Searching for consensus in ahp-group decision making. A bayesian perspective

This paper sets out to identify the initial positions of the different decision makers who intervene in a group decision making process with a reduced number of actors, and to establish possible consensus paths between these actors. As a methodological support, it employs one of the most widely-known multicriteria decision techniques, namely, the Analytic Hierarchy Process (AHP). Assuming that the judgements elicited by the decision makers follow the so-called multiplicative model (Crawford and Williams, 1985; Altuzarra et al., 1997; Laininen and Hämäläinen, 2003) with log-normal errors and unknown variance, a Bayesian approach is used in the estimation of the relative priorities of the alternatives being compared. These priorities, estimated by way of the median of the posterior distribution and normalised in a distributive manner (priorities add up to one), are a clear example of compositional data that will be used in the search for consensus between the actors involved in the resolution of the problem through the use of Multidimensional Scaling tools

Group preference structures in AHP–group decision making

This paper presents a procedure that allows us to determine the preference structures (PS) associated to each of the different groups of actors that can be identified in a group decision making problem with a large number of individuals. To that end, it makes use of the Analytic Hierarchy Process (AHP) (Saaty, 1980) as the technique to solve discrete multicriteria decision making problems. This technique permits the resolution of multicriteria, multienvironment and multiactor problems in which subjective aspects and uncertainty have been incorporated into the model, constructing ratio scales corresponding to the priorities relative to the elements being compared, normalised in a distributive manner (wi = 1). On the basis of the individuals’ priorities we identify different clusters for the decision makers and, for each of these, the associated preference structure using, to that end, tools analogous to those of Multidimensional Scaling. The resulting PS will be employed to extract knowledge for the subsequent negotiation processes and, should it be necessary, to determine the relative importance of the alternatives being compared using anyone of the existing procedures

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

Shifts in rhizosphere microbial communities and enzyme activity of Poa alpina across an alpine chronosequence

This study quantifies the influence of Poa alpina on the soil microbial community in primary succession of alpine ecosystems, and whether these effects are controlled by the successional stage. Four successional sites representative of four stages of grassland development (initial, 4 years (non-vegetated); pioneer, 20 years; transition, 75 years; mature, 9500 years old) on the Rotmoos glacier foreland, Austria, were sampled. The size, composition and activity of the microbial community in the rhizosphere and bulk soil were characterized using the chloroform-fumigation extraction procedure, phospholipid fatty acid (PLFA) analysis and measurements of the enzymes beta-glucosidase, beta-xylosidase, N-acetyl-beta-glucosaminidase, leucine aminopeptidase, acid phosphatase and sulfatase. The interplay between the host plant and the successional stage was quantified using principal component (PCA) and multidimensional scaling analyses. Correlation analyses were applied to evaluate the relationship between soil factors (C-org, N-t, C/N ratio, pH, ammonium, phosphorus, potassium) and microbial properties in the bulk soil. In the pioneer stage microbial colonization of the rhizosphere of P. alpina was dependent on the reservoir of microbial species in the bulk soil. As a consequence, the rhizosphere and bulk soil were similar in microbial biomass (ninhydrin-reactive nitrogen (NHR-N)), community composition (PLFA), and enzyme activity. In the transition and mature grassland stage, more benign soil conditions stimulated microbial growth (NHR-N, total amount of PLFA, bacterial PLFA, Gram-positive bacteria, Gram-negative bacteria), and microbial diversity (Shannon index H) in the rhizosphere either directly or indirectly through enhanced carbon allocation. In the same period, the rhizosphere microflora shifted from a G(-) to a more G(+), and from a fungal to a more bacteria-dominated community. Rhizosphere beta-xylosidase, N-acetyl-beta-glucosaminidase, and sulfatase activity peaked in the mature grassland soil, whereas rhizosphere leucine aminopeptidase, beta-glucosidase, and phosphatase activity were highest in the transition stage, probably because of enhanced carbon and nutrient allocation into the rhizosphere due to better growth conditions. Soil organic matter appeared to be the most important driver of microbial colonization in the bulk soil. The decrease in soil pH and soil C/N ratio mediated the shifts in the soil microbial community composition (bacPLFA, bacPLFA/fungPLFA, G(-), G(+)/G(-)). The activities of beta-glucosidase, beta-xylosidase and phosphatase were related to soil ammonium and phosphorus, indicating that higher decomposition rates enhanced the nutrient availability in the bulk soil. We conclude that the major determinants of the microllora vary along the successional gradient: in the pioneer stage the rhizosphere microflora was primarily determined by the harsh soil environment; under more favourable environmental conditions, however, the host plant selected for a specific microbial community that was related to the dynamic interplay between soil properties and carbon supply. (C) 2004 Elsevier Ltd. All rights reserved.

