L1-Norm Higher-Order Singular-Value Decomposition

Markopoulos, Panos P.; Chachlakis, Dimitris G.; Prater-Bennette, Ashley

doi:10.1109/globalsip.2018.8646385

Cited by 14 publications

(3 citation statements)

References 27 publications

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“…where [22,32,33] approximates the solution to L1-Tucker by N parallel L1-PCA problems. That is, for every n ∈ [N ], it finds Q n by solving (approximately or exactly) the L1-PCA max.…”

Section: Outliers and L1-tuckermentioning

confidence: 99%

Dynamic L1-Norm Tucker Tensor Decomposition

Chachlakis

Dhanaraj

Prater-Bennette

et al. 2021

IEEE J. Sel. Top. Signal Process.

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Tucker decomposition is a standard method for processing multi-way (tensor) measurements and finds many applications in machine learning and data mining, among other fields. When tensor measurements arrive in a streaming fashion or are too many to jointly decompose, incremental Tucker analysis is preferred. In addition, dynamic basis adaptation is desired when the nominal data subspaces change. At the same time, it has been documented that outliers in the data can significantly compromise the performance of existing methods for dynamic Tucker analysis. In this work, we present Dynamic L1-Tucker: an algorithm for dynamic and outlier-resistant Tucker analysis of tensor data. Our experimental studies on both real and synthetic datasets corroborate that the proposed method (i) attains high basis estimation performance, (ii) identifies/rejects outliers, and (iii) adapts to nominal subspace changes.

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“…where [22,32,33] approximates the solution to L1-Tucker by N parallel L1-PCA problems. That is, for every n ∈ [N ], it finds Q n by solving (approximately or exactly) the L1-PCA max.…”

Section: Outliers and L1-tuckermentioning

confidence: 99%

Dynamic L1-Norm Tucker Tensor Decomposition

Chachlakis

Dhanaraj

Prater-Bennette

et al. 2021

IEEE J. Sel. Top. Signal Process.

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“…For any {U n ∈ S(D n , d n )} n∈[N ] , it holds that Proof. Let Y = X × n∈[N ] U n ∈ R d1×...×d N and define y = vec([Y] (1) ) and x = vec([X ] (1) ). It holds that Y 1 = y 1…”

Section: ) Convergencementioning

confidence: 99%

“…This figure reveals the sensitivity of standard HOSVD and HOOI as the training data corruption probability increases. At the same time, the proposed 1 We consider a simple classifier, so that the study focuses to the impact of each compression method. 2 L1-Tucker methods exhibit robustness against the corruption, maintaining the highest average accuracy for every value of α.…”

Section: B Classificationmentioning

confidence: 99%

L1-Norm Tucker Tensor Decomposition

2019

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Tucker decomposition is a common method for the analysis of multi-way/tensor data. Standard Tucker has been shown to be sensitive against heavy corruptions, due to its L2-norm-based formulation which places squared emphasis to peripheral entries.In this work, we explore L1-Tucker, an L1-norm based reformulation of standard Tucker decomposition. After formulating the problem, we present two algorithms for its solution, namely L1-norm Higher-Order Singular Value Decomposition (L1-HOSVD) and L1-norm Higher-Order Orthogonal Iterations (L1-HOOI). The presented algorithms are accompanied by complexity and convergence analysis. Our numerical studies on tensor reconstruction and classification corroborate that L1-Tucker, implemented by means of the proposed methods, attains similar performance to standard Tucker when the processed data are corruption-free, while it exhibits sturdy resistance against heavily corrupted entries.

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