In the paper, two combinations (consecutive and integrated) of vector quantization methods (self-organizing map and neural gas) and multidimensional scaling (MDS) have been investigated and compared. The vector quantization is used to reduce the number of dataset items. The dataset with a smaller number of items is analyzed by multidimensional scaling in order to reduce the number of features o...

Multidimensional scaling (MDS) techniques are statistical techqnies that convert information about distances between a number of objects into a spatial representation of these objects. These techniques were first discussed systematically in psychometrics [Torgerson, 1958; Coombs, 1964] as multidimensional extensions of univariate psychophysics and sensory scaling. Because they needed considerab...

The smacof package offers a comprehensive implementation of multidimensional scaling (MDS) techniques in R. Since its first publication (De Leeuw and Mair 2009b) the functionality has been enhanced, several additional methods, features utilities were added. Major updates include complete re-implementation unfolding allowing for monotone dissimilarity transformations, including row-conditional, ...

Multidimensional scaling (MDS) is a set of data analysis techniques used to explore the structure of (dis)similarity data. MDS represents a set of objects as points in a multidimensional space in such a way that the points corresponding to similar objects are located close together, while those corresponding to dissimilar objects are located far apart. The investigator then attempts to “make se...

Although counseling psychologists conduct a great deal of research that attempts to reveal the structure of a given data set, rarely if ever do they utilize scaling procedures, preferring instead to rely on factor analytic strategies. In this article, we give a short introduction to the use of multidimensional scaling (MDS), with specific emphasis on applications in counseling and vocational ps...

Multidimensional scaling (MDS) is a generic name for a family of algorithms that construct a configuration of points in a target metric space from information about inter-point distances measured in some other metric space. Large-scale MDS problems often occur in data analysis, representation and visualization. Solving such problems efficiently is of key importance in many applications. In this...

We detail the investigation of the first application of several dissimilarity measures for large-scale solar image data analysis. Using a solar-domain-specific benchmark dataset that contains multiple types of phenomena, we analyzed combinations of image parameters with different dissimilarity measures in order to determine which combinations will allow us to differentiate among the multiple so...

GIS-MCE is the main method in land evaluation,but it is a linear method and neglects multidimensional complexity of factors used in land evaluation, which leads to information loss. Multidimensional scaling (MDS) originates from psychoanalysis, which is used to describe multidimensional data in higher dimensions by transforming data in higher dimensions into geometry structure in Lower dimensio...

As one of the most promising nonlinear dimensionality reduction techniques, Isometric Mapping (ISOMAP) performs well only when the data belong to a single well-sampled manifold, where geodesic distances can be well approximated by the corresponding shortest path distances in a suitable neighborhood graph. Unfortunately, the approximation gets less and less precise generally as the number of edg...

Multidimensional Scaling (MDS) is a classical technique for embedding data in low dimensions, still widespread use today. In this paper we study MDS modern setting - specifically, high dimensions and ambient measurement noise. We show that as the noise level increases, suffers sharp breakdown depends on dimension level, derive an explicit formula point case of white then introduce MDS+, simple ...