Abstract
In this work, we consider the Robust Principal Components Analysis, a popular method of dimensionality reduction. The corresponding optimization involves the minimization of \(l_0\)-norm which is known to be NP-hard. To deal with this problem, we replace the \(l_0\)-norm by a non-convex approximation, namely capped \(l_1\)-norm. The resulting optimization problem is non-convex for which we develop a reweighted \(l_1\) based algorithm. Numerical experiments on several synthetic datasets illustrate the efficiency of our algorithm and its superiority comparing to several state-of-the-art algorithms.
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Le, H.M., Xuanthanh, V. (2020). Reweighted \(\ell _1\) Algorithm for Robust Principal Component Analysis. In: Le Thi, H., Le, H., Pham Dinh, T., Nguyen, N. (eds) Advanced Computational Methods for Knowledge Engineering. ICCSAMA 2019. Advances in Intelligent Systems and Computing, vol 1121. Springer, Cham. https://doi.org/10.1007/978-3-030-38364-0_12
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DOI: https://doi.org/10.1007/978-3-030-38364-0_12
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