Lp Norm Relaxation Approach for Large Scale Data Analysis: A Review

Bui, Tien D.; Quach, Kha Gia; Duong, Chi Nhan; Luu, Khoa

doi:10.1007/978-3-319-93000-8_33

Cited by 2 publications

(3 citation statements)

References 19 publications

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“…For robustness to outliers, the l 0 -norm is often used for optimization; however, due to its combinatorial property, the optimization is difficult [4]. To avoid such difficulty, relaxation methods, i.e., the use of the l 1 -norm or other convex regularization terms, are used.…”

Section: Introductionmentioning

confidence: 99%

L0-norm Constrained Autoencoders for Unsupervised Outlier Detection

Ishii

Koide

Hayakawa

2020

Advances in Knowledge Discovery and Data Mining

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Unsupervised outlier detection is commonly performed using reconstruction-based methods such as Principal Component Analysis. A recent problem in this field is the learning of low-dimensional nonlinear manifolds under L0-norm constraints for error terms. Despite significant efforts, no method that consistently treats such features exists. We propose a novel unsupervised outlier detection method, L0-norm Constrained Autoencoders (L0-AE), based on an autoencoder-based detector with L0-norm constraints for error terms. Unlike existing methods, the proposed optimization procedure of L0-AE provably guarantees the convergence of the objective function under a mild condition, while neither the relaxation of the L0-norm constraint nor the linearity of the latent manifold is enforced. Experimental results show that the proposed L0-AE is more robust and accurate than other reconstruction-based methods, as well as conventional methods such as Isolation Forest.

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Section: Introductionmentioning

confidence: 99%

L0-norm Constrained Autoencoders for Unsupervised Outlier Detection

Ishii

Koide

Hayakawa

2020

Advances in Knowledge Discovery and Data Mining

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“…Improving the generality of the classification algorithm and inhibiting the effects of noise or outlier values require the improvement of the real-time correct identification rate of the curve radius. The classic recognition algorithm is built on the loss function of the L2 norm, 9 which intensifies outlier noises by squaring. However, the Lp ( p ≤ 1) norm has more significant suppression effects on outliers; so, pattern recognition algorithms based on sparse constraints are better.…”

Section: Methodsmentioning

confidence: 99%

“…The original RPA discrimination method directly presupposes the key parameters as some fixed values, regardless of various curve radii. In this article, we exploit the relationship between RPA parameters and curve radii to design multi-dimensional features and propose a real-time classification algorithm based on linear discriminant analysis 8 of an Lp norm 9 with sparsity constraint (LDA-Lp-SC), which can be embedded in the GJ-6A\D RTG real-time detection system. It can realize the automatic switching of RPA discrimination parameters to improve the accuracy of RPA discrimination to more than 90%, which is of great significance for guiding track maintenance.…”

Section: Introductionmentioning

confidence: 99%

Real-time railway plane alignment discrimination based on linear discriminant analysis of Lp norm with sparsity constraint

Qin

Zhang

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part F:

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To improve the accuracy of detected parameters at curves by an in-use track geometry measurement (TGM) system, a real-time railway plane alignment (RPA) discrimination method based on linear discriminant analysis of an Lp norm with sparsity constraint (LDA-Lp-SC) is proposed. A standard database to identify the radius of a track curve is established, using the relevant ledger and track TGM data. Multi-dimensional feature extraction is performed on the TGM data, and the parameters of the method are optimized to improve the accuracy of the model classification. Finally, the method is embedded in a TGM system combined with the original RPA discrimination method, so that the key parameters of RPA discrimination can be automatically switched in real time according to the classification result of the track curve radius. Compared with the original method, the method in this study greatly improves the recognition accuracy of track curve with a radius in the range of 150–20,000 m, while ensuring real-time performance.

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Lp Norm Relaxation Approach for Large Scale Data Analysis: A Review

Cited by 2 publications

References 19 publications

L0-norm Constrained Autoencoders for Unsupervised Outlier Detection

L0-norm Constrained Autoencoders for Unsupervised Outlier Detection

Real-time railway plane alignment discrimination based on linear discriminant analysis of Lp norm with sparsity constraint

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