Shifts in rhizosphere microbial communities and enzyme activity of Poa alpina across an alpine chronosequence

This study quantifies the influence of Poa alpina on the soil microbial community in primary succession of alpine ecosystems, and whether these effects are controlled by the successional stage. Four successional sites representative of four stages of grassland development (initial, 4 years (non-vegetated); pioneer, 20 years; transition, 75 years; mature, 9500 years old) on the Rotmoos glacier foreland, Austria, were sampled. The size, composition and activity of the microbial community in the rhizosphere and bulk soil were characterized using the chloroform-fumigation extraction procedure, phospholipid fatty acid (PLFA) analysis and measurements of the enzymes beta-glucosidase, beta-xylosidase, N-acetyl-beta-glucosaminidase, leucine aminopeptidase, acid phosphatase and sulfatase. The interplay between the host plant and the successional stage was quantified using principal component (PCA) and multidimensional scaling analyses. Correlation analyses were applied to evaluate the relationship between soil factors (C-org, N-t, C/N ratio, pH, ammonium, phosphorus, potassium) and microbial properties in the bulk soil. In the pioneer stage microbial colonization of the rhizosphere of P. alpina was dependent on the reservoir of microbial species in the bulk soil. As a consequence, the rhizosphere and bulk soil were similar in microbial biomass (ninhydrin-reactive nitrogen (NHR-N)), community composition (PLFA), and enzyme activity. In the transition and mature grassland stage, more benign soil conditions stimulated microbial growth (NHR-N, total amount of PLFA, bacterial PLFA, Gram-positive bacteria, Gram-negative bacteria), and microbial diversity (Shannon index H) in the rhizosphere either directly or indirectly through enhanced carbon allocation. In the same period, the rhizosphere microflora shifted from a G(-) to a more G(+), and from a fungal to a more bacteria-dominated community. Rhizosphere beta-xylosidase, N-acetyl-beta-glucosaminidase, and sulfatase activity peaked in the mature grassland soil, whereas rhizosphere leucine aminopeptidase, beta-glucosidase, and phosphatase activity were highest in the transition stage, probably because of enhanced carbon and nutrient allocation into the rhizosphere due to better growth conditions. Soil organic matter appeared to be the most important driver of microbial colonization in the bulk soil. The decrease in soil pH and soil C/N ratio mediated the shifts in the soil microbial community composition (bacPLFA, bacPLFA/fungPLFA, G(-), G(+)/G(-)). The activities of beta-glucosidase, beta-xylosidase and phosphatase were related to soil ammonium and phosphorus, indicating that higher decomposition rates enhanced the nutrient availability in the bulk soil. We conclude that the major determinants of the microllora vary along the successional gradient: in the pioneer stage the rhizosphere microflora was primarily determined by the harsh soil environment; under more favourable environmental conditions, however, the host plant selected for a specific microbial community that was related to the dynamic interplay between soil properties and carbon supply. (C) 2004 Elsevier Ltd. All rights reserved.

Multivariate relationships between groundwater chemistry and toxicity in an urban aquifer

Multivariate statistical methods were used to investigate file Causes of toxicity and controls on groundwater chemistry from 274 boreholes in an Urban area (London) of the United Kingdom. The groundwater was alkaline to neutral, and chemistry was dominated by calcium, sodium, and Sulfate. Contaminants included fuels, solvents, and organic compounds derived from landfill material. The presence of organic material in the aquifer caused decreases in dissolved oxygen, sulfate and nitrate concentrations. and increases in ferrous iron and ammoniacal nitrogen concentrations. Pearson correlations between toxicity results and the concentration of individual analytes indicated that concentrations of ammoinacal nitrogen, dissolved oxygen, ferrous iron, and hydrocarbons were important where present. However, principal component and regression analysis suggested no significant correlation between toxicity and chemistry over the whole area. Multidimensional Scaling was used to investigate differences in sites caused by historical use, landfill gas status, or position within the sample area. Significant differences were observed between sites with different historical land use and those with different gas status. Examination of the principal component matrix revealed that these differences are related to changes in the importance of reduced chemical species.

