Using self organizing maps on compositional data

Self-organizing maps (Kohonen 1997) is a type of artificial neural network developedto explore patterns in high-dimensional multivariate data. The conventional versionof the algorithm involves the use of Euclidean metric in the process of adaptation ofthe model vectors, thus rendering in theory a whole methodology incompatible withnon-Euclidean geometries.In this contribution we explore the two main aspects of the problem:1. Whether the conventional approach using Euclidean metric can shed valid resultswith compositional data.2. If a modification of the conventional approach replacing vectorial sum and scalarmultiplication by the canonical operators in the simplex (i.e. perturbation andpowering) can converge to an adequate solution.Preliminary tests showed that both methodologies can be used on compositional data.However, the modified version of the algorithm performs poorer than the conventionalversion, in particular, when the data is pathological. Moreover, the conventional ap-proach converges faster to a solution, when data is \well-behaved".Key words: Self Organizing Map; Artificial Neural networks; Compositional data

Scoring Methods for Ordinal Multidimensional Forced-Choice Items

In most psychological tests and questionnaires, a test score is obtained bytaking the sum of the item scores. In virtually all cases where the test orquestionnaire contains multidimensional forced-choice items, this traditionalscoring method is also applied. We argue that the summation of scores obtained with multidimensional forced-choice items produces uninterpretabletest scores. Therefore, we propose three alternative scoring methods: a weakand a strict rank preserving scoring method, which both allow an ordinalinterpretation of test scores; and a ratio preserving scoring method, whichallows a proportional interpretation of test scores. Each proposed scoringmethod yields an index for each respondent indicating the degree to whichthe response pattern is inconsistent. Analysis of real data showed that withrespect to rank preservation, the weak and strict rank preserving methodresulted in lower inconsistency indices than the traditional scoring method;with respect to ratio preservation, the ratio preserving scoring method resulted in lower inconsistency indices than the traditional scoring method

Comparing methods for dimensionality reduction when data are density functions

Functional Data Analysis (FDA) deals with samples where a whole function is observedfor each individual. A particular case of FDA is when the observed functions are densityfunctions, that are also an example of infinite dimensional compositional data. In thiswork we compare several methods for dimensionality reduction for this particular typeof data: functional principal components analysis (PCA) with or without a previousdata transformation and multidimensional scaling (MDS) for diferent inter-densitiesdistances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (householdsincome 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 oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper 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 considerationof densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermite-polynomials-based basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. 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 thereference density. Finally, for the case of 2-order Hermite polinomials (normal reference)and 1-order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize 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 orsediment, 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 startingpoint. Chemical compositional data, as used in provenance studies on archaeologicalmaterials, will be approached from the measurement theory. The results will show, in avery intuitive way that chemical data can only be treated by using the approachdeveloped for compositional data. It will be shown that compositional data analysis is aparticular case in projective geometry, when the projective coordinates are in thepositive 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 ofapplications, including shape analysis. This will be exemplified with a case study inarchitecture of Early Christian churches dated back to the 5th-7th centuries AD

Vertebrates Limb Geometry in the Simplex space

A novel metric comparison of the appendicular skeleton (fore and hind limb) ofdifferent vertebrates using the Compositional Data Analysis (CDA) methodologicalapproach it’s presented.355 specimens belonging in various taxa of Dinosauria (Sauropodomorpha, Theropoda,Ornithischia and Aves) and Mammalia (Prothotheria, Metatheria and Eutheria) wereanalyzed with CDA.A special focus has been put on Sauropodomorpha dinosaurs and the Aitchinsondistance has been used as a measure of disparity in limb elements proportions to infersome 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 istheny = 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 analysismodel (1) can be written asCov(y) = ΛΛT + ψ (2)where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as theloadings matrix Λ are estimated from an estimation of Cov(y).Given observed clr transformed data Y as realizations of the random vectory. Outliers or deviations from the idealized model assumptions of factor analysiscan severely effect the parameter estimation. As a way out, robust estimation ofthe covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), seePison et al. (2003). Well known robust covariance estimators with good statisticalproperties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), relyon 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 thissingularity problem. The data matrix Y is transformed to a matrix Z by usingan orthonormal basis of lower dimension. Using the ilr transformed data, a robustcovariance matrix C(Z) can be estimated. The result can be back-transformed tothe clr space byC(Y ) = V C(Z)V Twhere the matrix V with orthonormal columns comes from the relation betweenthe clr and the ilr transformation. Now the parameters in the model (2) can beestimated (Basilevsky, 1994) and the results have a direct interpretation since thelinks to the original variables are still preserved.The above procedure will be applied to data from geochemistry. Our specialinterest is on comparing the results with those of Reimann et al. (2002) for the Kolaproject data

Validation of the spanish version of the multiple sclerosis international quality of life (musiqol) questionnaire

