50,180 research outputs found
Multidimensional scaling
Multidimensional scaling is a statistical technique to visualize dissimilarity data. In multidimensional scaling, objects are represented as points in a usually two dimensional space, such that the distances between the points match the observed dissimilarities as closely as possible. Here, we discuss what kind of data can be used for multidimensional scaling, what the essence of the technique is, how to choose the dimensionality, transformations of the dissimilarities, and some pitfalls to watch out for when using multidimensional scaling.
A comparison of two techniques for bibliometric mapping: Multidimensional scaling and VOS
VOS is a new mapping technique that can serve as an alternative to the
well-known technique of multidimensional scaling. We present an extensive
comparison between the use of multidimensional scaling and the use of VOS for
constructing bibliometric maps. In our theoretical analysis, we show the
mathematical relation between the two techniques. In our experimental analysis,
we use the techniques for constructing maps of authors, journals, and keywords.
Two commonly used approaches to bibliometric mapping, both based on
multidimensional scaling, turn out to produce maps that suffer from artifacts.
Maps constructed using VOS turn out not to have this problem. We conclude that
in general maps constructed using VOS provide a more satisfactory
representation of a data set than maps constructed using well-known
multidimensional scaling approaches
Weighted metric multidimensional scaling
This paper establishes a general framework for metric scaling of any distance measure between individuals based on a rectangular individuals-by-variables data matrix. The method allows visualization of both individuals and variables as well as preserving all the good properties of principal axis methods such as principal components and correspondence analysis, based on the singular-value decomposition, including the decomposition of variance into components along principal axes which provide the numerical diagnostics known as contributions. The idea is inspired from the chi-square distance in correspondence analysis which weights each coordinate by an amount calculated from the margins of the data table. In weighted metric multidimensional scaling (WMDS) we allow these weights to be unknown parameters which are estimated from the data to maximize the fit to the original distances. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing a matrix and displaying its rows and columns in biplots.Biplot, correspondence analysis, distance, multidimensional scaling, singular-value decomposition
Multidimensional Scaling on Multiple Input Distance Matrices
Multidimensional Scaling (MDS) is a classic technique that seeks vectorial
representations for data points, given the pairwise distances between them.
However, in recent years, data are usually collected from diverse sources or
have multiple heterogeneous representations. How to do multidimensional scaling
on multiple input distance matrices is still unsolved to our best knowledge. In
this paper, we first define this new task formally. Then, we propose a new
algorithm called Multi-View Multidimensional Scaling (MVMDS) by considering
each input distance matrix as one view. Our algorithm is able to learn the
weights of views (i.e., distance matrices) automatically by exploring the
consensus information and complementary nature of views. Experimental results
on synthetic as well as real datasets demonstrate the effectiveness of MVMDS.
We hope that our work encourages a wider consideration in many domains where
MDS is needed
Multidimensional scaling
Multidimensional scaling is a statistical technique to visualize dissimilarity data. In multidimensional scaling, objects are represented as points in a usually two dimensional space, such that the distances between the points match the observed dissimilarities as closely as possible. Here, we discuss what kind of data can be used for multidimensional scaling, what the essence of the technique is, how to choose the dimensionality, transformations of the dissimilarities, and some pitfalls to watch out for when using multidimensional scaling
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