Abstract principal component analysis

作者：Li TianJiang; Du Qiang^*

来源：Science China Mathematics, 2013, 56(12): 2783-2798.

DOI：10.1007/s11425-013-4715-9

• abstract principal component analysis
• pattern recognition
• mode extraction
• reduced order modeling
• traveling waves

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.

• 出版日期2013-12
• 单位北京计算科学研究中心