ResearchTrend.AI
  • Papers
  • Communities
  • Events
  • Blog
  • Pricing
Papers
Communities
Social Events
Terms and Conditions
Pricing
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2025 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 1703.10381
24
16

Blind source separation of tensor-valued time series

30 March 2017
Joni Virta
K. Nordhausen
    AI4TS
ArXiv (abs)PDFHTML
Abstract

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.

View on arXiv
Comments on this paper