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Dimensionality Reduction — Nonlinear Methods
Published in Wendy L. Martinez, Angel R. Martinez, Jeffrey L. Solka, Exploratory Data Analysis with MATLAB®, 2017
Wendy L. Martinez, Angel R. Martinez, Jeffrey L. Solka
In general, multidimensional scaling (MDS) is a set of techniques for the analysis of proximity data measured on a set of objects in order to reveal hidden structure. The purpose of MDS is to find a configuration of the data points in a low-dimensional space such that the proximity between objects in the full-dimensional space is represented with some degree of fidelity by the distances between points in the low-dimensional space. This means that observations that are close together in a high-dimensional space should be close in the low-dimensional space. Many aspects of MDS were originally developed by researchers in the social science community, and the method is now widely available in most statistical packages, including the MATLAB Statistics Toolbox.
Methods for the Reduction of Dimensionality
Published in Shayne C. Gad, Carrol S. Weil, Statistics and Experimental Design for Toxicologists, 1988
We will then move on to two collections of methodologies which combine graphic and computational methods, multidimensional/non-metric scaling and cluster analysis. Multidimensional scaling (MDS) is a set of techniques for quantitatively analyzing similarities, dissimilarities and distances between data in a display-like manner. Nonmetric scaling is an analogous set of methods for displaying and relating data when measurements are non-quantative (the data are described by attributes or ranks). Cluster analysis is a collection of graphic and numerical methodologies for classifying things based on the relationships between the values of the variables that they share.
The perception of ride is multidimensional for running footwear
Published in Footwear Science, 2020
Cristine Agresta, Jillian Peacock, Alicia Carmichael, Karen E Nielsen, Jessica Zendler, Richard Gonzalez
The R package ‘smacof’ was used to perform the individual difference multidimensional scaling (de Leeuw & Mair, 2009). We used the nonmetric form of INDSCAL given that the ride ratings were ordinal five-point ratings; thus, our findings are unique up to monotonic transformation of the rating scale and is more general than PCA where results are unique up to a linear transformation. We conducted a nonmetric INDSCAL on the eight ride ratings across the five shoes to assess how the estimated dimensions are differentially weighted in the evaluations of the five shoes (i.e. for this analysis the units l are the five shoes). Similarly, we conducted a second nonmetric INDSCAL on the eight ideal ride qualities for the four running purposes to assess how the estimated dimensions are differentially weighted across running purposes (i.e. for this analysis the units l are the four running purposes). Stress was used as a measure of goodness of fit (the objective function to minimise) and we estimated nonparametric bootstrapped confidence intervals (500 bootstrap samples) around the estimated stress value (Weinberg, Carroll, & Cohen, 1984); a screeplot was used to decide on the number of dimensions t and we examined t = 2 to t = 6.
Irrigation with permeates to upgrade the quality of red pepper: a case study in Arava region, Israel
Published in Environmental Technology, 2022
Beni Lew, Olga Tarnapolski, Yiftah Afgin, Yosi Portal, Timea Ignat, Vladimir Yudachev, Amos Bick
Mathematical way of thinking follows functional thinking, which consists of thinking in terms of indicators and functions and builds up functions mapping [38]. The term ‘Multi-dimensional Scaling’ or MDS refers to any technique that produces a multi-dimensional geometric representation of data. This is an interdependence method that quantitative or qualitative relationship in the data and corresponds to geometric relationships in the representation. Reducing of multivariate data into a two-dimensional structure or mapping image of the data facilitates the examination [39]. By this way, we can use mathematical thinking to address chemical and biological questions in irrigation research.