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_beesnew_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;endend% 搜索选定蜜蜂邻域for i = (elite_bees+1):selected_beesnew_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;endend% 更新其余蜜蜂位置for i = (selected_bees+1):num_beesbees(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_clustersscatter(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);endtitle('聚类结果');xlabel('Feature 1');ylabel('Feature 2');hold off;
endfunction 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);
endfunction 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_beescenters = 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
endfunction 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);