Doing More with Less: Mutual Interdependence Analysis
The mean of a data set is one trivial representation of data from a class. Recently, mutual interdependence analysis (MIA) has been successfully used to extract more involved representations, or "mutual features", accounting for samples in the class. For example a mutual feature is a speaker signature under varying channel conditions or a face signature under varying illumination conditions. A mutual representation is a linear regression that is equally correlated with all samples of the input class. We present the MIA optimization criterion from the perspectives of regression, canonical correlation analysis and Bayesian estimation. This allows us to state and solve the MIA criterion concisely, to contrast the MIA solution to the sample mean, and to infer other properties of its closed form, unique solution under various statistical assumptions.