Semi-blind bilinear matrix system, BYY harmony learning, and gene analysis applications

摘要

A bilinear matrix system (BMS) is proposed as a general semi-blind learning framework for modeling matrix-formatted data and for extracting matrix-formatted inner factors. Different special cases of this framework lead to a family of typical learning tasks. The problem of learning such a semi-blind BMS learning is formulated as a problem of learning a particular BYY system for estimating unknown parameters and for making model selection. We develop a BYY harmony learning algorithm for learning matrix normal distribution based BMS, which relates to and also generalizes typical learning methods, such as factor analyses, 2D-PCA, and manifold learning, …, etc, featured with automatic model selection on the bi-perspective dimensions. Also, we apply this algorithm for estimating the profiles of transcriptional factor activities from gene expression data. Moreover, we briefly outline typical applications of BMS, especially a new perspective of Yang domain based hypothesis test versus Ying domain based test, exampled by schematic algorithms and genetic diagnoses applications.