孤立森林算法matlab代码

下面是孤立森林的MATLAB代码实现，其中包括了孤立树和孤立森林的实现：

function [IForest, Outliers] = iForest(X, nTrees, sampleSize)
% X: 输入的数据集，每一行表示一个样本
% nTrees: 孤立森林中包含的孤立树数目
% sampleSize: 每个孤立树中包含的样本数目
% IForest: 输出的孤立森林，包含nTrees棵孤立树
% Outliers: 输出的异常值，其中每个元素表示该样本的异常得分

if nargin < 3
    sampleSize = 256;
end
if nargin < 2
    nTrees = 100;
end

[nSamples, nFeatures] = size(X);

% 构造孤立森林
IForest = cell(nTrees, 1);
for i = 1:nTrees
    IForest{i} = iTree(X, sampleSize, 0);
end

% 计算异常得分
Outliers = zeros(nSamples, 1);
for i = 1:nSamples
    hTemp = 0;
    for j = 1:nTrees
        hTemp = hTemp + pathLength(X(i,:), IForest{j});
    end
    Eh = hTemp/nTrees;
    c = cValue(sampleSize);
    Outliers(i) = 2^(-Eh/c);
end

end

function Tree = iTree(X, sampleSize, height)
% 构造孤立树

[nSamples, nFeatures] = size(X);

if height >= 30 || nSamples <= 1
    % 树的高度达到设定的最大值，或者样本数小于等于1
    Tree = struct('left', [], 'right', [], 'splitAttr', [], 'splitValue', [], 'size', nSamples, 'height', height);
    return;
end

% 随机选择一个属性和一个分割值
splitAttr = randi(nFeatures, 1);
splitValue = min(X(:,splitAttr)) + rand(1)*(max(X(:,splitAttr))-min(X(:,splitAttr)));

% 选择子样本集
if nSamples > sampleSize
    % 如果样本数大于设定的子样本集大小，则随机选择子样本集
    subIdx = randperm(nSamples, sampleSize);
    Xsub = X(subIdx,:);
else
    % 如果样本数小于等于设定的子样本集大小，则使用全部样本
    Xsub = X;
end

% 递归构造左子树和右子树
idxLeft = Xsub(:,splitAttr) < splitValue;
idxRight = Xsub(:,splitAttr) >= splitValue;
Tree = struct('left', iTree(Xsub(idxLeft,:), sampleSize, height+1), 'right', iTree(Xsub(idxRight,:), sampleSize, height+1), 'splitAttr', splitAttr, 'splitValue', splitValue, 'size', nSamples, 'height', height);

end

function pl = pathLength(X, Tree)
% 计算样本X在孤立树Tree中的路径长度

pl = 0;
while true
    if isempty(Tree.left) && isempty(Tree.right)
        % 叶子节点
        pl = pl + cValue(Tree.size);
        break;
    end
    
    if X(Tree.splitAttr) < Tree.splitValue
        Tree = Tree.left;
    else
        Tree = Tree.right;
    end
    
    pl = pl + 1;
end

end

function c = cValue(n)
% 计算c(n)

if n <= 1
    c = 0;
else
    c = 2*harmlog(n-1) - 2*(n-1)/n;
end

end

function h = harmlog(n)
% 计算调和平均数的对数

h = 0;
for i = 1:n
    h = h + 1/i;
end
h = log(h);

end

其中，`iTree`函数用于构造孤立树，`pathLength`函数用于计算样本在孤立树中的路径长度，`cValue`函数用于计算c(n)，`harmlog`函数用于计算调和平均数的对数，`iForest`函数用于构造孤立森林以及计算异常得分。