Comparing methods for dimensionality reduction when data are density functions

Functional Data Analysis (FDA) deals with samples where a whole function is observed for each individual. A particular case of FDA is when the observed functions are density functions, that are also an example of infinite dimensional compositional data. In this work we compare several methods for dimensionality reduction for this particular type of data: functional principal components analysis (PCA) with or without a previous data transformation and multidimensional scaling (MDS) for diferent inter-densities distances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (households income distributions)

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing one or more parameters in their definition. Methods that can be linked in this way are correspondence analysis, unweighted or weighted logratio analysis (the latter also known as "spectral mapping"), nonsymmetric correspondence analysis, principal component analysis (with and without logarithmic transformation of the data) and multidimensional scaling. In this presentation I will show how several of these methods, which are frequently used in compositional data analysis, may be linked through parametrizations such as power transformations, linear transformations and convex linear combinations. Since the methods of interest here all lead to visual maps of data, a "movie" can be made where where the linking parameter is allowed to vary in small steps: the results are recalculated "frame by frame" and one can see the smooth change from one method to another. Several of these "movies" will be shown, giving a deeper insight into the similarities and differences between these methods

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

Revisiting the compositional data. Some fundamental questions and new prospects in Archaeometry and Archaeology

In this paper we examine the problem of compositional data from a different starting point. Chemical compositional data, as used in provenance studies on archaeological materials, will be approached from the measurement theory. The results will show, in a very intuitive way that chemical data can only be treated by using the approach developed for compositional data. It will be shown that compositional data analysis is a particular case in projective geometry, when the projective coordinates are in the positive orthant, and they have the properties of logarithmic interval metrics. Moreover, it will be shown that this approach can be extended to a very large number of applications, including shape analysis. This will be exemplified with a case study in architecture of Early Christian churches dated back to the 5th-7th centuries AD

Modelling of Mercury’s surface composition and remote detection from the orbit with the BepiColombo Mercury Planetary Orbiter

It can be assumed that the composition of Mercury’s thin gas envelope (exosphere) is related to the composition of the planets crustal materials. If this relationship is true, then inferences regarding the bulk chemistry of the planet might be made from a thorough exospheric study. The most vexing of all unsolved problems is the uncertainty in the source of each component. Historically, it has been believed that H and He come primarily from the solar wind, while Na and K originate from volatilized materials partitioned between Mercury’s crust and meteoritic impactors. The processes that eject atoms and molecules into the exosphere of Mercury are generally considered to be thermal vaporization, photonstimulated desorption (PSD), impact vaporization, and ion sputtering. Each of these processes has its own temporal and spatial dependence. The exosphere is strongly influenced by Mercury’s highly elliptical orbit and rapid orbital speed. As a consequence the surface undergoes large fluctuations in temperature and experiences differences of insolation with longitude. We will discuss these processes but focus more on the expected surface composition and solar wind particle sputtering which releases material like Ca and other elements from the surface minerals and discuss the relevance of composition modelling

Vertebrates Limb Geometry in the Simplex space

A novel metric comparison of the appendicular skeleton (fore and hind limb) of different vertebrates using the Compositional Data Analysis (CDA) methodological approach it’s presented. 355 specimens belonging in various taxa of Dinosauria (Sauropodomorpha, Theropoda, Ornithischia and Aves) and Mammalia (Prothotheria, Metatheria and Eutheria) were analyzed with CDA. A special focus has been put on Sauropodomorpha dinosaurs and the Aitchinson distance has been used as a measure of disparity in limb elements proportions to infer some aspects of functional morphology

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr) transformation to obtain the random vector y of dimension D. The factor model is then y = Λf + e (1) with the factors f of dimension k < D, the error term e, and the loadings matrix Λ. Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysis model (1) can be written as Cov(y) = ΛΛT + ψ (2) where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as the loadings matrix Λ are estimated from an estimation of Cov(y). Given observed clr transformed data Y as realizations of the random vector y. Outliers or deviations from the idealized model assumptions of factor analysis can severely effect the parameter estimation. As a way out, robust estimation of the covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), see Pison et al. (2003). Well known robust covariance estimators with good statistical properties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), rely on a full-rank data matrix Y which is not the case for clr transformed data (see, e.g., Aitchison, 1986). The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves this singularity problem. The data matrix Y is transformed to a matrix Z by using an orthonormal basis of lower dimension. Using the ilr transformed data, a robust covariance matrix C(Z) can be estimated. The result can be back-transformed to the clr space by C(Y ) = V C(Z)V T where the matrix V with orthonormal columns comes from the relation between the clr and the ilr transformation. Now the parameters in the model (2) can be estimated (Basilevsky, 1994) and the results have a direct interpretation since the links to the original variables are still preserved. The above procedure will be applied to data from geochemistry. Our special interest is on comparing the results with those of Reimann et al. (2002) for the Kola project data

Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model and the design region. The talk will consider the design of experiments for regression models in which there is a single response with the explanatory variables lying in a simplex. One example is experiments on various compositions of glass such as those considered by Martin, Bursnall, and Stillman (2001). Because of the highly symmetric nature of the simplex, the class of models that are of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather different from those of standard regression analysis. The optimum designs are also rather different, inheriting a high degree of symmetry from the models. In the talk I will hope to discuss a variety of modes for such experiments. Then I will discuss constrained mixture experiments, when not all the simplex is available for experimentation. Other important aspects include mixture experiments with extra non-mixture factors and the blocking of mixture experiments. Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007). If time and my research allows, I would hope to finish with a few comments on design when the responses, rather than the explanatory variables, lie in a simplex. References Atkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum Experimental Designs, with SAS. Oxford: Oxford University Press. Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results on optimal and efficient designs for constrained mixture experiments. In A. C. Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000, pp. 225–239. Dordrecht: Kluwer. Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal Statistical Society, Ser. B 20, 344–360. 1

Portal web per la localitzacó de restaurants

Desenvolupament,anàlisi, disseny i implementació d’un portal web, tipus cercador, per la recerca i localització d’establiments tipus restaurant, bars, bufets, etc,. Per altra banda es pretén oferir un sistema de gestió d’informació on les empreses del sector gastronòmic puguin mostrar la seva informació i la seva oferta

Passeig per l'invisible: itinerari químic per Girona

La finalitat d'aquesta proposta és facilitar l'aprenentatge de la química a través de l'exposició d'exemples diaris, en una activitat que desenvolupa a més les competències actitudinals. S'ha observat que alguns estudiants de la Facultat de Ciències tenen dificultats per seguir assignatures de química a causa de la seva nul·la o dèbil formació en química a secundària. A més, molts d'ells consideren la química com una ciència complicada, inútil o perillosa. L’activitat presentada és un itinerari químic: un passeig per a una ciutat amb tradició química que mostra exemples quotidians de la presència de la química arreu. S'hi afegeixen experiments i demostracions, a més d'exercicis adaptables al nivell dels estudiants. Tots els professors volem tenir estudiants motivats en les nostres classes perquè sabem que això és bàsic per al seu aprenentatge. L'itinerari ha demostrat la seva validesa especialment en aquest aspecte. A més, permet treballar determinats conceptes del contingut curricular de química. Tot i que els beneficis a llarg termini de la realització de l'itinerari no s'han avaluat encara, els estudiants estan molt satisfets amb el desenvolupament de l'itinerari. Consideren que la informació donada ha millorat la imatge que tenien de química. D'alguna manera, descobreixen quelcom que fins aleshores els havia estat invisible

Public and student awareness science: recreational science as a catalyst

When discussing the traditional and new missions of higher education (1996 Report to UNESCO of the International Commission on Education for the 21st Century) Jacques Delors stated that "Excessive attraction to social sciences has broken equilibrium of available graduates for workforce, thus causing doubts of graduates and employers on the quality of knowledge provided by higher education". Likewise, when discussing the progress of science and technology, the 1998 UNESCO World Conference on Higher Education concluded that "Another challenge concerts the latest advancements of Science, the sine qua non of sustainable development"; and that “with Information Technology, the unavoidable invasion of virtual reality has increased the distance between industrial and developing countries". Recreational Science has a long tradition all over the Educational World; it aims to show the basic aspects of Science, aims to entertain, and aims to induce thinking. Until a few years ago, this field of knowledge consisted of a few books, a few kits and other classical (yet innovative) ways to popularize the knowledge of Nature and the laws governing it. In Spain, the interest for recreational science has increased in the last years. First, new recreational books are being published and found in bookstores. Second the number of Science-related museums and exhibits is increasing. And third, new television shows are produced and new short science-based, superficial sketches are found in variety programs. However, actual programs in Spanish television dealing seriously with Science are scarce. Recreational Science, especially that related to physical phenomena like light or motion, is generally found at Science Museums because special equipment is required. On the contrary, Science related mathematics, quizzes and puzzles use to gather into books, e.g. the extensive collections by Martin Gardner. However, lately Science podcasts have entered the field of science communication. Not only traditional science journals and television channels are providing audio and video podcasts, but new websites deal exclusively with science podcasts, in particular on Recreational Science. In this communication we discuss the above mentioned trends and show our experience in the last two years in participating at Science Fairs and university-sponsored events to attract students to science and technology careers. We show a combination of real examples (e.g., mathemagic), imagination, use of information technology, and use of social networks. We present as well an experience on designing a computational, interactive tool to promote chemistry among high school, prospective students using computers ("Dancing with Bionanomolecules"). Like the concepts related to Web 2.0, it has been already proposed that a new framework for communication of science is emerging, i.e., Science Communication 2.0, where people and institutions develop new innovative ways to explain science topics to diverse publics – and where Recreational Science is likely to play a leading role

Sistema d'anà lisi financer: tresoreria amb eines Business Intelligence

El projecte tracte d' implementar una solució de Business Intelligence sota la plataforma Microsoft.Aquest projecte va destinat al Departament de Comptabilitat de l' Ajuntament de Cambrils, i està relacionat amb la funció del control de les despeses i els ingressos

