Covariance-Generalized Matching Component Analysis for Data Fusion and Transfer Learning

Abstract

In order to allow for the encoding of additional statistical information in data fusion and transfer learning applications, we introduce a generalized covariance constraint for the matching component analysis (MCA) transfer learning technique. After proving a semi-orthogonally constrained trace maximization lemma, we develop a closed-form solution to the resulting covariance-generalized optimization problem and provide an algorithm for its computation. We call this technique -applicable to both data fusion and transfer learning -covariance-generalized MCA (CGMCA).

Microtexture region segmentation of eddy current testing data using a structural prior

“…It was originally developed for transfer learning; one of its initial applications was to find a common domain between experimental and simulated synthetic aperture radar (SAR) data to improve classification. We use an extension of MCA known as covariance generalized matching component analysis (CGMCA) [32]. For this application, the two data domains of interest are (1) the underlying segmentation of a known microstructure into MTR and (2) the corresponding ECT data of the microstructure.…”

“…is the dimension of the common domain, and the symmetric positive definite matrix Γ i ∈ R k×k is the covariance matrix prescribed to the map g i . It was shown in [32] that if we require that…”

Microtexture region segmentation using matching component analysis applied to eddy current testing data

“…A closed-form solution exists to this problem if the maps g i are restricted to the set of affine linear transformations. 4…”

“…This method combines a machine learning technique known as covariance generalized matching component analysis 4 (CGMCA) with a method developed for edge preservation in image deblurring. 5 We demonstrate it on simulated ECT data of a realistic titanium alloy specimen.…”