Anthropometry: An R Package for Analysis of Anthropometric Data

The development of powerful new 3D scanning techniques has enabled the generation of large up-to-date anthropometric databases which provide highly valued data to improve the ergonomic design of products adapted to the user population. As a consequence, Ergonomics and Anthropometry are two increasingly quantitative fields, so advanced statistical methodologies and modern software tools are required to get the maximum benefit from anthropometric data. This paper presents a new R package, called Anthropometry, which is available on the Comprehensive R Archive Network. It brings together some statistical methodologies concerning clustering, statistical shape analysis, statistical archetypal analysis and the statistical concept of data depth, which have been especially developed to deal with anthropometric data. They are proposed with the aim of providing effective solutions to some common anthropometric problems, such as clothing design or workstation design (focusing on the particular case of aircraft cockpits). The utility of the package is shown by analyzing the anthropometric data obtained from a survey of the Spanish female population performed in 2006 and from the 1967 United States Air Force survey. This manuscript is also contained in Anthropometry as a vignette

Archetypoid analysis for sports analytics

We intend to understand the growing amount of sports performance data by finding extreme data points, which makes human interpretation easier. In archetypoid analysis each datum is expressed as a mixture of actual observations (archetypoids). Therefore, it allows us to identify not only extreme athletes and teams, but also the composition of other athletes (or teams) according to the archetypoid athletes, and to establish a ranking. The utility of archetypoids in sports is illustrated with basketball and soccer data in three scenarios. Firstly, with multivariate data, where they are compared with other alternatives, showing their best results. Secondly, despite the fact that functional data are common in sports (time series or trajectories), functional data analysis has not been exploited until now, due to the sparseness of functions. In the second scenario, we extend archetypoid analysis for sparse functional data, furthermore showing the potential of functional data analysis in sports analytics. Finally, in the third scenario, features are not available, so we use proximities. We extend archetypoid analysis when asymmetric relations are present in data. This study provides information that will provide valuable knowledge about player/team/league performance so that we can analyze athlete’s careers.This work has been partially supported by Grant DPI2013-47279-C2-1-R. The databases and R code (including the web application) to reproduce the results can be freely accessed at www.uv.es/vivigui/software

Transformation and decomposition of clutters into matroids

A clutter is a family of mutually incomparable sets. The set of circuits of a matroid, its set of bases, and its set of hyperplanes are examples of clutters arising from matroids. In this paper we address the question of determining which are the matroidal clutters that best approximate an arbitrary clutter ¿. For this, we first define two orders under which to compare clutters, which give a total of four possibilities for approximating ¿ (i.e., above or below with respect to each order); in fact, we actually consider the problem of approximating ¿ with clutters from any collection of clutters S, not necessarily arising from matroids. We show that, under some mild conditions, there is a finite non-empty set of clutters from S that are the closest to ¿ and, moreover, that ¿ is uniquely determined by them, in the sense that it can be recovered using a suitable clutter operation. We then particularize these results to the case where S is a collection of matroidal clutters and give algorithmic procedures to compute these clutters.Peer ReviewedPostprint (author's final draft

Lower bounds on the maximum number of non-crossing acyclic graphs

This paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain point configuration of N points has Omega (12.52(N)) non-crossing spanning trees and Omega (13.61(N)) non-crossing forests. This improves the previous lower bounds on the maximum number of non-crossing spanning trees and of non-crossing forests among all sets of N points in general position given by Dumitrescu, Schulz, Sheffer and Toth (2013). Our analysis relies on the tools of analytic combinatorics, which enable us to count certain families of forests on points in convex position, and to estimate their average number of components. A new upper bound of O(22.12(N)) for the number of non-crossing spanning trees of the double chain is also obtained. (C) 2015 Elsevier Ltd. All rights reserved.Postprint (author's final draft

Tutte polynomials of generalized parallel connections

We use weighted characteristic polynomials to compute Tutte polynomials of generalized parallel connections in the case in which the simplification of the maximal common restriction of the two constituent matroids is a modular flat of the simplifications of both matroids. In particular, this includes cycle matroids of graphs that are identified along complete subgraphs. We also develop formulas for Tutte polynomials of the k-sums that are obtained from such generalized parallel connections.Postprint (published version

T-uniqueness of some families of k-chordal matroids

We define k-chordal matroids as a generalization of chordal matroids, and develop tools for proving that some k-chordal matroids are T-unique, that is, determined up to isomorphism by their Tutte polynomials. We apply this theory to wheels, whirls, free spikes, binary spikes, and certain generalizations.Postprint (published version

Completion and decomposition of a clutter into representable matroids

This paper deals with the question of completing a monotone increasing family of subsets Gamma of a finite set Omega to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we prove that such vectorial completions of the family of subsets Gamma exist and, in addition, we show that the minimal vectorial completions of the family Gamma provide a decomposition of the clutter Lambda of the inclusion-minimal elements of Gamma. The computation of such vectorial decomposition of clutters is also discussed in some cases. (C) 2015 Elsevier Inc. All rights reserved.Peer ReviewedPostprint (author’s final draft

A solution to the tennis ball problem

We present a complete solution to the so-called tennis ball problem, which is equivalent to counting the number of lattice paths in the plane that use North and East steps and lie between certain boundaries. The solution takes the form of explicit expressions for the corresponding generating functions. Our method is based on the properties of Tutte polynomials of matroids associated to lattice paths. We also show how the same method provides a solution to a wide generalization of the problem.Postprint (published version

Lattice path matroids: structural properties

This paper studies structural aspects of lattice path matroids. Among the basic topics treated are direct sums, duals, minors, circuits, and connected flats. One of the main results is a characterization of lattice path matroids in terms of fundamental flats, which are special connected flats from which one can recover the paths that define the matroid. We examine some aspects related to key topics in the literature of transversal matroids and we determine the connectivity of lattice path matroids. We also introduce notch matroids, a minor-closed, dual-closed subclass of lattice path matroids, and we find their excluded minors.Postprint (published version

Archetypal analysis: contributions for estimating boundary cases in multivariate accommodation problem

The use of archetypal analysis is proposed in order to determine a set of representative cases that entail a certain percentage of the population, in the accommodation problem. A well-known anthropometric database has been used in order to compare our methodology with the common used PCA- approach, showing the advantages of our methodology: the level of accom- modation is reached unlike the PCA approach, no more adjustments are nec- essary, the user can decide the number of archetypes to consider or leave the selection by a criterion. Unlike PCA, the objective of the archetypal analysis is obtaining extreme individuals, so it is the appropriate statistical technique for solving this type of problem. Archetypes cannot be obtained with PCA even if we consider all the components, as we show in the application