3. Multilinear Independent Component Analysis (MultilinearICA)

In iTensor: ICA-Based Matrix/Tensor Decomposition

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.

library("iTensor")
library("nnTensor")
data <- nnTensor::toyModel("CP")
str(data, 2)

You will see that there are four small blocks in the diagonal direction of the data tensor.

plotTensor3D(data)

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 [@multilinearica]).

MultilinearICA can be performed as follows.

out <- MultilinearICA(data, Js=c(4,4,4), algorithm="FastICA")

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.

rec_data <- recTensor(out$S, out$As)
plotTensor3D(rec_data)

Session Information {.unnumbered}

sessionInfo()

References

iTensor documentation built on April 28, 2023, 9:11 a.m.