孤立森林matlab代码

孤立森林（Isolation Forest）是一种用于异常检测的机器学习算法。它的主要思想是通过随机的方式来构建一个隔离树（Isolation Tree），然后通过统计样本点在树上的深度来判断其是否为异常点。以下是一个基于 MATLAB 的孤立森林算法的代码实现：

function [anomaly_scores, isolation_trees] = isolation_forest(X, n_trees, sub_sample_size)

[n_samples, n_features] = size(X);

if nargin < 3
    sub_sample_size = min(256, n_samples);
end

% Build isolation trees
isolation_trees = cell(n_trees, 1);
for i = 1:n_trees
    isolation_trees{i} = build_isolation_tree(X, sub_sample_size);
end

% Compute anomaly scores
anomaly_scores = zeros(n_samples, 1);
for i = 1:n_samples
    depth_sum = 0;
    for j = 1:n_trees
        depth_sum = depth_sum + path_length(X(i,:), isolation_trees{j});
    end
    average_depth = depth_sum / n_trees;
    c = c_value(sub_sample_size);
    anomaly_scores(i) = 2^(-average_depth/c);
end

end

function tree = build_isolation_tree(X, max_height)

[n_samples, n_features] = size(X);

if n_samples <= 1 || max_height == 0
    tree = struct('left', [], 'right', [], 'split_feature', [], 'split_value', []);
    return
end

% Randomly choose a feature to split on
split_feature = randi(n_features);
% Randomly choose a split value between the min and max of the feature
split_value = X(randi(n_samples), split_feature);

% Split the data
left_mask = X(:, split_feature) < split_value;
right_mask = ~left_mask;
left_data = X(left_mask, :);
right_data = X(right_mask, :);

% Recursively build the left and right subtrees
tree = struct('left', build_isolation_tree(left_data, max_height-1), ...
              'right', build_isolation_tree(right_data, max_height-1), ...
              'split_feature', split_feature, ...
              'split_value', split_value);

end

function length = path_length(x, tree)

if isempty(tree.left) && isempty(tree.right)
    length = 0;
    return
end

split_feature = tree.split_feature;
if x(split_feature) < tree.split_value
    length = 1 + path_length(x, tree.left);
else
    length = 1 + path_length(x, tree.right);
end

end

function c = c_value(n)

if n > 2
    c = 2 * (log(n-1) + 0.5772) - 2*(n-1)/n;
elseif n == 2
    c = 1;
else
    c = 0;
end

end

其中，`X` 是一个 `n_samples x n_features` 的矩阵，表示样本数据；`n_trees` 是随机森林中树的数量；`sub_sample_size` 是每个随机森林的样本子集大小。`isolation_forest` 函数用于构建孤立森林并计算每个样本的异常得分；`build_isolation_tree` 函数用于递归地构建隔离树；`path_length` 函数用于计算样本点在树上的深度；`c_value` 函数用于计算常数项。