Multidimensional scaling (MDS) is a class of methods used to find a low-dimensional representation of a set of points given a matrix of pairwise distances between them. Problems of this kind arise in various applications, from dimensionality reduction of image manifolds to psychology and statistics. In many of these applications, efficient and accurate solution of an MDS problem is required. In...

Multidimensional scaling (MDS) has established itself as a standard tool for statisticians and applied researchers. Its success is due to its simple and easily interpretable representation of potentially complex structural data. These data are typically embedded into a 2-dimensional map, where the objects of interest (items, attributes, stimuli, respondents, etc.) correspond to points such that...

Although the assignment was to write a note about the famous, highly cited Kruskal 1964 papers, it would hardly be fair if the topic wasn’t described in the context of two other papers, being Shepard’s 1962 papers (with 2309 citations in Google Scholar as of 4/1/2016) that started the development of what is called nonmetric multidimensional scaling. Before getting into more detail, some of the ...

Multidimensional scaling (MDS) was applied to the numerical taxonomy of Candida species based on isoenzyme profiles. Multidimensional scaling uses proximity measures to generate a spatial configuration of points in multidimensional space where distances between points reflect similarity among types. The biochemical profiles of 35 types of Candida species based on 26 tests consisting of isoenzym...

The TriVis algorithm for visualization of multidimensional data proximities in two dimensions is presented. The algorithm preserves maximum number of exact distances, has simple interpretation, and unlike multidimensional scaling (MDS) does not require costly minimization. It may also provide an excellent starting point significantly reducing the number of required iterations in MDS.

Principal component analysis (PCA) and multidimensional scaling (MDS) are a set of mathematical techniques which uncover the underlying structure of data by examining the relationships between variables. Both MDS and PCA use proximity measures such as correlation coefficients or Euclidean distances to generate a spatial configuration (map) of points where distances between points reflect the re...

We show that neural networks, with a suitable error function for backpropagation, can be successfully used for metric multidimensional scaling (MDS) (i.e., dimensional reduction while trying to preserve the original distances between patterns) and are in fact able to outdo the standard algebraic approach to MDS, known as classical scaling.

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Teuvo Kohonen Name of the publication New Developments of Nonlinear Projections for the Visualization of Structures in Nonvectorial Data Sets Publisher School of Science Unit Department of Information and Computer Science Series Aalto University publication series SCIENCE + TECHNOLOGY 8/2011 Field of research Computer science ...