SPARSE DECENTRALIZED PRINCIPAL COMPONENTS ANALYSIS FOR DIMENSIONALITY REDUCTION

Abstract

Principal components analysis (PCA) is a data compression technology relying on dimensionality reduction. In a wireless sensor network, the acquired data may be spatially scattered and include many zero variables, for which a standard PCA approach cannot account for. To this end, a new algorithm is designed to solve both problems. We combine sparse principal components analysis (SPCA) and distributed principal components analysis (DPCA) together to obtain a sparse distributed principal components analysis (SDPCA) algorithm. Norm-one regularization along with the alternating direction method of multipliers (ADMM) is used for SPCA. ADMM is also employed to obtain a distributed compression algorithm that consists of computationally simple local updating recursions. Further, inter-sensor communication noise is considered. Numerical tests using both synthetic and real data demonstrate that the novel SDPCA algorithm can be applied in different situations and gives a good principal subspace estimation result.