Adaptive L1-Norm Principal-Component Analysis With Online Outlier Rejection

Markopoulos, Panos P.; Dhanaraj, Mayur; Savakis, Andreas

doi:10.1109/jstsp.2018.2874165

Cited by 28 publications

(11 citation statements)

References 55 publications

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“…When a new measurementX t , t ≥ 1 is collected 1 we perform a reliability check on it to assess its reliability based on the most recently updated set of bases Q t−1 . Motivated by [27,48], we define the reliability as…”

Section: B Streaming Updatesmentioning

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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Section: B Streaming Updatesmentioning

confidence: 99%

Dynamic L1-Norm Tucker Tensor Decomposition

Chachlakis

Dhanaraj

Prater-Bennette

et al. 2021

IEEE J. Sel. Top. Signal Process.

Self Cite

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“…Some other RST algorithms are able to track the underlying subspace over time from measurements corrupted by sparse outliers such as MRMD [19], OTNNR [24], L1-PCA [26], L1-IRW [30], OLP-RPCA [25], and OSTP [31]. Most of them use a pregularization (0 ≤ p ≤ 1) to discard the effect of outliers.…”

Section: Other Algorithmsmentioning

confidence: 99%

Robust Subspace Tracking Algorithms in Signal Processing: A Brief Survey

Thanh

Dũng

Trung

et al. 2021

REV J. Electron. Commun.

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Principal component analysis (PCA) and subspace estimation (SE) are popular data analysis tools and used in a wide range of applications. The main interest in PCA/SE is for dimensionality reduction and low-rank approximation purposes. The emergence of big data streams have led to several essential issues for performing PCA/SE. Among them are (i) the size of such data streams increases over time, (ii) the underlying models may be time-dependent, and (iii) problem of dealing with the uncertainty and incompleteness in data. A robust variant of PCA/SE for such data streams, namely robust online PCA or robust subspace tracking (RST), has been introduced as a good alternative. The main goal of this paper is to provide a brief survey on recent RST algorithms in signal processing. Particularly, we begin this survey by introducing the basic ideas of the RST problem. Then, different aspects of RST are reviewed with respect to different kinds of non-Gaussian noises and sparse constraints. Our own contributions on this topic are also highlighted.

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“…To attain the fast robust version TWSVC, the FRTWSVC replaces the L2 norm term in the objective of formula (4) and inequality constraint with L1 norm and equality constraint. Our discussed is obviously different from robust principal components analysis (PCA) [44], [45], which aims to seek multiple principle components by maximizing the projections, instead of the foresaid objectives, i.e. minimization of the sum of point-to-plane distance.…”

Section: Twsvc: Twin Support Vector Clusteringmentioning

confidence: 99%

Robust Plane Clustering Based on L1-Norm Minimization

Yang

Zhang

et al. 2020

IEEE Access

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Plane clustering methods, typically, k plane clustering (kPC), play conclusive roles in the family of data clustering. Instead of point-prototype, they aim to seek multiple plane-prototype fitting planes as centers to group the given data into their corresponding clusters based on L2 norm metric. However, they are usually sensitive to outliers because of square operation on the L2 norm. In this paper, we focus on robust plane clustering and propose a L1 norm plane clustering method, termed as L1kPC. The leading problem is optimized on the L1 ball hull, a non-convex feasible domain. To handle the problem, we provide a new strategy and its related mathematical proofs for L1 norm optimization. Compared to state-of-the-art methods, the advantages of our proposed lie in 4 folds: 1) similar to kPC, it has clear geometrical interpretation; 2) it is more capable of resisting to outlier; 3) theoretically, it is proved that the leading non-convex problem is equivalent to several convex sub-problems. To our best knowledge, this opens up a new way for L1 norm optimization; 4) the k fitting planes are solved by k individual linear programming problems, rather than higher time-consuming eigenvalue equations or quadratic programming problems used in the conventional plane clustering methods. Experiments on some artificial, benchmark UCI and human face datasets show its superiorities in robustness, training time, and clustering accuracy. INDEX TERMS L1 norm, plane clustering, eigenvalue problem, linear programming.

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Adaptive L1-Norm Principal-Component Analysis With Online Outlier Rejection

Cited by 28 publications

References 55 publications

Dynamic L1-Norm Tucker Tensor Decomposition

Dynamic L1-Norm Tucker Tensor Decomposition

Robust Subspace Tracking Algorithms in Signal Processing: A Brief Survey

Robust Plane Clustering Based on L1-Norm Minimization

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