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Blind source separation of tensor-valued time series
Tekijät: Virta Joni, Nordhausen Klaus
Kustantaja: ELSEVIER SCIENCE BV
Julkaisuvuosi: 2017
Journal: Signal Processing
Tietokannassa oleva lehden nimi: SIGNAL PROCESSING
Lehden akronyymi: SIGNAL PROCESS
Vuosikerta: 141
Aloitussivu: 204
Lopetussivu: 216
Sivujen määrä: 13
ISSN: 0165-1684
eISSN: 1879-2677
DOI: https://doi.org/10.1016/j.sigpro.2017.06.008
Tiivistelmä
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. (C) 2017 Elsevier B.V. All rights reserved.
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. (C) 2017 Elsevier B.V. All rights reserved.
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