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Low-rank and sparse optimization for GPCA with applications to SARX system identification

This paper proposes a low-rank and sparse optimization approach to generalized principal component analysis (GPCA) problems. The GPCA problem has a lot of applications in control, system identification, signal processing, and machine learning, however, is a kind of combinatorial problems and NP hard in general. This paper formulates the GPCA problem as a low-rank and sparse optimization problem, that is, matrix rank and l0 norm minimization problem, and proposes a new algorithm based on the iterative reweighed least squares (IRLS) algorithm. This paper applies this algorithm to the system identification problem of switched autoregressive exogenous (SARX) systems, where the model order of each submodel is unknown. Numerical examples show that the proposed algorithm can identify the switching sequence, system order and parameters of submodels simultaneously.