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Principal component analysis for 'signal extraction'

Mathematics Asked by Mat P on February 7, 2021

This question might sound very odd to people with better understanding and the question is very fundamental, but lets try:
I have for example 1000 individual signals that are not totally random but there are like, lets say, 5 main groups or shapes that roughly divides these signals to 5 groups. These 1000 signals (we can assume that I know the amount of originals signals) are summed into 10 or more fairly heterogeneous outputs, so that every output have about 100 signals summed. Using PCA to analyze these 10 or more fairly heterogeneous outputs, i can clearly notice the difference of these outputs and even do some kind of clustering. But is there a way to extract the dominant 5 signals with PCA results? I know there are methods like ICA, but if I only use SVD to create the principal components, does this allow me to rebuild some kind of averages of the 5(or less) original ‘shapes’ of signals?

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