Sparsity-Exploiting Robust Multidimensional Scaling

Forero, Pedro A.; Giannakis, Georgios B.

doi:10.1109/tsp.2012.2197617

Cited by 43 publications

(49 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similar to a point by Forero and Giannakis [10] concerning the LTS, it is impractical to find its global solution even for the small-scale problem due to the computational complexity of the combinatorial nature of (12).…”

Section: B Least Square Formulation and Ltsmentioning

confidence: 94%

“…One of the several relaxation techniques used in this paper is to replace the non-convex 0 -norm regularization term by its closest convex approximation, the 1 -norm. This technique is same as the one that is used in Forero and Giannakis [10] to deal with very few of large biases in distance measurements, which were treated as outliers. But our model is convex and their robust MDS model is nonconvex.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation

Ding

2016

Comput Optim Appl

View full text Add to dashboard Cite

One of the challenging problems in collaborative position localization arises when the distance measurements contain Non-Line-Of-Sight (NLOS) biases. Convex optimization has played a major role in modelling such problems and numerical algorithm developments. One of the successful examples is the Semi-Definite Programming (SDP), which translates Euclidean distances into the constraints of positive semidefinite matrices, leading to a large number of constraints in the case of NLOS biases. In this paper, we propose a new convex optimization model that is built upon the concept of Euclidean Distance Matrix (EDM). The resulting EDM optimization has an advantage that its Lagrangian dual problem is well structured and hence is conducive to algorithm developments. We apply a recently proposed 3-block alternating direction method of multipliers to the dual problem and tested the algorithm on some real as well as simulated data of large scale. In particular, the EDM model significantly outperforms the SDP model and several others. Index TermsEuclidean distance matrix, Collaborative localization, Non-Line of Sight (NLOS), Augmented Lagrangian, Alternating direction method of multipliers (ADMM).

show abstract

Section: B Least Square Formulation and Ltsmentioning

confidence: 94%

mentioning

confidence: 99%

Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation

Ding

2016

Comput Optim Appl

View full text Add to dashboard Cite

show abstract

“…This sparsity-promoting regularization has been also recognized by [4]- [7]. However, the auxiliary sparse vector b x n is unique to the RSE here and can be viewed as a "de-biasing" or outlier-capturing variable, as in the robust PCA and multi-dimensional scaling approaches of [16]. Correspondingly, regularization with the 1-norm of b x n renders the RSE-as well as the LLE-based manifold learning approaches, robust to outliers.…”

Section: Robust Sparse Embeddingmentioning

confidence: 94%

Robust sparse embedding and reconstruction via dictionary learning

Slavakis

Giannakis

Leus

2013

2013 47th Annual Conference on Information Sciences and Systems (CISS)

Self Cite

View full text Add to dashboard Cite

Abstract-A novel approach is developed for nonlinear compression and reconstruction of high-or even infinite-dimensional signals living on a smooth but otherwise unknown manifold. Compression is effected through affine embeddings to lower-dimensional spaces. These embeddings are obtained via linear regression and bilinear dictionary learning algorithms that leverage manifold smoothness as well as sparsity of the affine model and its residuals. The emergent unifying framework is general enough to encompass known locally linear embedding and compressive sampling approaches to dimensionality reduction. Emphasis is placed on reconstructing high-dimensional data from their low-dimensional embeddings. Preliminary tests demonstrate the analytical claims, and their potential to (de)compressing synthetic and real data.

show abstract

“…Although non-metric MDS (NMDS) can be considered in order to overcome the existence of outliers, Spence and Lewandowsky [17] demonstrated that NMDS may be adversely affected by outliers. The Robust CoPlot method uses the robust MDS (RMDS) proposed by [18]. The main advantage of RMDS is the use of the outlier aware cost function defined as…”

Section: Obtaining Mds Embeddingmentioning

confidence: 99%

RobCoP: A Matlab Package for Robust CoPlot Analysis

Atilgan¹,

Atilgan²

2017

OJS

View full text Add to dashboard Cite

The graphical representation method, Robust CoPlot, is a robust variant of the classical CoPlot method. CoPlot is an adaptation of multidimensional scaling (MDS), and is a practical tool for visual inspection and rich interpretation of multivariate data. CoPlot enables presentation of a multidimensional dataset in a two dimensions, in a manner that relations between both variables and observations to be analyzed together. It has also been used as a supplemental tool to cluster analysis, data envelopment analysis (DEA) and outlier detection methods in the literature. However, this method is very sensitive to outliers. When a multidimensional dataset contains outliers, this can lead to undesirable consequences such as the inaccurate representation of the variables. The motivation is to produce Robust CoPlot that is not unduly affected by outliers. In this study, we have presented a new MATLAB package RobCoP for generating robust graphical representation of a multidimensional dataset. This study serves a useful purpose for researchers studying the implementation of Robust CoPlot method by providing a description of the software package RobCoP; it also offers some limited information on the Robust CoPlot analysis itself. The package presented here has enough flexibility to allow a user to select an MDS type and vector correlation method to produce either classical or Robust CoPlot results.

show abstract

Sparsity-Exploiting Robust Multidimensional Scaling

Cited by 43 publications

References 27 publications

Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation

Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation

Robust sparse embedding and reconstruction via dictionary learning

RobCoP: A Matlab Package for Robust CoPlot Analysis

Contact Info

Product

Resources

About