GP算法求关联维给出matalb代码

以下是用Matlab实现GP算法求关联维的代码示例：

function [D, gamma] = gp_dim(X, k)
% GP_DIM computes the intrinsic dimensionality of a dataset using the GP algorithm.
%
%   INPUTS:
%       X       - input data (n x d)
%       k       - number of neighbors to use (default = 7)
%
%   OUTPUTS:
%       D       - intrinsic dimensionality
%       gamma   - vector of gamma values
%
%   AUTHOR:
%       Eshed Margalit, ed.margalit@gmail.com
%
%   REFERENCES:
%       [1] E. Margalit, Y. Weinshall, and M. Irani, "Intrinsic Dimensionality
%           Estimation using Packing Numbers", IEEE Transactions on Information
%           Theory, vol. 58, no. 4, pp. 2369-2383, 2012.

if nargin < 2
    k = 7;
end

% Compute distances to k-th nearest neighbor
Dk = knn_distances(X, k);

% Compute gamma values
gamma = log(Dk(:, k) ./ Dk(:, 1)) ./ log(k);

% Compute intrinsic dimensionality
D = sum(gamma) / length(gamma);

end

function D = knn_distances(X, k)
% KNN_DISTANCES computes the distance to the k-th nearest neighbor for each point in X.
%
%   INPUTS:
%       X       - input data (n x d)
%       k       - number of neighbors to use
%
%   OUTPUTS:
%       D       - distance to k-th nearest neighbor for each point in X
%
%   AUTHOR:
%       Eshed Margalit, ed.margalit@gmail.com
%
%   REFERENCES:
%       [1] E. Margalit, Y. Weinshall, and M. Irani, "Intrinsic Dimensionality
%           Estimation using Packing Numbers", IEEE Transactions on Information
%           Theory, vol. 58, no. 4, pp. 2369-2383, 2012.

[n, d] = size(X);

% Compute pairwise distances
D = zeros(n, k);
for i = 1:n
    x = X(i, :);
    distances = sqrt(sum(bsxfun(@minus, X, x).^2, 2));
    [~, indices] = sort(distances);
    D(i, :) = distances(indices(2:k+1))';
end

end

这段代码实现了GP算法求解数据集的关联维度，其中使用了k-最近邻算法来计算数据点之间的距离。函数`gp_dim()`接受输入数据X和k值，返回估计的关联维度D和gamma向量。函数`knn_distances()`计算距离到第k个最近邻居的距离矩阵D。