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Sparse online principal component analysis for parameter estimation in factor model

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Abstract

Factor model has the capacity of reducing redundant information in real data analysis. Note that sparse principal component (SPC) method is developed to obtain sparse solutions from the model, online principal component (OPC) method is used to handle with online dimension reduction problem. It is worth considering how to obtain a sparse solution with online learning. In this paper we propose a novel sparse online principal component (SOPC) method for sparse parameter estimation in factor model, where we combine the advantages of the SPC and OPC methods in estimating the loading matrix and the idiosyncratic variance matrix. By integrating sparse modelling with online update, the SOPC is capable of finding the sparse solution through iterative online updating, leading to a consistent and easily interpretable solution. Stability and sensitivity of the SOPC are assessed through a simulation study. The method is then applied to analyze two real data sets concerning drug efficacy and human activity recognition.

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Acknowledgements

We thank the associate editor and the reviewers for their useful feedback that improved this paper. This work was supported by a grant from Natural Science Foundation of Shandong under project ID ZR2020MA022.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, China

    Guangbao Guo & Chunjie Wei

  2. School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia

    Guoqi Qian

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  1. Guangbao Guo
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  2. Chunjie Wei
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  3. Guoqi Qian
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Correspondence to Guangbao Guo.

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Supplementary materials

The codes of the SOPC in R software are presented in supplementary materials, which is available as package \emph{SOPC} (Guo, et al. [2022]). (PDF 220KB).

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Guo, G., Wei, C. & Qian, G. Sparse online principal component analysis for parameter estimation in factor model. Comput Stat 38, 1095–1116 (2023). https://doi.org/10.1007/s00180-022-01270-z

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