Multidimensional Scaling Using Majorization: SMACOF in<i>R</i>

Leeuw, Jan de; Mair, Patrick

doi:10.18637/jss.v031.i03

Cited by 422 publications

(341 citation statements)

References 44 publications

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“…Second, by means of multidimensional scaling, insights are gained into which connotations respondents associate with the respective skiing destinations. For this analysis, the smacof package, as implemented in the R system, is used (De Leeuw & Mair, 2009). The last step of data analysis aims at validating findings resulting from the two preceding methods (i.e., hierarchical clustering and multidimensional scaling).…”

Section: Discussionmentioning

confidence: 99%

Competitor Detection: An Investigation of Consumers' Perceived Similarity

Ring¹,

Teichmann²

2011

Tourism Analysis

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This article focuses on the consumer's perception of skiing destinations in terms of competitive position in consumers' minds. More specifically, the article explores factors that shape individuals' perceptions about which destinations compete with each other while centering on the categorization process itself. To detect competitors in customers' minds, unconstrained sorting data is used. Results are further analyzed by means of three different methods: hierarchical clustering, (spherical) MDS, and nondisjunctive clustering. A comparison of the findings shows that all three approaches produce rather consistent results. National boundaries are the dominant factor for the categorization of skiing destinations. In addition, the emotional element of luxury is a relevant criterion to detect competing destinations. The study provides theoretical and managerial implications.

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Section: Discussionmentioning

confidence: 99%

Competitor Detection: An Investigation of Consumers' Perceived Similarity

Ring¹,

Teichmann²

2011

Tourism Analysis

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“…In such cases, the configuration X is constructed from a subset of the distances, and, at the same time, the other (missing) distances are estimated by monotonic regression. In nonmetric MDS it is assumed that d ij ≈ f(δ ij ), therefore f(δ ij ) are often referred as the disparities [55][56][57] in contrast to the original dissimilarities δ ij , on one hand, and the distances d ij of the configuration space on the other hand. In this context, the disparity is a measure of how well the distance d ij matches the dissimilarity δ ij .…”

Section: Multidimensional Scalingmentioning

confidence: 99%

Dynamical analysis of compositions

Machado

Costa

Lima³

2010

Nonlinear Dyn

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This paper analyzes musical opus from the point of view of two mathematical tools, namely the entropy and the multidimensional scaling (MDS). The Fourier analysis reveals a fractional dynamics, but the time rhythm variations are diluted along the spectrum. The combination of time-window entropy and MDS copes with the time characteristics and is well suited to treat a large volume of data. The experiments focus on a large number of compositions classified along three sets of musical styles, namely "Classical", "Jazz" and "Pop & Rock" compositions. Without lack of generality, the present study describes the application of the tools and the sets of musical compositions in a methodology leading to clear conclusions, but extensions to other possibilities are straightforward. The results reveal significant differences in the musical styles, demonstrating the feasibility of the proposed strategy and motivating further developments towards a dynamical analysis of musical compositions.

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“…Otherwise, one has to opt for many of its variants. Well-known ones include SMACOF [7], weighted-MDS [8], and MDS-MAP [9,10]. In particular, MDS-MAP often works when nodes are positioned relatively uniformly in the space, but does not perform well on networks with irregular topology, where the shortest path distance does not correlate well with the true Euclidean distance.…”

Section: Introductionmentioning

confidence: 99%

Tackling the flip ambiguity in wireless sensor network localization and beyond

Bai

2016

Digital Signal Processing

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There have been significant advances in range-based numerical methods for sensor network localizations over the past decade. However, there remain a few challenges to be resolved to satisfaction. Those issues include, for example, the flip ambiguity, high level of noises in distance measurements, and irregular topology of the concerning network. Each or a combination of them often severely degrades the otherwise good performance of existing methods. Integrating the connectivity constraints is an effective way to deal with those issues. However, there are too many of such constraints, especially in a large and sparse network. This presents a challenging computational problem to existing methods. In this paper, we propose a convex optimization model based on the Euclidean Distance Matrix (EDM). In our model, the connectivity constraints can be simply represented as lower and upper bounds on the elements of EDM, resulting in a standard 3-block quadratic conic programming, which can be efficiently solved by a recently proposed 3-block alternating direction method of multipliers. Numerical experiments show that the EDM model effectively eliminates the flip ambiguity and retains robustness in terms of being resistance to irregular wireless sensor network topology and high noise levels.

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Multidimensional Scaling Using Majorization: SMACOF inR

Cited by 422 publications

References 44 publications

Competitor Detection: An Investigation of Consumers' Perceived Similarity

Competitor Detection: An Investigation of Consumers' Perceived Similarity

Dynamical analysis of compositions

Tackling the flip ambiguity in wireless sensor network localization and beyond

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