群体优化算法---蜂群优化算法应用于数据挖掘

介绍

蜂群优化算法（Bee Algorithm, BA）及其变种主要模拟蜜蜂的觅食行为，以解决复杂的优化问题。这类算法通过蜜蜂之间的信息交流和协作来探索解空间，寻找全局最优解。主要应用于参数优化，结构优化，机器学习，数据挖掘等各个领域。

本文示例

本文将应用于数据挖掘，来解决聚类问题

代码

bee_algorithm_clustering

function bee_algorithm_clustering(data, num_clusters, num_bees, num_iterations, elite_bees, selected_bees, patch_size)

    % data: 输入的数据集 (rows: samples, columns: features)
    % num_clusters: 聚类数
    % num_bees: 总蜜蜂数量
    % num_iterations: 最大迭代次数
    % elite_bees: 精英蜜蜂数量
    % selected_bees: 选定蜜蜂数量
    % patch_size: 搜索邻域大小

    % 初始化蜜蜂群
    [num_samples, num_features] = size(data);
    bees = initialize_bees(num_bees, num_clusters, num_features);
    
    % 计算每只蜜蜂的适应度
    fitness = evaluate_bees(bees, data);
    
    for iter = 1:num_iterations
        % 排序蜜蜂根据适应度
        [fitness, idx] = sort(fitness);
        bees = bees(idx, :);
        
        % 搜索精英蜜蜂邻域
        for i = 1:elite_bees
            new_bees = local_search(bees(i, :), patch_size, num_clusters, num_features);
            new_fitness = evaluate_bees(new_bees, data);
            
            % 选择适应度更好的蜜蜂
            [best_new_fitness, best_idx] = min(new_fitness);
            if best_new_fitness < fitness(i)
                bees(i, :) = new_bees(best_idx, :);
                fitness(i) = best_new_fitness;
            end
        end
        
        % 搜索选定蜜蜂邻域
        for i = (elite_bees+1):selected_bees
            new_bees = local_search(bees(i, :), patch_size, num_clusters, num_features);
            new_fitness = evaluate_bees(new_bees, data);
            
            % 选择适应度更好的蜜蜂
            [best_new_fitness, best_idx] = min(new_fitness);
            if best_new_fitness < fitness(i)
                bees(i, :) = new_bees(best_idx, :);
                fitness(i) = best_new_fitness;
            end
        end
        
        % 更新其余蜜蜂位置
        for i = (selected_bees+1):num_bees
            bees(i, :) = initialize_bees(1, num_clusters, num_features);
            fitness(i) = evaluate_bees(bees(i, :), data);
        end
        
        % 输出当前最优适应度
        disp(['Iteration ', num2str(iter), ': Best Fitness = ', num2str(fitness(1))]);
    end
    
    % 输出最优聚类中心
    best_bee = reshape(bees(1, :), num_clusters, num_features);
    disp('Best Cluster Centers:');
    disp(best_bee);
    
    % 绘制聚类结果
    distances = pdist2(data, best_bee);
    [~, assignments] = min(distances, [], 2);
    figure;
    hold on;
    colors = lines(num_clusters);
    for k = 1:num_clusters
        scatter(data(assignments == k, 1), data(assignments == k, 2), 36, colors(k, :), 'filled');
        scatter(best_bee(k, 1), best_bee(k, 2), 100, colors(k, :), 'x', 'LineWidth', 2);
    end
    title('聚类结果');
    xlabel('Feature 1');
    ylabel('Feature 2');
    hold off;
end

function bees = initialize_bees(num_bees, num_clusters, num_features)
    % 随机初始化蜜蜂位置
    bees = rand(num_bees, num_clusters * num_features);
end

function fitness = evaluate_bees(bees, data)
    % 评估每只蜜蜂的适应度 (SSE)
    [num_bees, ~] = size(bees);
    [num_samples, ~] = size(data);
    num_clusters = size(bees, 2) / size(data, 2);
    fitness = zeros(num_bees, 1);
    
    for i = 1:num_bees
        centers = reshape(bees(i, :), num_clusters, size(data, 2));
        distances = pdist2(data, centers);
        [~, assignments] = min(distances, [], 2);
        fitness(i) = sum(sum((data - centers(assignments, :)).^2));
    end
end

function new_bees = local_search(bee, patch_size, num_clusters, num_features)
    % 局部搜索生成新蜜蜂
    new_bees = repmat(bee, patch_size, 1);
    perturbations = randn(patch_size, num_clusters * num_features) * 0.1;
    new_bees = new_bees + perturbations;
end

说明

bee_algorithm_clustering 函数：该函数是蜂群优化算法的主函数，用于执行聚类任务。

data：输入的数据集。

num_clusters：要找到的聚类中心的数量。

num_bees：蜜蜂总数。

num_iterations：最大迭代次数。

elite_bees：精英蜜蜂的数量。

selected_bees：选定蜜蜂的数量。

patch_size：搜索邻域的大小。

初始化蜜蜂群：使用随机位置初始化蜜蜂

评估适应度：使用均方误差（SSE）评估每只蜜蜂的适应度

局部搜索：对精英蜜蜂和选定蜜蜂进行局部搜索，生成新的蜜蜂并评估其适应度

更新蜜蜂位置：根据适应度更新蜜蜂的位置

输出结果：输出最佳聚类中心

使用以下代码生成数据集，然后保存名为run_bee_algorithm_clustering，运行

% 生成数据集
rng(1); % 设置随机种子以便重复实验
num_samples_per_cluster = 50;
cluster1 = bsxfun(@plus, randn(num_samples_per_cluster, 2), [2, 2]);
cluster2 = bsxfun(@plus, randn(num_samples_per_cluster, 2), [-2, -2]);
cluster3 = bsxfun(@plus, randn(num_samples_per_cluster, 2), [2, -2]);

data = [cluster1; cluster2; cluster3];

% 绘制数据集
figure;
scatter(data(:, 1), data(:, 2), 'filled');
title('原始数据集');
xlabel('Feature 1');
ylabel('Feature 2');

% 参数设置
num_clusters = 3;
num_bees = 50;
num_iterations = 100;
elite_bees = 5;
selected_bees = 15;
patch_size = 10;

% 运行蜂群优化算法进行聚类
bee_algorithm_clustering(data, num_clusters, num_bees, num_iterations, elite_bees, selected_bees, patch_size);

说明

生成数据集：生成一个包含三类数据点的二维数据集

效果