Dataset Information

Spectral multidimensional scaling.

ABSTRACT: An important tool in information analysis is dimensionality reduction. There are various approaches for large data simplification by scaling its dimensions down that play a significant role in recognition and classification tasks. The efficiency of dimension reduction tools is measured in terms of memory and computational complexity, which are usually a function of the number of the given data points. Sparse local operators that involve substantially less than quadratic complexity at one end, and faithful multiscale models with quadratic cost at the other end, make the design of dimension reduction procedure a delicate balance between modeling accuracy and efficiency. Here, we combine the benefits of both and propose a low-dimensional multiscale modeling of the data, at a modest computational cost. The idea is to project the classical multidimensional scaling problem into the data spectral domain extracted from its Laplace-Beltrami operator. There, embedding into a small dimensional Euclidean space is accomplished while optimizing for a small number of coefficients. We provide a theoretical support and demonstrate that working in the natural eigenspace of the data, one could reduce the process complexity while maintaining the model fidelity. As examples, we efficiently canonize nonrigid shapes by embedding their intrinsic metric into , a method often used for matching and classifying almost isometric articulated objects. Finally, we demonstrate the method by exposing the style in which handwritten digits appear in a large collection of images. We also visualize clustering of digits by treating images as feature points that we map to a plane.

SUBMITTER: Aflalo Y

PROVIDER: S-EPMC3831466 | biostudies-other | 2013 Nov

REPOSITORIES: biostudies-other

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Publications

Spectral multidimensional scaling.

Aflalo Yonathan Y Kimmel Ron R

Proceedings of the National Academy of Sciences of the United States of America 20131009 45

An important tool in information analysis is dimensionality reduction. There are various approaches for large data simplification by scaling its dimensions down that play a significant role in recognition and classification tasks. The efficiency of dimension reduction tools is measured in terms of memory and computational complexity, which are usually a function of the number of the given data points. Sparse local operators that involve substantially less than quadratic complexity at one end, an ...[more]

PMID: 24108352

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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.

Dataset Information

Spectral multidimensional scaling.

Publications

Spectral multidimensional scaling.

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