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Technical University of Crete
Technical University of Crete
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| URI | http://purl.tuc.gr/dl/dias/D7DF54F9-9BF5-46CB-8EAB-48F03F73F4F0 | - |
| Identifier | https://www.spiedigitallibrary.org/conference-proceedings-of-spie/10211/1/L1-norm-principal-component-analysis-in-L2-norm-reduced-rank/10.1117/12.2263733.short?SSO=1 | - |
| Identifier | https://doi.org/10.1117/12.2263733 | - |
| Language | en | - |
| Title | L1-norm principal-component analysis in L2-norm-reduced-rank data subspaces | en |
| Creator | Markopoulos, Panos | en |
| Creator | Pados Dimitris A. | en |
| Creator | Karystinos Georgios | en |
| Creator | Καρυστινος Γεωργιος | el |
| Creator | Langberg Michael | en |
| Publisher | Society of Photo-optical Instrumentation Engineers | en |
| Content Summary | Standard Principal-Component Analysis (PCA) is known to be very sensitive to outliers among the processed data.1 On the other hand, it has been recently shown that L1-norm-based PCA (L1-PCA) exhibits sturdy resistance against outliers, while it performs similar to standard PCA when applied to nominal or smoothly corrupted data.2, 3 Exact calculation of the K L1-norm Principal Components (L1-PCs) of a rank-r data matrix X∈ RD×N costs O(2NK), in the general case, and O(N(r-1)K+1) when r is fixed with respect to N.2, 3 In this work, we examine approximating the K L1-PCs of X by the K L1-PCs of its L2-norm-based rank-d approximation (K≤d≤r), calculable exactly with reduced complexity O(N(d-1)K+1). Reduced-rank L1-PCA aims at leveraging both the low computational cost of standard PCA and the outlier-resistance of L1-PCA. Our novel approximation guarantees and experiments on dimensionality reduction show that, for appropriately chosen d, reduced-rank L1-PCA performs almost identical to L1-PCA. | en |
| Type of Item | Πλήρης Δημοσίευση σε Συνέδριο | el |
| Type of Item | Conference Full Paper | en |
| License | http://creativecommons.org/licenses/by/4.0/ | en |
| Date of Item | 2018-06-19 | - |
| Date of Publication | 2017 | - |
| Subject | Dimensionality reduction | en |
| Subject | Eigen-decomposition | en |
| Subject | Faulty measurements | en |
| Subject | L1-norm | en |
| Subject | Outlier resistance | en |
| Subject | Subspace signal processing | en |
| Bibliographic Citation | P. P. Markopoulos, D. A. Pados, G. N. Karystinos and M. Langberg, "L1-norm principal-component analysis in L2-norm-reduced-rank data subspaces," in Compressive Sensing VI: From Diverse Modalities to Big Data Analytics, vol. 10211, 2017. doi: 10.1117/12.2263733 | en |
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