Transcription of Blind Source Separation: PCA & ICA - mit.edu
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Blind Source Separation: PCA & ICA - mit.edu
D. Clifford gari [at] mit . ~gari G. D. Clifford 2005-2009 Blind Source Separation: PCA & ICAWhat is BSS?Assume an observation (signal) is a linear mix of >1 unknown independentsource signalsThe mixing (not the signals) is stationaryWe have as manyobservations as unknown sources To find sources in observations- need to define a suitable measure of For example - the cocktail party problem(sources are speakers and background noise):The cocktail party problem - find ZAz1z2zNXTZTXT=AZTx1x2xN2 Formal statement of problem N independentsources ..Zmn( MxN) linear square mixing ..Ann( NxN) (#sources=#sensors) produces a set of observations ..Xmn( MxN).. XT= AZTF ormal statement of solution demix observations ..XT( NxM)into YT= WXTYT(NxM) ZTW(NxN) A-1 How do we recover the independent sources?
6 SVD noise/signal separation To perform SVD filtering of a signal, use a truncated SVD decomposition (using the first p eigenvectors) Y=USpVT [Reduce the dimensionality of the data by discarding noise projections Snoise=0 Then reconstruct the data with just the signal subsapce]
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