3. Multilinear Independent Component Analysis (MultilinearICA)
Introduction
In this vignette we consider approximating a tensor as a product of multiple low-rank matrices (a.k.a., factor matrices) and a core tensor.
Test data is available from toyModel.
##
## Attaching package: 'nnTensor'## The following object is masked from 'package:iTensor':
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## toyModel## Formal class 'Tensor' [package "rTensor"] with 3 slots
## ..@ num_modes: int 3
## ..@ modes : int [1:3] 30 30 30
## ..@ data : num [1:30, 1:30, 1:30] 113 81 120 95 102 2 4 2 0 1 ...You will see that there are four small blocks in the diagonal direction of the data tensor.
Multilinear Independent Component Analysis (MultilinearICA)
There are so many tensor decomposition algorithms but here we consider that each factor matrix is extracted by Independent Component Analysis (ICA). This is called Multilinear Independent Component Analysis (MultilinearICA (Vasilescu 2005)).
MultilinearICA can be performed as follows.
The rank for each factor matrix can be set as Js and the
decomposition algorithm can be easily switched by
algorithm.
By using recTensor of nnTensor, user can
easily reconstruct the data from core tensor and factor matrices as
follows.
Session Information
## R version 4.4.1 (2024-06-14)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.1 LTS
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