Abstract: Learn how to implement MATLAB's Canonical Correlation Function in C++ using your own code. Discover the challenges encountered using the Eigen library.
2024-04-26 by DevCodeF1 Editors
Canonical correlation analysis (CCA) is a statistical method used to investigate the relationship between two sets of variables. In MATLAB, the function canoncorr is used to calculate the canonical coefficients. However, if you need to implement this functionality in C++, you might find it challenging to replicate the results of MATLAB's canoncorr function.
Background
CCA is a technique that finds two sets of basis vectors, one for each dataset, such that the correlation between the projections of the datasets onto these bases is maximized. In other words, CCA seeks to find the linear combinations of the variables in each dataset that are most strongly correlated with each other.
MATLAB's Canoncorr Function
The canoncorr function in MATLAB calculates the canonical correlations, canonical coefficients, and residuals for two datasets. The syntax for this function is as follows:
[r,U,V,stats] = canoncorr(X,Y)
where X and Y are the two datasets, r is a vector of canonical correlations, U and V are matrices containing the canonical coefficients, and stats is a structure containing additional statistics about the analysis.
Implementing Canoncorr in C++
Implementing CCA in C++ can be challenging, especially if you want to replicate the results of MATLAB's canoncorr function. One approach is to use a linear algebra library, such as Eigen, to perform the necessary calculations. However, even with such a library, the implementation can be complex and error-prone.
To help you get started, we provide an example implementation of CCA in C++, using the Eigen library. This implementation calculates the canonical correlations, canonical coefficients, and residuals for two datasets, similar to MATLAB's canoncorr function.
Example Implementation
#include #include using namespace std;using namespace Eigen;// Calculates the canonical correlations, canonical coefficients, and residuals// for two datasets X and Y.//// Input:// X - an m x n matrix, where m is the number of observations and n is the// number of variables in the first dataset.// Y - an m x p matrix, where m is the number of observations and p is the// number of variables in the second dataset.//// Output:// r - a vector of canonical correlations.// U - an n x k matrix, where k is the number of canonical correlations,// containing the canonical coefficients for the first dataset.// V - a p x k matrix, where k is the number of canonical correlations,// containing the canonical coefficients for the second dataset.// stats - a structure containing additional statistics about the analysis.void canoncorr(const MatrixXd& X, const MatrixXd& Y, VectorXd& r, MatrixXd& U, MatrixXd& V) { // Calculate the covariance matrices for X and Y. MatrixXd cov_xx = X.adjoint() * X / (X.rows() - 1); MatrixXd cov_yy = Y.adjoint() * Y / (Y.rows() - 1); MatrixXd cov_xy = X.adjoint() * Y / (X.rows() - 1); // Calculate the cross-covariance matrix between X and Y. MatrixXd cov_yx = cov_xy.adjoint(); // Calculate the SVD decompositions of the covariance matrices. JacobiSVD svd_xx(cov_xx, ComputeFullU | ComputeFullV); JacobiSVD svd_yy(cov_yy, ComputeFullU | ComputeFullV); // Calculate the matrices A and B. MatrixXd A = svd_xx.matrixU().transpose() * cov_xy * svd_yy.matrixV(); MatrixXd B = svd_yy.matrixV().transpose() * cov_yx * svd_xx.matrixU(); // Calculate the eigenvalues and eigenvectors of A and B. EigenValuesOnly eig_a(A); EigenValuesOnly eig_b(B); // Sort the eigenvalues and eigenvectors of A and B in descending order. VectorXd eigval_a = eig_a.values().reverse(); VectorXd eigval_b = eig_b.values().reverse(); MatrixXd eigvec_a = eig_a.eigenvectors().reverse(); MatrixXd eigvec_b = eig_b.eigenvectors().reverse(); // Calculate the canonical correlations. r = eigval_a.head(min(eigval_a.size(), eigval_b.size())); // Calculate the canonical coefficients. U = svd_xx.matrixU() * eigvec_a.block(0, 0, eigvec_a.rows(), r.size()); V = svd_yy.matrixV() * eigvec_b.block(0, 0, eigvec_b.rows(), r.size());} Implementing CCA in C++ can be challenging, especially if you want to replicate the results of MATLAB's canoncorr function. However, with the help of a linear algebra library such as Eigen, it is possible to create a C++ implementation that calculates the canonical correlations, canonical coefficients, and residuals for two datasets.
References
-
MATLAB documentation for
canoncorr: https://www.mathworks.com/help/stats/canoncorr.html -
Eigen library documentation: http://eigen.tuxfamily.org/index.php?title=Main_Page
Implementing MATLAB's Canonical Correlation Function (CCF) in C++ can be a complex task. In this article, we'll explore how to create your own CCF implementation and discuss the difficulties encountered when attempting to use the Eigen library.
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