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I would like recommendations on textbooks (or online resources) covering MWPCA theoretically and with application examples (preferably in R, but also in Python, Mathematica, Matlab).

A brief intro:

Moving Window Principal Component Analysis is the usual PCA on a windowed (sub-sample of the) data. A window slides along (ordered) observations, dropping old ones and including new ones (1 or $n$ at a time). Window can be fixed or variable, depending on desired complexity of implementation and underlying distributions of the observed values.

Time series example: consider daily observations of air pollutants (say ozone, NOx, SO2, etc) for several years. Naturally, they depend on

  1. external factors (car exhausts (hence, a weekday), weather (hence, seasonal factors), air pressure, etc.)
  2. on each other (contemporaneous and cross-dependence)
  3. on themselves (auto)

The recorded observations (collected data) will certainly look differently, but the underlying distribution could still be fixed (same distribution family, same parameters). More likely this distribution changes from one season to another. In computing PCA on a window, we hope that for the duration of this window, the observations have derived from the same distribution (or, at least the effect of a different distribution is insignificant). For example, we could could consider a window of size 31 (one month, less than any of the four "calendar" seasons). A shorter window may result in larger variability in PCA. A variable window could adapt its size to the stability of observations (more stable observations - larger window size).

Challenges:

  • applicability of PCA to windowed data (meeting assumptions)
  • choice of a window size or choice of a factor (or rule) controlling the (variable) window size
  • computational performance
    • since computing PCA requires costly iterative methods in computing svd decomposition of data matrix, $X$ (rows=observations, columns=variables/features), or eigendecomposition of data's (unscaled) covariance matrix, $X'X$
  • interpretability of PCs
  • ...
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