Abstract
ℓ 2∕ℓ 1-norm is widely used to measure coding residual in principal component analysis (PCA). In this case, it usually assumes that the residual follows Gaussian/Laplacian distribution. However, it may fail to describe the coding errors in practice when there are outliers. Toward this end, this paper proposes a robust sparse PCA (RSPCA) approach to solve the outlier problem, by modeling the sparse coding as a sparsity-constrained weighted regression problem. By using a series of equivalent transformations, we show RSPCA is equivalent to the weighted elastic net (WEN) problem and thus the least angle regression elastic net (LARS-EN) method is used to yield the optimal solution. Simulation results illustrated the effectiveness of this approach.
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Acknowledgements
This work was supported by “the Fundamental Research Funds for the Central Universities” under award number ZYGX2010J016.
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Ling, W., Yin, J. (2012). The Robust Sparse PCA for Data Reconstructive via Weighted Elastic Net. In: Liang, Q., et al. Communications, Signal Processing, and Systems. Lecture Notes in Electrical Engineering, vol 202. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5803-6_23
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DOI: https://doi.org/10.1007/978-1-4614-5803-6_23
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