Sparse online principal component analysis for parameter estimation in factor model

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.