Using PCA to reduce dimensionality of multivariate time series

Question

I have multiple (12000) multivariate time series datasets. Each MTS has 4 dimensions and 3500 time-points.

I want to reduce each MTS into a single vector of features using PCA. As far as I've seen, in a lot of cases dataset is reduced using PCA either by dimensions or time points. But not both.

Is it possible to do it?

Answer 1

Your data is 3-order tensor (no_examples x no_features x no_time_steps), so as you remarked, you can't use just PCA which works for matrices (matrices are 2-tensors, since a matrix $M = (M_{ij})_{i < n, j < m} = \sum_{i < n, j < m} M_{ij} e_i^T e'_j$)

You can use a technique that is called higher-order, or tensor, SVD. This technique is a generalization of SVD to higher order tensors.

In R there is a package rTensor which seems to be aimed at this.