Generalized mutual interdependence analysis

Abstract

The mean of a data set is one trivial representation of data from one 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 above 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. We define a generalized MIA solution (GMIA) and apply MIA and GMIA in a text-independent speaker verification task using the NTIMIT database. Both methods show competitive performance with equal-error-rates of 7.5 % and 6.5 % respectively over 630 speakers.

Signature extraction using mutual interdependencies

“…The understanding of how this problem can be succinctly and elegantly stated has been evolved and generalized [6]. In this section we present an up to date statement of MIA.…”

“…This motivated the comparison with CCA as a generalization of FLDA, and the discovery of an equivalent, CCA-based formulation of the MIA problem. We revisit this new definition following and extending Claussen et al [6]. First, we review CCA and its FLDA equivalent formulation.…”

“…A unique solution can be found by further constraining Eq. (6). One such constraint is that a be a linear combination of the inputs X (p) :…”

“…Claussen et al [6] analyzed MIA's sensitivity to noise and extended its model to capture this effect in the data with a Bayesian MIA interpretation. This section provides a complete presentation of this analysis.…”

“…We aim to extract an invariant representation of high-dimensional instances of a single class, where the number of input instances N is smaller than their dimensionality D. An invariant is a property or feature of the input data that does not change within its class. Approaches that have been designed for this purpose are mutual interdependence analysis (MIA) and generalized MIA (GMIA) [4][5][6]. We revisit both methods in Sections 2 and 3, respectively, and parametrize GMIA with l, which subsumes MIA for l ¼ 0.…”