## PCA with Rubner-Tavan Networks

One of the most interesting effects of PCA (Principal Component Analysis) is to decorrelate the input covariance matrix C, by computing the eigenvectors and operating a base change using a matrix V: The eigenvectors are sorted in descending order considering the corresponding eigenvalue, therefore Cpca is a diagonal matrix where the non-null elements are λ1 >= λ2 >= λ3 >= … >= λn. By selecting the top p eigenvalues, it’s possible to operate a dimensionality reduction by projecting the samples in the new sub-space determined by the p top eigenvectors (it’s possible to use Gram-Schmidt orthonormalization if they don’t have a unitary length). The standard PCA procedure works with a bottom-up approach, obtaining the decorrelation of C as a final effect, however, it’s possible to employ neural networks, imposing this condition as an optimization step. One the most effective model has been proposed by Rubner and Tavan (and it’s named after them). Its […]