2017/10/25 by Gang Wang, Jia Chen, Wang, Gang +3
Chemistry · Computer Science · Engineering · Mathematics · #Blind Source Separation Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Spectroscopy and Chemometric Analyses #cs.IT #cs.LG #math.IT #stat.ML
paper · pdf · doi:10.48550/arxiv.1710.09429
5 pages, 2 figures
arxiv created 2017/10/25 · openalex publication_date 2017/10/25 · arxiv updated 2017/10/27 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain setups, one wishes to extract the most significant information of one dataset relative to other datasets. Specifically, the interest may be on identifying, namely extracting features that are specific to a single target dataset but not the others. This paper develops a novel approach for such so-termed discriminative data analysis, and establishes its optimality in the least-squares (LS) sense under suitable data modeling assumptions. The criterion reveals linear combinations of variables by maximizing the ratio of the variance of the target data to that of the remainders. The novel approach solves a generalized eigenvalue problem by performing SVD just once. Numerical tests using synthetic and real datasets showcase the merits of the proposed approach relative to its competing alternatives.