Constrained multidimensional scaling inN spaces

Abstract

individual differences in multidimensional scaling, least squares estimation,

Multidimensional successive categories scaling: A maximum likelihood method

“…The importance of this is in the fact that MAXSCAL-2.1 can provide suitable statistical criteria for identification of the best fitting model. Although the range of constraints that can be handled by MAXSCAL-2.1 is still limited, it should not be very difficult to extend its scope to the kinds of constraints discussed by Bentler and Weeks [1978] and Bloxom [1978]. (See also Ramsay, 1980a.…”

Spherical Similarity Explorer for Comparative Case Analysis

“…In theory any Dimenionlity Reduction (DR) method can be extended to fit the purpose by adding constraints. For example, a "dummy point" that has the same distance to all the other points can be added to a MDS approach to achieve a circular or spherical embedding [10,8,27]. Also, methods were developed to generate spherical embeddings using a SOM [45].…”

“…Compared to other spherical embedding approaches that requires the generation of an artificial "dummy point" [10], [8] and [27] or tuning of parameters [45], Cox and Cox's method achieves non-metric MDS on a sphere in a simpler manner. SSE extends the capability of Cox and Cox's method by integrating it with a series of interactions and detail-on-demand visualizations, and embedding the spherical view in a multiple-coordinated-view where the analyst can examine the data from different perspectives.…”

“…The metaphor can be effectively adopted to support explorative analysis of distances and relations between objects in HD data. In the past various visual embedding methods have been proposed to map HD data to a 3D spherical surface [8,10,17,27,45], but little work has been reported on integrating them to VA tools for visual data exploration. This is hardly surprising, because without effective interactions and detail-on-demand visualizations, the method cannot fully support explorative analysis.…”

Unimodal Models to Relate Species to Environment.

“…These latent variables are constructed without reference to environmental measurements, but they can subsequently be compared with actual environmental data if available. To these three well-known types of gradient analysis we add a fourth, constrained ordination, which has its roots in the psychometric literature on multidimensional scaling (Bloxom, 1978;De Leeuw and Heiser, 1980;. Constrained ordination also constructs axes of variation in overall community composition, but does so in such a way as to explicitly optimize the fit to supplied environmental data (Ter Braak, 1986a, 1987c.…”