Virtual landmarking for locality aware peer IDs

In Peer-to-Peer (P2P) networks, it is often desirable to assign node IDs which preserve locality relationships in the underlying topology. Node locality can be embedded into node IDs by utilizing a one dimensional mapping by a Hilbert space filling curve on a vector of network distances from each node to a subset of reference landmark nodes within the network. However this approach is fundamentally limited because while robustness and accuracy might be expected to improve with the number of landmarks, the effectiveness of 1 dimensional Hilbert Curve mapping falls for the curse of dimensionality. This work proposes an approach to solve this issue using Landmark Multidimensional Scaling (LMDS) to reduce a large set of landmarks to a smaller set of virtual landmarks. This smaller set of landmarks has been postulated to represent the intrinsic dimensionality of the network space and therefore a space filling curve applied to these virtual landmarks is expected to produce a better mapping of the node ID space. The proposed approach, the Virtual Landmarks Hilbert Curve (VLHC), is particularly suitable for decentralised systems like P2P networks. In the experimental simulations the effectiveness of the methods is measured by means of the locality preservation derived from node IDs in terms of latency to nearest neighbours. A variety of realistic network topologies are simulated and this work provides strong evidence to suggest that VLHC performs better than either Hilbert Curves or LMDS use independently of each other.

Error, reproducibility and sensitivity: a pipeline for data processing of Agilent oligonucleotide expression arrays

Background: Expression microarrays are increasingly used to obtain large scale transcriptomic information on a wide range of biological samples. Nevertheless, there is still much debate on the best ways to process data, to design experiments and analyse the output. Furthermore, many of the more sophisticated mathematical approaches to data analysis in the literature remain inaccessible to much of the biological research community. In this study we examine ways of extracting and analysing a large data set obtained using the Agilent long oligonucleotide transcriptomics platform, applied to a set of human macrophage and dendritic cell samples. Results: We describe and validate a series of data extraction, transformation and normalisation steps which are implemented via a new R function. Analysis of replicate normalised reference data demonstrate that intrarray variability is small (only around 2 of the mean log signal), while interarray variability from replicate array measurements has a standard deviation (SD) of around 0.5 log(2) units (6 of mean). The common practise of working with ratios of Cy5/Cy3 signal offers little further improvement in terms of reducing error. Comparison to expression data obtained using Arabidopsis samples demonstrates that the large number of genes in each sample showing a low level of transcription reflect the real complexity of the cellular transcriptome. Multidimensional scaling is used to show that the processed data identifies an underlying structure which reflect some of the key biological variables which define the data set. This structure is robust, allowing reliable comparison of samples collected over a number of years and collected by a variety of operators. Conclusions: This study outlines a robust and easily implemented pipeline for extracting, transforming normalising and visualising transcriptomic array data from Agilent expression platform. The analysis is used to obtain quantitative estimates of the SD arising from experimental (non biological) intra- and interarray variability, and for a lower threshold for determining whether an individual gene is expressed. The study provides a reliable basis for further more extensive studies of the systems biology of eukaryotic cells.

Age and microenvironment outweigh genetic influence on the Zucker rat microbiome

Animal models are invaluable tools which allow us to investigate the microbiome-host dialogue. However, experimental design introduces biases in the data that we collect, also potentially leading to biased conclusions. With obesity at pandemic levels animal models of this disease have been developed; we investigated the role of experimental design on one such rodent model. We used 454 pyrosequencing to profile the faecal bacteria of obese (n = 6) and lean (homozygous n = 6; heterozygous n = 6) Zucker rats over a 10 week period, maintained in mixed-genotype cages, to further understand the relationships between the composition of the intestinal bacteria and age, obesity progression, genetic background and cage environment. Phylogenetic and taxon-based univariate and multivariate analyses (non-metric multidimensional scaling, principal component analysis) showed that age was the most significant source of variation in the composition of the faecal microbiota. Second to this, cage environment was found to clearly impact the composition of the faecal microbiota, with samples from animals from within the same cage showing high community structure concordance, but large differences seen between cages. Importantly, the genetically induced obese phenotype was not found to impact the faecal bacterial profiles. These findings demonstrate that the age and local environmental cage variables were driving the composition of the faecal bacteria and were more deterministically important than the host genotype. These findings have major implications for understanding the significance of functional metagenomic data in experimental studies and beg the question; what is being measured in animal experiments in which different strains are housed separately, nature or nurture?

