Regularized multidimensional scaling with radial basis functions

Jahan, Sadia; Qi, Houduo

doi:10.3934/jimo.2016.12.543

Cited by 5 publications

(20 citation statements)

References 32 publications

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“…General convergence properties of Alg. 3.1 is similar to that stated as [11], which is also discussed in ( [30]).…”

Section: Regularized Multidimensional Scaling (Rmdssupporting

confidence: 88%

“…In [30], problem (6) after several modifiation is proved to be equivalent to the problem As mentioned in [30] , problem (8) is not attainable, but the infimum is finite. Argyrion et.…”

Section: Regularized Multidimensional Scaling (Rmdsmentioning

confidence: 97%

“…3.1 to get its final iterative matrix W ∈ ×m . Select the most important 0 centers using the method discussed in [30]. S.2 Apply the iterative block majorization algorithm of Webb [34] to minimize (2).…”

Section: Algorithm 32 Two-stage Algorithmmentioning

confidence: 99%

“…. RMDS [30] do not take any advantages of some priori information concerning the data sets. For example, some data points may be known beforehand to belong to certain class.…”

Section: Supervised Regularized Multidimensional Scaling (Srmds)mentioning

confidence: 99%

“…In RMDS [30] a regularization term γ W 2 2,1 is added to the stress. The optimization model thus becomes…”

Section: Introduction Nonlinear Variants Of Classical Multi-dimensiomentioning

confidence: 99%

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Discriminant analysis of regularized multidimensional scaling

Jahan¹

2021

NACO

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Regularized Multidimensional Scaling with Radial basis function (RMDS) is a nonlinear variant of classical Multi-Dimensional Scaling (cMDS). A key issue that has been addressed in RMDS is the effective selection of centers of the radial basis functions that plays a very important role in reducing the dimension preserving the structure of the data in higher dimensional space. RMDS uses data in unsupervised settings that means RMDS does not use any prior information of the dataset. This article is concerned on the supervised setting. Here we have incorporated the class information of some members of data to the RMDS model. The class separability term improved the method RMDS significantly and also outperforms other discriminant analysis methods such as Linear discriminant analysis (LDA) which is documented through numerical experiments.

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“…General convergence properties of Alg. 3.1 is similar to that stated as [11], which is also discussed in ( [30]).…”

Section: Regularized Multidimensional Scaling (Rmdssupporting

confidence: 88%

“…In [30], problem (6) after several modifiation is proved to be equivalent to the problem As mentioned in [30] , problem (8) is not attainable, but the infimum is finite. Argyrion et.…”

Section: Regularized Multidimensional Scaling (Rmdsmentioning

confidence: 97%

Section: Algorithm 32 Two-stage Algorithmmentioning

confidence: 99%

“…. RMDS [30] do not take any advantages of some priori information concerning the data sets. For example, some data points may be known beforehand to belong to certain class.…”

Section: Supervised Regularized Multidimensional Scaling (Srmds)mentioning

confidence: 99%

“…In RMDS [30] a regularization term γ W 2 2,1 is added to the stress. The optimization model thus becomes…”

Section: Introduction Nonlinear Variants Of Classical Multi-dimensiomentioning

confidence: 99%

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Discriminant analysis of regularized multidimensional scaling

Jahan¹

2021

NACO

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Supervised Regularized Multidimensional Scaling Using Weighted Stress Measure

Islam¹,

Bhuiyan²,

Jahan³

2022

ujam

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Supervised Regularized Multidimensional Scaling (SRMDS), a non-linear variant of classical Multi-Dimensional Scaling (cMDS) is proposed recently which involves Radial basis function. The method is focused on the effective selection of centers of the radial basis functions in transforming data from a higher dimensional space to a lower dimension. The transformation matrix is determined by minimizing stress. Weights of components of the stress that are of great importance for classification of data got less focus in Supervised Regularized Multidimensional Scaling. In this article, we have investigated several forms of non-linear functions which may be used as weights of the stress measure. A new form of Z-shape weight function dependent on intraclass information of the dataset is introduced which prefers to preserve global structure of the dataset. The efficiency of the proposed approach is illustrated on several benchmarking datasets which shows that the weighted Supervised Regularized Multidimensional Scaling (WSRMDS) outperforms the base method and some other state of the art approaches such as Linear Discriminant Analysis (LDA), and Supervised Principal Component Analysis (SPCA). Observing the finding of this research, among different weight functions, Z-shape weight function is recommended to use since it works better then any other weight functions for most of the data sets.

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