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Abstract principal component analysis

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    TianJiang Li & Qiang Du

  2. CGG, Houston, TX, 77072, USA

    TianJiang Li

  3. Lab of Applied Mathematics, Beijing Computational Science Research Center, Beijing, 100084, China

    Qiang Du

Authors
  1. TianJiang Li
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  2. Qiang Du
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Correspondence to Qiang Du.

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Dedicated to Professor Shi Zhong-Ci on the Occasion of his 80th Birthday

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Li, T., Du, Q. Abstract principal component analysis. Sci. China Math. 56, 2783–2798 (2013). https://doi.org/10.1007/s11425-013-4715-9

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  • DOI: https://doi.org/10.1007/s11425-013-4715-9

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