L1-Subspace Tracking for Streaming Data

Abstract

High-dimensional data usually exhibit intrinsic low-rank structures. With tremendous amount of streaming data generated by ubiquitous sensors in the world of Internet-of-Things, fast detection of such low-rank pattern is of utmost importance to a wide range of applications. In this work, we present an L1-subspace tracking method to capture the low-rank structure of streaming data. The method is based on the L1-norm principal-component analysis (L1-PCA) theory that offers outlier resistance in subspace calculation. The proposed method updates the L1-subspace as new data are acquired by sensors. In each time slot, the conformity of each datum is measured by the L1-subspace calculated in the previous time slot and used to weigh the datum. Iterative weighted L1-PCA is then executed through a refining function. The superiority of the proposed L1-subspace tracking method compared to existing approaches is demonstrated through experimental studies in various application fields.