2. Multimodal Independent Component Analysis (MICA) and Group Independent Component Analysis (GroupICA)

In iTensor: ICA-Based Matrix/Tensor Decomposition

Introduction

In this vignette we consider approximating multiple data matrices as a product of multiple low-rank matrices (a.k.a., factor matrices).

Test data is available from toyModel.

library("iTensor")
data1 <- iTensor::toyModel("MICA")
data2 <- iTensor::toyModel("GroupICA")
str(data1, 2)
str(data2, 2)

Both data1 and data2 contain two time-series data X and Y as follows.

plot.ts(data1$X[7700:8000,], main="data1 (X)")
plot.ts(data1$Y[7700:8000,], main="data1 (Y)")

plot.ts(data2$X[4700:5000,], main="data2 (X)")
plot.ts(data2$Y[4700:5000,], main="data2 (Y)")

Multimodal Independent Component Analysis (MICA)

As a formulation that extends ICA (independent component analysis) to the multiple matrices case, Multimodal Independent Component Analysis (MICA) was proposed ([@mica]). MICA extracts statistically dependent pairs of features from the sources, where the components of feature vector extracted from each source are independent.

MICA can be performed as follows.

t_series <- seq(from = 0.00, to = 1.000, by = 1e-4)
out.MICA <- MICA(data1$X, data1$Y, J=3, gamma_ts = 1 - 1 / (1 + exp(-100 * (t_series - 0.3))))

J is the rank parameter for ICA and gamma_ts is the weighting factor for dependence on independence. You will see that MICA could extract some time-series signals.

plot.ts(out.MICA$U[7700:8000, ], main="Source Signal (X)")
plot.ts(out.MICA$V[7700:8000, ], main="Source Signal (Y)")

Group Independent Component Analysis (GroupICA)

Another formulation of the decomposition is Group Independent Component Analysis (GroupICA [@groupica1; @groupica2]). GroupICA can be performed as follows.

out_groupica <- GroupICA(data2, J1=6, algorithm="pooled")

The rank for each factor matrix can be set as J1 and the decomposition algorithm can be easily switched by ica.algorithm (algorithm of ICA and ICA2 can be specified). To pool the results of ICA against each data matrix, we implemented three algorithms such as pooled, Calhoun2009, and Pfister2018. For the details, see the references [@groupica1; @groupica2].

You will see that GroupICA could extract some time-series signals.

plot.ts(out_groupica$Ss[[1]], main="Source Signal (X)")
plot.ts(out_groupica$Ss[[2]], main="Source Signal (Y)")

Unlike MICA, GroupICA can also be applied to more than three matrices.

Session Information {.unnumbered}

sessionInfo()

References

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