In the probabilistic framework of multivariate regular variation, first order behavior heavy-tailed random vectors above large radial thresholds is ruled by a homogeneous limit measure. For high dimensional vector, reasonable assumption that support this measure concentrated on lower subspace, meaning certain linear combinations components are much likelier to be than others. Identifying subspa...

Principal component analysis (PCA) is one of the most popular tools in multivariate exploratory data analysis. Its probabilistic version (PPCA) based on maximum likelihood procedure provides a manner to implement dimension reduction. Recently, bilinear PPCA (BPPCA) model, which assumes that noise terms follow matrix variate Gaussian distributions, has been introduced directly deal with two-dime...

Functional Principal Component Analysis (FPCA) has become a widely used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or both and covariance function. However, methods of first kind not suitable that display second-order variation, while those second time-consuming make it difficul...