Journal ArticleDOI
A Latent Class Multidimensional Scaling Model for Two-Way One-Mode Continuous Rating Dissimilarity Data
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TLDR
A cluster-MDS model for two-way one-mode continuous rating dissimilarity data that aims at partitioning the objects into classes and simultaneously representing the cluster centers in a low-dimensional space is proposed.Abstract:
In this paper, we propose a cluster-MDS model for two-way one-mode continuous rating dissimilarity data. The model aims at partitioning the objects into classes and simultaneously representing the cluster centers in a low-dimensional space. Under the normal distribution assumption, a latent class model is developed in terms of the set of dissimilarities in a maximum likelihood framework. In each iteration, the probability that a dissimilarity belongs to each of the blocks conforming to a partition of the original dissimilarity matrix, and the rest of parameters, are estimated in a simulated annealing based algorithm. A model selection strategy is used to test the number of latent classes and the dimensionality of the problem. Both simulated and classical dissimilarity data are analyzed to illustrate the model.read more
Citations
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Journal ArticleDOI
Global Optimization in Any Minkowski Metric: A Permutation-Translation Simulated Annealing Algorithm for Multidimensional Scaling
TL;DR: The experimental results confirm the theoretical expectation that Simulated Annealing is a suitable strategy to deal by itself with the optimization problems in Multidimensional Scaling, in particular for City-Block, Euclidean and Infinity metrics.
Journal ArticleDOI
A latent class MDS model with spatial constraints for non-stationary spatial covariance estimation
TL;DR: A general latent class model with spatial constraints that allows to partition the sample stations into classes and simultaneously to represent the cluster centers in a low-dimensional space, while the stations and clusters retain their spatial relationships is formulated.
Journal ArticleDOI
A dual latent class unfolding model for two-way two-mode preference rating data
TL;DR: A dual latent class model is proposed for a matrix of preference ratings data, which will partition the individuals and the objects into classes, and simultaneously represent the cluster centers in a low dimensional space, while individuals and objects retain their preference relationship.
Journal ArticleDOI
Variance-Based Cluster Selection Criteria in a K-Means Framework for One-Mode Dissimilarity Data
J. Fernando Vera,Rodrigo Macías +1 more
TL;DR: This paper addresses the formulation of criteria to determine the number of clusters, in the general situation in which the available information for clustering is a one-mode $$N\times N$$N×N dissimilarity matrix describing the objects.
Journal ArticleDOI
Cluster Differences Unfolding for Two-Way Two-Mode Preference Rating Data
TL;DR: An alternating least squares procedure is proposed, in which the individuals and the objects are partitioned into clusters, while at the same time the cluster centers are represented by unfolding.
References
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Journal ArticleDOI
ConPar: a method for identifying groups of concordant subject proximity matrices for subsequent multidimensional scaling analyses
TL;DR: This work proposes a straightforward new method (CONcordance PARtitioning—ConPar), which can be used to identify groups of individual-subject matrices with concordant proximity structures, and reveals that, when compared to K -means clustering of the proximity data, ConPar generally provided better recovery of the true subject cluster memberships.
Journal ArticleDOI
Global Optimization in Any Minkowski Metric: A Permutation-Translation Simulated Annealing Algorithm for Multidimensional Scaling
TL;DR: The experimental results confirm the theoretical expectation that Simulated Annealing is a suitable strategy to deal by itself with the optimization problems in Multidimensional Scaling, in particular for City-Block, Euclidean and Infinity metrics.
Journal ArticleDOI
A latent class vector model for preference ratings
Geert De Soete,Suzanne Winsberg +1 more
TL;DR: In this article, a latent class formulation of the well-known vector model for preference data is presented, where the model simultaneously clusters the subjects into a small number of homogeneous groups (or latent classes) and constructs a joint geometric representation of the choice objects and the latent classes according to a vector model.
Journal ArticleDOI
A Permutation-Translation Simulated Annealing Algorithm for L1 and L2 Unidimensional Scaling
TL;DR: The weighted, alternating process is shown to outperform earlier implementations of Simulated Annealing and other optimization strategies for Unidimensional Scaling in run time efficiency, in solution quality, or in both.
Book ChapterDOI
Clustering in Low-Dimensional Space
TL;DR: It may be argued that clustering is a way to stabilize and robustify the multidimensional scaling task, the aim being to fit a low-dimensional distance model to groups of points, rather than to single points.
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