MATLAB编写LOF算法

LOF算法是一种基于密度的异常点检测算法。下面是MATLAB实现：

1. 导入数据

data = load('data.txt');

2. 计算每个点的k距离

k = 5; % k值
m = size(data, 1); % 数据集大小
distances = zeros(m, m);
k_distances = zeros(m, 1);
for i = 1:m
    for j = i+1:m
        distances(i, j) = norm(data(i,:) - data(j,:));
        distances(j, i) = distances(i, j);
    end
    k_distances(i) = max(sort(distances(i,:)), k);
end

3. 计算每个点的可达距离

reachability_distances = zeros(m, m);
for i = 1:m
    for j = i+1:m
        reachability_distances(i, j) = max([distances(i, j), k_distances(j)]);
        reachability_distances(j, i) = reachability_distances(i, j);
    end
end

4. 计算每个点的局部可达密度

local_reachability_density = zeros(m, 1);
for i = 1:m
    indices = find(reachability_distances(i,:) <= k_distances(i));
    local_reachability_density(i) = length(indices) / sum(reachability_distances(i, indices));
end

5. 计算每个点的局部异常因子

LOF = zeros(m, 1);
for i = 1:m
    indices = find(reachability_distances(i,:) <= k_distances(i));
    LOF(i) = sum(local_reachability_density(indices)) / (local_reachability_density(i) * length(indices));
end

6. 可视化结果

scatter(data(:,1), data(:,2), 20, LOF, 'filled');
colorbar;

完整代码如下：

data = load('data.txt');

k = 5; % k值
m = size(data, 1); % 数据集大小

% 计算每个点的k距离
distances = zeros(m, m);
k_distances = zeros(m, 1);
for i = 1:m
    for j = i+1:m
        distances(i, j) = norm(data(i,:) - data(j,:));
        distances(j, i) = distances(i, j);
    end
    k_distances(i) = max(sort(distances(i,:)), k);
end

% 计算每个点的可达距离
reachability_distances = zeros(m, m);
for i = 1:m
    for j = i+1:m
        reachability_distances(i, j) = max([distances(i, j), k_distances(j)]);
        reachability_distances(j, i) = reachability_distances(i, j);
    end
end

% 计算每个点的局部可达密度
local_reachability_density = zeros(m, 1);
for i = 1:m
    indices = find(reachability_distances(i,:) <= k_distances(i));
    local_reachability_density(i) = length(indices) / sum(reachability_distances(i, indices));
end

% 计算每个点的局部异常因子
LOF = zeros(m, 1);
for i = 1:m
    indices = find(reachability_distances(i,:) <= k_distances(i));
    LOF(i) = sum(local_reachability_density(indices)) / (local_reachability_density(i) * length(indices));
end

% 可视化结果
scatter(data(:,1), data(:,2), 20, LOF, 'filled');
colorbar;