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L1-norm principal-component analysis in L2-norm-reduced-rank data subspaces

Markopoulos, Panos, Pados Dimitris A., Karystinos Georgios, Langberg Michael

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URIhttp://purl.tuc.gr/dl/dias/D7DF54F9-9BF5-46CB-8EAB-48F03F73F4F0-
Identifierhttps://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-
Identifierhttps://doi.org/10.1117/12.2263733-
Languageen-
TitleL1-norm principal-component analysis in L2-norm-reduced-rank data subspacesen
CreatorMarkopoulos, Panosen
CreatorPados Dimitris A.en
CreatorKarystinos Georgiosen
CreatorΚαρυστινος Γεωργιοςel
CreatorLangberg Michaelen
PublisherSociety of Photo-optical Instrumentation Engineersen
Content SummaryStandard 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 ItemΠλήρης Δημοσίευση σε Συνέδριοel
Type of ItemConference Full Paperen
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2018-06-19-
Date of Publication2017-
SubjectDimensionality reductionen
SubjectEigen-decompositionen
SubjectFaulty measurementsen
SubjectL1-normen
SubjectOutlier resistanceen
SubjectSubspace signal processingen
Bibliographic CitationP. 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: 10.1117/12.2263733en

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