We present the basic idea of abstract principal component analysis(APCA)as a general approach that extends various popular data analysis techniques such as PCA and GPCA.We describe the mathematical theory behind APCA ...We present the basic idea of abstract principal component analysis(APCA)as a general approach that extends various popular data analysis techniques such as PCA and GPCA.We describe the mathematical theory behind APCA and focus on a particular application to mode extractions from a data set of mixed temporal and spatial signals.For illustration,algorithmic implementation details and numerical examples are presented for the extraction of a number of basic types of wave modes including,in particular,dynamic modes involving spatial shifts.展开更多
基金supported by National Science Foundation of USA(Grant No.DMS101607)
文摘We present the basic idea of abstract principal component analysis(APCA)as a general approach that extends various popular data analysis techniques such as PCA and GPCA.We describe the mathematical theory behind APCA and focus on a particular application to mode extractions from a data set of mixed temporal and spatial signals.For illustration,algorithmic implementation details and numerical examples are presented for the extraction of a number of basic types of wave modes including,in particular,dynamic modes involving spatial shifts.
