2017/03/30 by Joni Virta, Klaus Nordhausen
Computer Science · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Blind Source Separation Techniques #Blind signal separation #Computer science #Dimension (graph theory) #Mathematics #Pattern recognition (psychology) #Pure mathematics #Series (stratigraphy) #Speech and Audio Processing #Tensor (intrinsic definition) #Tensor decomposition and applications #Transformation (genetics) #math.ST #msc:62H12 #msc:62M10 #stat.TH
paper · pdf · doi:10.1016/j.sigpro.2017.06.008
published as Signal Processing, Vol 141, 204-216 (2017) · 26 pages, 6 figures
arxiv created 2017/03/30 · openalex publication_date 2017/06/10 · arxiv updated 2017/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The blind source separation model for multivariate time series generally assumes that the observed series is a linear transformation of an unobserved series with temporally uncorrelated or independent components. Given the observations, the objective is to find a linear transformation that recovers the latent series. Several methods for accomplishing this exist and three particular ones are the classic SOBI and the recently proposed generalized FOBI (gFOBI) and generalized JADE (gJADE), each based on the use of joint lagged moments. In this paper we generalize the methodologies behind these algorithms for tensor-valued time series. We assume that our data consists of a tensor observed at each time point and that the observations are linear transformations of latent tensors we wish to estimate. The tensorial generalizations are shown to have particularly elegant forms and we show that each of them is Fisher consistent and orthogonal equivariant. Comparing the new methods with the original ones in various settings shows that the tensorial extensions are superior to both their vector-valued counterparts and to two existing tensorial dimension reduction methods for i.i.d. data. Finally, applications to fMRI-data and video processing show that the methods are capable of extracting relevant information from noisy high-dimensional data.