Robust multidimensional scaling employing M-estimators and nuclear norm regularization

Mandanas, Fotios D.; Kotropoulos, Constantine

doi:10.1109/globalsip.2017.8308615

Cited by 4 publications

(7 citation statements)

References 18 publications

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“…As seen in Appendix C, the proof of Theorem 5.2 makes use of the differentiability of F (D, Z), which is a direct consequence of cMDS objective. In contrast, the objectives in [9], [11], [12] are not differentiable.…”

Section: B Convergence Analysismentioning

confidence: 98%

“…This is particularly useful if we know priori the level of outliers in the data matrix. We are not aware whether the sparsitydriven method in [9] or [11], [12] (or any of its variants) has such a useful property. As seen in Appendix C, the proof of Theorem 5.2 makes use of the differentiability of F (D, Z), which is a direct consequence of cMDS objective.…”

Section: B Convergence Analysismentioning

confidence: 99%

“…To improve the robustness of RMDS, Mandanas and Kotropoulos [11] replaced the least-square solution of the residual equation at each step of RMDS by a M -estimator, resulting in several robust algorithms depending on the M -estimator being used. We refer to [12] for further development along this line, in particular on using 21 regularization. We note that the models behind those methods are non-convex optimization.…”

Section: Introductionmentioning

confidence: 99%

“…5.2. This is in contrast to the 1 -regularized methods in [9], [11], [12] where it still remains unknown how to control the sparsity level. (iii) Numerically, we demonstrate the capability and efficiency of the proposed methods in denoising and outlier detection in comparison with the state-of-the-art MDS methods, using both artificial and real test data.…”

Section: Introductionmentioning

confidence: 99%

“…The powerful framework of our study is through the Euclidean distance matrix optimization, which is drastically different from the studies in [9], [11], [12], where the coordinates descent optimization was employed. However, they share a same feature that both approaches are of non-convex optimization.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Classical Multidimensional Scaling: A Subspace Perspective, Over-Denoising, and Outlier Detection

Kong

2019

IEEE Trans. Signal Process.

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The classical Multi-Dimensional Scaling (cMDS) has become a cornerstone for analyzing metric dissimilarity data due to its simplicity in derivation, low computational complexity and its nice interpretation via the principle component analysis. This paper focuses on its capability of denoising and outlier detection. Our new interpretation shows that cMDS always overly denoises a sparsely perturbed data by subtracting a fully dense denoising matrix in a subspace from the given data matrix. This leads us to consider two types of sparsity-driven models: Subspace sparse MDS and Full-space sparse MDS, which respectively uses the 1 and 1−2 regularization to induce sparsity. We then develop fast majorization algorithms for both models and establish their convergence. In particular, we are able to control the sparsity level at every iterate provided that the sparsity control parameter is above a computable threshold. This is a desirable property that has not been enjoyed by any of existing sparse MDS methods.Our numerical experiments on both artificial and real data demonstrates that cMDS with appropriate regularization can perform the tasks of denoising and outlier detection, and inherits the efficiency of cMDS in comparison with several state-of-the-art sparsity-driven MDS methods.

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Section: B Convergence Analysismentioning

confidence: 98%

Section: B Convergence Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Classical Multidimensional Scaling: A Subspace Perspective, Over-Denoising, and Outlier Detection

Kong

2019

IEEE Trans. Signal Process.

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Constructing renewable energy sphere for efficient search

Shih,

Chang

2024

Journal of Cleaner Production

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Efficient robust methods via monitoring for clustering and multivariate data analysis

Riani

Atkinson

Cerioli

et al. 2019

Pattern Recognition

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Monitoring the properties of single sample robust analyses of multivariate data as a function of breakdown point or efficiency leads to the adaptive choice of the best values of these parameters, eliminating arbitrary decisions about their values and so increasing the quality of estimators. Monitoring the trimming proportion in robust cluster analysis likewise leads to improved estimators. We illustrate these procedures on a sample of 424 cows with bovine phlegmon. For clustering we use a method which includes constraints on the eigenvalues of the dispersion matrices, so avoiding thread shaped clusters. The "car-bike" plot reveals the stability of clustering as the trimming level changes. The pattern of clusters and outliers alters appreciably for low levels of trimming.

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Robust multidimensional scaling employing M-estimators and nuclear norm regularization

Cited by 4 publications

References 18 publications

Classical Multidimensional Scaling: A Subspace Perspective, Over-Denoising, and Outlier Detection

Classical Multidimensional Scaling: A Subspace Perspective, Over-Denoising, and Outlier Detection

Constructing renewable energy sphere for efficient search

Efficient robust methods via monitoring for clustering and multivariate data analysis

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