Interpreters’ perception of linguistic and non linguistic factors affecting quality: a survey through the World Wide Web

This paper will present and discuss the results of an empirical study on perception of quality in interpretation carried out on a sample of 286 interpreters across five continents. Since the 1980’s the field of Interpreting Studies has been witnessing an ever growing interest in the issue of quality in interpretation both in academia and in professional circles, but research undertaken so far is surprisingly lacking in methodological rigour. This survey is an attempt to revise previous studies on interpreters’ perception of quality through the implementation of new Information Technology which allowed us to administer a traditional research tool such as a questionnaire, in a highly innovative way; i.e., through the World Wide Web. Using multidimensional scaling, a perceptual map based upon the results of the manner in which interpreters ranked a list of linguistic and nonlinguistic criteria according to their perception of importance in the interpretative process,was devised.

Evaluating perceptual separation in a pilot system for affective composition

Research evaluating perceptual responses to music has identified many structural features as correlates that might be incorporated in computer music systems for affectively charged algorithmic composition and/or expressive music performance. In order to investigate the possible integration of isolated musical features to such a system, a discrete feature known to correlate some with emotional responses – rhythmic density – was selected from a literature review and incorporated into a prototype system. This system produces variation in rhythm density via a transformative process. A stimulus set created using this system was then subjected to a perceptual evaluation. Pairwise comparisons were used to scale differences between 48 stimuli. Listener responses were analysed with Multidimensional scaling (MDS). The 2-Dimensional solution was then rotated to place the stimuli with the largest range of variation across the horizontal plane. Stimuli with variation in rhythmic density were placed further from the source material than stimuli that were generated by random permutation. This, combined with the striking similarity between the MDS scaling and that of the 2-dimensional emotional model used by some affective algorithmic composition systems, suggests that isolated musical feature manipulation can now be used to parametrically control affectively charged automated composition in a larger system.

An incremental space to visualize dynamic data sets

In Information Visualization, adding and removing data elements can strongly impact the underlying visual space. We have developed an inherently incremental technique (incBoard) that maintains a coherent disposition of elements from a dynamic multidimensional data set on a 2D grid as the set changes. Here, we introduce a novel layout that uses pairwise similarity from grid neighbors, as defined in incBoard, to reposition elements on the visual space, free from constraints imposed by the grid. The board continues to be updated and can be displayed alongside the new space. As similar items are placed together, while dissimilar neighbors are moved apart, it supports users in the identification of clusters and subsets of related elements. Densely populated areas identified in the incSpace can be efficiently explored with the corresponding incBoard visualization, which is not susceptible to occlusion. The solution remains inherently incremental and maintains a coherent disposition of elements, even for fully renewed sets. The algorithm considers relative positions for the initial placement of elements, and raw dissimilarity to fine tune the visualization. It has low computational cost, with complexity depending only on the size of the currently viewed subset, V. Thus, a data set of size N can be sequentially displayed in O(N) time, reaching O(N (2)) only if the complete set is simultaneously displayed.

Fast long-range connections in transportation networks

Multidimensional scaling is applied in order to visualize an analogue of the small-world effect implied by edges having different displacement velocities in transportation networks. Our findings are illustrated for two real-world systems, namely the London urban network (streets and underground) and the US highway network enhanced by some of the main US airlines routes. We also show that the travel time in these two networks is drastically changed by attacks targeting the edges with large displacement velocities. (C) 2011 Elsevier By. All rights reserved.

Data mining por meio de análise de redes, no contexto de filtro colaborativo

Tendo como motivação o desenvolvimento de uma representação gráfica de redes com grande número de vértices, útil para aplicações de filtro colaborativo, este trabalho propõe a utilização de superfícies de coesão sobre uma base temática multidimensionalmente escalonada. Para isso, utiliza uma combinação de escalonamento multidimensional clássico e análise de procrustes, em algoritmo iterativo que encaminha soluções parciais, depois combinadas numa solução global. Aplicado a um exemplo de transações de empréstimo de livros pela Biblioteca Karl A. Boedecker, o algoritmo proposto produz saídas interpretáveis e coerentes tematicamente, e apresenta um stress menor que a solução por escalonamento clássico.