粒子群logistic多分类python

以下是一个使用粒子群优化算法进行逻辑回归多分类的 Python 代码示例：

import numpy as np
import random

# sigmoid 函数
def sigmoid(z):
    return 1 / (1 + np.exp(-z))

# 逻辑回归函数
def logistic_regression(x, w):
    z = np.dot(x, w)
    return sigmoid(z)

# 目标函数
def objective_function(x, y, w):
    num_classes = len(np.unique(y))
    m = x.shape[0]
    scores = np.zeros((m, num_classes))
    for c in range(num_classes):
        binary_y = np.where(y == c, 1, 0)
        scores[:, c] = logistic_regression(x, w[c])
    softmax_scores = np.exp(scores) / np.sum(np.exp(scores), axis=1, keepdims=True)
    loss = -np.sum(binary_y * np.log(softmax_scores[:, c]) for c in range(num_classes)) / m
    return loss

# 初始化粒子群
def initialize_swarm(num_particles, num_classes, num_features):
    particles = []
    for i in range(num_particles):
        particle = {}
        particle['position'] = [np.random.randn(num_features) for c in range(num_classes)]
        particle['velocity'] = [np.random.randn(num_features) for c in range(num_classes)]
        particle['best_position'] = particle['position']
        particle['best_score'] = float('inf')
        particles.append(particle)
    return particles

# 更新粒子群
def update_swarm(particles, global_best_position, c1, c2, w):
    for particle in particles:
        for c in range(len(particle['position'])):
            for i in range(len(particle['position'][c])):
                r1 = random.random()
                r2 = random.random()
                particle['velocity'][c][i] = w*particle['velocity'][c][i] + c1*r1*(particle['best_position'][c][i]-particle['position'][c][i]) + c2*r2*(global_best_position[c][i]-particle['position'][c][i])
                particle['position'][c][i] += particle['velocity'][c][i]
            score = objective_function(x, y, particle['position'])
            if score < particle['best_score']:
                particle['best_score'] = score
                particle['best_position'] = particle['position']
    return particles

# 找到全局最优解
def find_global_best(particles):
    best_particle = min(particles, key=lambda particle: particle['best_score'])
    return best_particle['best_position']

# 粒子群优化主函数
def particle_swarm_optimization(num_particles, num_classes, num_features, x, y, max_iterations, c1, c2, w):
    particles = initialize_swarm(num_particles, num_classes, num_features)
    global_best_position = find_global_best(particles)
    for i in range(max_iterations):
        particles = update_swarm(particles, global_best_position, c1, c2, w)
        global_best_position = find_global_best(particles)
    return global_best_position

# 示例
x = np.random.randn(1000, 10)
y = np.random.randint(0, 3, 1000)
num_classes = len(np.unique(y))
num_features = x.shape[1]
best = particle_swarm_optimization(num_particles=20, num_classes=num_classes, num_features=num_features, x=x, y=y, max_iterations=100, c1=0.5, c2=0.5, w=0.9)
print('Best Parameters:', best)

在这个示例中，我们定义了一个逻辑回归函数`logistic_regression`，它接受一个输入向量和一个权重向量，并返回一个标量预测。我们还定义了一个目标函数`objective_function`，它接受输入数据、标签和权重向量，并返回一个标量损失。我们使用粒子群优化算法来最小化这个目标函数，其参数包括粒子数量、类别数量、特征数量、输入数据、标签、最大迭代次数、加速常数和惯性权重。

请注意，这只是一个简单的示例，可以根据需要进行修改和扩展。在实际应用中，可能需要对代码进行调整以适应具体的数据和问题。