新粒子位置和速度
    def update_particles(self, X, particles, best_particle, gbest):
        w = 0.729 # 惯性权重
        c1 = 1.49445 # 学习因子
        c2 = 1.49445 # 学习因子
        v = np.random.uniform(-1, 1, particles.shape)
        particles = w * particles + c1 * np.random.uniform(0, 1, particles.shape) * (best_particle - particles) + c2 * np.random.uniform(0, 1, particles.shape) * (gbest - particles)
        particles = np.clip(particles, X.min(axis=0)[:, np.newaxis], X.max(axis=0)[:, np.newaxis])
        return particles

    # 训练模型
    def fit(self, X):
        particles = self.init_particles(X)
        best_particle = particles.copy()
        best_fitness = np.array([self.fitness(X, particle) for particle in particles])
        gbest = particles[best_fitness.argmin()].copy()
        gbest_fitness = best_fitness.min()
        for i in range(self.max_iter):
            particles = self.update_particles(X, particles, best_particle, gbest)
            fitness_particles = np.array([self.fitness(X, particle) for particle in particles])
            best_particle, best_fitness, gbest, gbest_fitness = self.update_best(X, particles, fitness_particles, best_particle, best_fitness)
        return gbest.T

使用方法：

from sklearn.datasets import make_blobs
from PSO_Kmeans import PSO_Kmeans

# 生成数据集
X, y = make_blobs(n_samples=1000, centers=3, random_state=42)

# 初始化PSO_Kmeans模型
pso_kmeans = PSO_Kmeans(n_clusters=3, n_particles=10, max_iter=50)

# 训练模型
centers = pso_kmeans.fit(X)

# 使用聚类中心进行聚类
labels = KMeans(n_clusters=3, init=centers, n_init=1).fit(X).labels_

其中，`n_clusters`为聚类个数，`n_particles`为粒子数，`max_iter`为最大迭代次数。