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...

worldwide networks of seismic recording instruments mostly record only translational ground motion in two or three orthogonal directions. rotational component of earthquake is not commonly recorded. several theories are available to estimate a torsional component from recorded translational components of ground motion. in this paper detailed investigations are made to study the relative perform...

Background Various clinical (disease activity, seropositive RA etc.) and metabolic risk factors (Dkk1 have been associated with erosive rheumatoid arthritis (RA). However, such might be intertwined, multicollinearity reduce our ability to discern the individual contribution score. Principal component analysis (PCA) is statistical technique for reducing dataset’s dimension principal regression (...