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All all these terms mean the same thing? Are there other terms for MWPCA? Are there any decent online references to theory and applications? Which term is most popular (if they are equivalent)?

I'm asking in the context of article search in Google Scholar. The search result is limited for rolling PCA, but more diverse, if I use other terms. Naturally, while I'm trying to figure out (takes time) how all these PCAs relate, I was hoping there is a clear answer explaining the differences or similarities.

Thanks in advance for your effort and guidance.

Oleg Melnikov
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  • They are not equivalent; *kernel PCA* has nothing to do with localization. – usεr11852 Nov 13 '15 at 22:15
  • Thanks. What if a kernel is from truncated distribution (uniform, triangular, truncated normal, etc.). Would it not be similar to a rolling PCA computed centrally on each interval? Any accessible educational reference? Thanks again for the input! – Oleg Melnikov Nov 13 '15 at 22:21
  • Kernel PCA essentially projects the data in a new space (the RKHS) and performs PCA there. It has nothing to do with windowing your data. Kernel PCA is a non-linear extension of PCA, not a localized one. – usεr11852 Nov 13 '15 at 22:36
  • I see. So, for instance, we use a kernel to move data to spectral domain and the apply PCA to it. I confused it with kernel windowing. Thanks. – Oleg Melnikov Nov 13 '15 at 22:41
  • Yeah, that is the right idea. Transferring them back is a bit non-trivial (it is relates to a procedure known as *preimaging*). – usεr11852 Nov 13 '15 at 22:57

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Local PCA: non-linear data $X$ is partitioned into Q (piece-wise linear) regions and usual PCA is applied to each region separately. See Dimension Reduction by Local Principal Component Analysis, Kambhatla and Leen, 1997

Kernel PCA: see comments from usεr11852

Moving Window PCA (MWPCA): usual PCA is computed on first $n$ observations (window of size $n$), then new observation is added and the oldest is deleted (if data is indexed by time), this slides the window along data by one element. PCA is recomputed. The window can shift 1 observation at a time or more. Thus, local PCA is a special case of MWPCA with window shifting $n$ observations at once. See Process Monitoring Approach Using Fast Moving Window PCA, Wang, Iwing, and Kruger, 2005.

Rolling PCA, dynamic PCA, time-dependent PCA, etc. are just different names of MWPCA

Oleg Melnikov
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