HÃ bits de treball dels usuaris d'ACME

Els hàbits de treball i el coneixement adquirit pels alumnes de les universitats al llarg d’un curs cada cop ha estat més fàcil de saber per part dels professors. L’aparició de noves metodologies i nous sistemes d’avaluació junt amb les millores tecnològiques i les millores incorporades al sistema educatiu, han facilitat i promogut l’accés aquest tipus d’informació. En els darrers anys aquest tema ha adquirit una importància capdal gràcies a l’Espai Europeu d’Educació Superior (EEES). En el nou marc de l’EEES els alumnes han d’adquirir unes competències realitzant diferents activitats d’aprenentatge presencials i no presencials. Per tant un dels aspectes fonamentals per desenvolupar amb garanties l’EEES és portar a terme per part del professorat un seguiment de l’aprenentatge de l’alumne i el control de les activitats proposades. Aquestes feines comporten, sens dubte, una major dedicació del professor a les tasques docents. Són moltes les tècniques que es poden utilitzar per fer el seguiment de l’aprenentatge dels alumnes, però en els darrers anys apareix amb força l’ús de les TIC, i més concretament l’ús de plataformes d’e-learning, que permeten tant als alumnes com als professors realitzar el treball des d’on volen i quan volen. Aquestes eines han suposat un canvi en el model d’aprenentatge dels alumnes, una revolució en la comunicació entre professors i alumnes i fins hi tot un replantejament en la confecció i difusió del material que s’ha de treballar tant a classe com a fora. Hom veu que l’ús d’aquestes plataformes s’ha anat generalitzant de tal forma que aquestes han esdevingut una eina de treball més d’alumnes i professors. A la Universitat de Girona una de les plataformes d’e-learning més utilitzades per fer un seguiment del treball dels alumnes és la plataforma ACME (Avaluació Continuada i Millora de l’Ensenyament). Aquesta plataforma web, a més a més del seguiment i control de l’alumnat, permet la correcció automàtica i on-line de gran varietat de problemes i activitats de temàtiques com matemàtiques, química, economia, electrònica, publicitat i relacions públiques, bases de dades, estadística... L’ACME és una eina que realitza un seguiment exhaustiu del treball realitzat per l’alumne a través de la plataforma, permeten al professor conèixer tot un seguit d’informació que anys endarrere era impensable. El volum de dades recollit en els darrers 3 anys ens permet veure quins són els comportaments de treball semipresencial que tenen els alumnes: quins dies treballen, a quines hores, durant quines hores del dia són més efectius, quantes hores dediquen... i tot un seguit de dades que ens pot donar un punt de referència dels hàbits de treballs dels nostres alumnes

Experiència del treball cooperatiu en una assignatura prà ctica de laboratori

L’experiència que es presenta s’ha dut a terme en l’assignatura Introducció a l’Experimentació en síntesi química, que és la primera assignatura de tipus sintètic que els estudiants es troben a la llicenciatura de química de la Universitat de Girona. Des del curs 2001-2002 s’han introduït canvis en l’assignatura amb la intenció de millorar els aprenentatges per part dels alumnes, però els canvis més significatius en aquesta assignatura es produeixen a partir del curs 2005-2006 en que s’incorporen nous mètodes d’avaluació. Entre aquests nous mètodes s’ha incorporat d’una experiència combinada d’aprenentatge basat en projectes i de treball cooperatiu. Consisteix en què els alumnes han de proposar la síntesi d’un producte químic. El procés que han de realitzar durant l’exercici és el mateix que haurien de dur a terme en una síntesi real fora del laboratori docent. Aquest procés inclou: recerca bibliogràfica, disseny del procediment, comprovació del material disponible, síntesi i valoració de la qualitat del producte i, finalment, redacció i presentació d’un informe. En l’exercici d’aprenentatge basat en projectes hi intervenen a més tots els elements bàsics de l’aprenentatge cooperatiu. La primera part de l’exercici és una tasca de grup, els alumnes han de desenvolupar la interacció positiva cara a cara, les habilitats personals i de grup, el group processing i la interdependència positiva. La segona part és més individual i els alumnes desenvolupen l’exigibilitat personal. L’equip de professors implicats en aquest projecte estem molt satisfets dels resultats obtinguts en l’avaluació dels aprenentatges, i especialment en aquesta experiència

Diagnosi de les potencialitats silvoramaderes per a la prevenció d’incendis forestals a Fitor (EIN Gavarres)

Diagnosi ambiental de la zona de Fitor (EIN Gavarres) per tal de gestionar aquesta zona, reduint el risc d’ incendi forestal. Amb l’ objectiu de reduir el risc d’ incendi en aquesta zona es proposa la introducció d’ un ramat de 350 individus per rebaixar la fitomassa del sotabosc, tenint en compte els PEG’s (Punts Estratègics de Gestió) marcats en el PPIF (Pla de Prevenció d’ Incendis Forestals). Es proposen una sèrie de recorreguts i àrees de pastura per tal de reduir o mantenir la fitomassa del sotabosc, i unes propostes d’actuació a nivell executiu i divulgatiu per dinamitzar el sector ramader