BACKGROUND: The Multiple Sclerosis International Quality Of Life (MusiQoL) questionnaire, a 31-item, multidimensional, self-administrated questionnaire that is available in 14 languages including Spanish, has been validated using a large international sample. We investigated the validity and reliability of the Spanish version of MusiQoL in Spain. METHODS: Consecutive patients with different types and severities of multiple sclerosis (MS) were recruited from 22 centres across Spain. All patients completed the MusiQoL questionnaire, the 36-Item Short Form (SF-36) health survey, and a symptoms checklist at baseline and 21 days later. External validity, internal consistency, reliability and reproducibility were tested. RESULTS: A total of 224 Spanish patients were evaluated. Dimensions of MusiQoL generally demonstrated a high internal consistency (Cronbach's alpha: 0.70-0.92 for all but two MusiQoL domain scores). External validity testing revealed that the MusiQoL index score correlated significantly with all SF-36 dimension scores (Pearson's correlation: 0.46-0.76), reproducibility was satisfactory (intraclass correlation coefficient: 0.60-0.91), acceptability was high, and the time taken to complete the 31-item questionnaire was reasonable (mean [standard deviation]: 9.8 [11.8] minutes). CONCLUSIONS: The Spanish version of the MusiQoL questionnaire appears to be a valid and reliable instrument for measuring quality of life in patients with MS in Spain and constitutes a useful instrument to measure health-related quality of life in the clinical setting.

Outcome after relapse of acute lymphoblastic leukemia in adult patients included in four consecutive risk-adapted trials by the PETHEMA Study Group

BACKGROUND About one half of adults with acute lymphoblastic leukemia are not cured of the disease and ultimately die. The objective of this study was to explore the factors influencing the outcome of adult patients with relapsed acute lymphoblastic leukemia. DESIGN AND METHODS. We analyzed the characteristics, the outcome and the prognostic factors for survival after first relapse in a series of 263 adult patients with acute lymphoblastic leukemia (excluding those with mature B-cell acute lymphoblastic leukemia) prospectively enrolled in four consecutive risk-adapted PETHEMA trials. RESULTS. The median overall survival after relapse was 4.5 months (95% CI, 4-5 months) with a 5-year overall survival of 10% (95% CI, 8%-12%); 45% of patients receiving intensive second-line treatment achieved a second complete remission and 22% (95% CI, 14%-30%) of them remained disease free at 5 years. Factors predicting a good outcome after rescue therapy were age less than 30 years (2-year overall survival of 21% versus 10% for those over 30 years old; P<0.022) and a first remission lasting more than 2 years (2-year overall survival of 36% versus 17% among those with a shorter first remission; P<0.001). Patients under 30 years old whose first complete remission lasted longer than 2 years had a 5-year overall survival of 38% (95% CI, 23%-53%) and a 5-year disease-free survival of 53% (95% CI, 34%-72%). CONCLUSIONS The prognosis of adult patients with acute lymphoblastic leukemia who relapse is poor. Those aged less than 30 years with a first complete remission lasting longer than 2 years have reasonable possibilities of becoming long-term survivors while patients over this age or those who relapse early cannot be successfully rescued using the therapies currently available.

Treatment and seroconversion in a cohort of children suffering from recent chronic Chagas infection in Yoro, Honduras

Between 1999-2002, Médécins Sans Frontières-Spain implemented a project seeking to determine the efficacy and safety of benznidazole in the treatment of recent chronic Chagas disease in a cohort of seropositive children in the Yoro Department, Honduras. A total of 24,471 children were screened for Trypanosoma cruzi IgG antibodies through conventional enzyme-linked immunosorbent assays (ELISA) on filter paper. Recombinant ELISA (0.93% seroprevalence) showed 256 initially reactive cases, including 232 confirmed positive cases. Of these, 231 individuals were treated with benznidazole (7.5 mg/kg/day) for 60 days and were followed with a strict weekly medical control and follow-up protocol. At the end of the project, 229 patients were examined by the Honduras Secretariat of Health for post-treatment serological assessments; 88.2% seroconverted after 18 months and 93.9% seroconverted after three years. No differences were found in the seroconversion rates according to age or sex. Most of the side effects of the treatment were minor. These results support the argument that in areas where T. cruzi I is predominant and in areas affected by T. cruzi II, when vector transmission has been interrupted, Chagas disease diagnosis and treatment are feasible, necessary and ethically indisputable.

La vil·la romana de la casa del Racó

Aquest article presenta els resultats de l'excavació arqueològica de la vil·la romana de la 'Casa del Racó', al terme municipal de Sant Julià de Ramis, entre 1991 i 1992

Gerunda i els ausetans: una qüestió recurrent

Article que tracta del tema recurrent de la pertinença o no de Gerunda a la tribu ibèrica dels ausetans

Una peça notable procedent de Sant Julià de Ramis

Article que descriu i analitza un fragment d'una gran gerra ceràmica amb decoració grafitada al damunt de la paret externa procedent del poblat ibèric de Sant Julià de Ramis, situat en el límit nord-oriental del Pla de Girona

Alfons Miàs, catalanista i col·laboracionista

Article sobre l' escriptor i activista cultural Alfons Miàs