Canonical analysis based on mutual information

Allan Aasbjerg Nielsen, Jacob Schack Vestergaard

AbstractCanonical correlation analysis (CCA) is an established multivariate statistical method for finding similarities between linear combinations of (normally two) sets of multivariate observations. In this contribution we replace (linear) correlation as the measure of association between the linear combinations with the information theoretical measure mutual information (MI). We term this type of analysis canonical information analysis (CIA). MI allows for the actual joint distribution of the variables involved and not just second order statistics. While CCA is ideal for Gaussian data, CIA facilitates analysis of variables with different genesis and therefore different statistical distributions and different modalities. As a proof of concept we give a toy example. We also give an example with one (weather radar based) variable in the one set and eight spectral bands of optical satellite data in the other set.
Keywordscanonical correlation analysis (CCA), canonical information analysis (CIA), entropy, mutual information.
TypeConference paper [With referee]
Year2015    Month July    pp. 1068-1071
AddressMilan, Italy
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IMM Group(s)Image Analysis & Computer Graphics, Geoinformatics