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?
4 BSS is a transform? • Like Fourier, we decompose into components by transforming the observations into another vector space which maximises the separation between interesting (signal) and unwanted (noise).• Unlike Fourier, separation is not based on frequency- It’s based on independence • Sources can have the same frequency …
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