Learning the higher-order structure of a natural sound

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Abstract
Unsupervised learning algorithms paying attention only to second-order statistics ignore the phase structure (higher-order statistics) of signals, which contains all the informative temporal and spatial coincidences which we think of as 'features'. Here we discuss how an Independent Component Analysis (ICA) algorithm may be used to elucidate the higher-order structure of natural signals, yielding their independent basis functions. This is illustrated with the ICA transform of the sound of a fingernail tapping musically on a tooth. The resulting independent basis functions look like the sounds themselves, having similar temporal envelopes and the same musical pitches. Thus they reflect both the phase and frequency information inherent in the data.