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")## Warning: no DISPLAY variable so Tk is not available
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## Attaching package: 'nnTensor'
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## toyModel
data <- nnTensor::toyModel("CP")
str(data, 2)## 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.
plotTensor3D(data)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.
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)## R version 4.3.0 (2023-04-21)
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## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
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