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Multidimensional scaling.

ABSTRACT: The concept of similarity, or a sense of 'sameness' among things, is pivotal to theories in the cognitive sciences and beyond. Similarity, however, is a difficult thing to measure. Multidimensional scaling (MDS) is a tool by which researchers can obtain quantitative estimates of similarity among groups of items. More formally, MDS refers to a set of statistical techniques that are used to reduce the complexity of a data set, permitting visual appreciation of the underlying relational structures contained therein. The current paper provides an overview of MDS. We discuss key aspects of performing this technique, such as methods that can be used to collect similarity estimates, analytic techniques for treating proximity data, and various concerns regarding interpretation of the MDS output. MDS analyses of two novel data sets are also included, highlighting in step-by-step fashion how MDS is performed, and key issues that may arise during analysis. WIREs Cogn Sci 2013, 4:93-103. doi: 10.1002/wcs.1203 This article is categorized under: Psychology > Perception and Psychophysics.

SUBMITTER: Hout MC

PROVIDER: S-EPMC3555222 | biostudies-literature | 2013 Jan

REPOSITORIES: biostudies-literature

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Multidimensional scaling.

Hout Michael C MC Papesh Megan H MH Goldinger Stephen D SD

Wiley interdisciplinary reviews. Cognitive science 20121008 1

The concept of similarity, or a sense of 'sameness' among things, is pivotal to theories in the cognitive sciences and beyond. Similarity, however, is a difficult thing to measure. Multidimensional scaling (MDS) is a tool by which researchers can obtain quantitative estimates of similarity among groups of items. More formally, MDS refers to a set of statistical techniques that are used to reduce the complexity of a data set, permitting visual appreciation of the underlying relational structures ...[more]

PMID: 23359318

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Project description:BackgroundMulti-dimensional scaling (MDS) is aimed to represent high dimensional data in a low dimensional space with preservation of the similarities between data points. This reduction in dimensionality is crucial for analyzing and revealing the genuine structure hidden in the data. For noisy data, dimension reduction can effectively reduce the effect of noise on the embedded structure. For large data set, dimension reduction can effectively reduce information retrieval complexity. Thus, MDS techniques are used in many applications of data mining and gene network research. However, although there have been a number of studies that applied MDS techniques to genomics research, the number of analyzed data points was restricted by the high computational complexity of MDS. In general, a non-metric MDS method is faster than a metric MDS, but it does not preserve the true relationships. The computational complexity of most metric MDS methods is over O(N2), so that it is difficult to process a data set of a large number of genes N, such as in the case of whole genome microarray data.ResultsWe developed a new rapid metric MDS method with a low computational complexity, making metric MDS applicable for large data sets. Computer simulation showed that the new method of split-and-combine MDS (SC-MDS) is fast, accurate and efficient. Our empirical studies using microarray data on the yeast cell cycle showed that the performance of K-means in the reduced dimensional space is similar to or slightly better than that of K-means in the original space, but about three times faster to obtain the clustering results. Our clustering results using SC-MDS are more stable than those in the original space. Hence, the proposed SC-MDS is useful for analyzing whole genome data.ConclusionOur new method reduces the computational complexity from O(N3) to O(N) when the dimension of the feature space is far less than the number of genes N, and it successfully reconstructs the low dimensional representation as does the classical MDS. Its performance depends on the grouping method and the minimal number of the intersection points between groups. Feasible methods for grouping methods are suggested; each group must contain both neighboring and far apart data points. Our method can represent high dimensional large data set in a low dimensional space not only efficiently but also effectively.

Project description:The physical activity-related health competence (PAHCO) model assumes that individuals require movement competence, control competence, and self-regulation competence to lead a healthy, physically active lifestyle. Although previous research has already established some measurement factors (n = 8) of the three dimensions, no attempts have so far been made to statistically aggregate them on the sub-competence level. Therefore, the goal of the present study was to test two additional factors for PAHCO and subsequently model the second-order structure with two samples from the fields of rehabilitation and prevention. We conducted two questionnaire surveys with persons with multiple sclerosis (n = 475) and teaching students undergoing a basic qualification course in physical education (n = 502). After performing exploratory items analysis, we used second-order confirmatory factor analysis (CFA) and multidimensional scaling to investigate whether the scales could be bundled in accordance with the PAHCO model. The CFAs with 10 factors (42 items) demonstrated a good model fit. In contrast, the second-order analysis with a simple loading structure on the three sub-competencies revealed an unacceptable model fit. Instead, a second-order model variant was preferred [comparative fit index (CFI) = 0.926, root mean square error of approximation (RMSEA) = 0.048, standardized root mean square residual (SRMR) = 0.065] in which body awareness and self-efficacy had theory-conform cross-loadings. The results of multidimensional scaling (two-dimensional solution) were in line with the extracted second-order structure. The present results suggested that the extension of the measurement instrument to 10 first-order factors was psychometrically justified for the two populations. The results from the second-order analyses provided the basis for the creation of sum scores, representing manifest indicators of movement competence, control competence, and self-regulation competence. Future studies are needed that cross-validate the extended measurement model with other populations and that relate the sub-competencies of PAHCO to indicators of health-enhancing physical activity.

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Multidimensional scaling.

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Multidimensional scaling.

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