Orderings of fuzzy sets based on fuzzy orderings. Part II: generalizations

In Part I of this series of papers, a general approach for ordering fuzzy sets with respect to fuzzy orderings was presented. Part I also highlighted three limitations of this approach. The present paper addresses these lim- itations and proposes solutions for overcoming them. We rst consider a fuzzi cation of the ordering relation, then ways to compare fuzzy sets with di erent heights, and nally we introduce how to re ne the ordering relation by lexicographic hybridization with a di erent ordering methodPeer Reviewe

Orderings of fuzzy sets based on fuzzy orderings. Part I: the basic approach

The aim of this paper is to present a general framework for comparing fuzzy sets with respect to a general class of fuzzy orderings. This approach includes known techniques based on generalizing the crisp linear ordering of real numbers by means of the extension principle, however, in its general form, it is applicable to any fuzzy subsets of any kind of universe for which a fuzzy ordering is known|no matter whether linear or partialPeer Reviewe

On the Preservation of Monotonicity by Extended Mappings

Abstract Images of fuzzy relations provide powerful access to fuzzifications of properties of and/or relationships between fuzzy sets. As an important example, images of fuzzy orderings canonically lead to a concept of ordering of fuzzy sets. This contribution studies in which way the partial (i.e. componentwise) monotonicity of an n-ary mapping transfers to its extension to fuzzy sets

Decoding Sequence Classification Models for Acquiring New Biological Insights

Classifying biological sequences is one of the most important tasks in computational biology. In the last decade, support vector machines (SVMs) in combination with sequence kernels have emerged as a de-facto standard. These methods are theoretically well-founded, reliable, and provide high-accuracy solutions at low computational cost. However, obtaining a highly accurate classifier is rarely the end of the story in many practical situations. Instead, one often aims to acquire biological knowledge about the principles underlying a given classification task. SVMs with traditional sequence kernels do not offer a straightforward way of accessing this knowledge.

In this contribution, we propose a new approach to analyzing biological sequences on the basis of support vector machines with sequence kernels. We first extract explicit pattern weights from a given SVM. When classifying a sequence, we then compute a prediction profile by distributing the weight of each pattern to the sequence positions that match the pattern. The final profile not only allows assessing the importance of a position, but also determining for which class it is indicative. Since it is unfeasible to analyze profiles of all sequences in a given data set, we advocate using affinity propagation (AP) clustering to narrow down the analysis to a small set of typical sequences.

The proposed approach is applicable to a wide range of biological sequences and a wide selection of sequence kernels. To illustrate our framework, we present the prediction of oligomerization tendencies of coiled coil proteins as a case study.
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Approximation of Belief Functions by Minimizing Euclidean Distance

Abstract. This paper addresses the approximation of belief functions by minimizing the Euclidean distance to a given belief function in the set of probability functions. The special case of Dempster-Shafer belief functions is considered in particular detail. It turns out that, in this case, an explicit solution by means of a projective transformation can be given. Furthermore, we also consider more general concepts of belief. We state that the approximation by means of minimizing the Euclidean distance, unlike other methods that are restricted to Dempster-Shafer belief, works as well. However, the projective transformation formula cannot necessarily be applied in these more general settings

Hsa-miR-375 is a predictor of local control in early stage breast cancer

Background: A long-term analysis by the Early Breast Cancer Trialist Group (EBCTG) revealed a strong correlation between local control and cancer-specific mortality. MicroRNAs (miRs), short (20-25 nucleotides) non-coding RNAs, have been described as prognosticators and predictors for breast cancer in recent years. The aim of the current study was to identify miRs that can predict local control after breast conserving therapy (BCT) in early stage breast cancer. Results: Clinical data of 46 early stage breast cancer patients with local relapse after BCT were selected from the institutional database. These patients were matched to 101 control patients showing identical clinical features but without local relapse. The study was conducted in two steps. (1) In the pilot study, 32 patients (16 relapses versus 16 controls) were screened for the most de-regulated microRNAs (= candidate microRNAs) in a panel of 1250 miRs by microarray technology. Eight miRs were found to be significantly de-regulated. (2) In the validation study, the candidate microRNAs were analyzed in an independent cohort of 115 patients (30 relapses versus 85 controls) with reverse transcription quantitative polymerase chain reaction (RT-qPCR). From these eight candidates, hsa-miR-375 could be validated. Its median fold change was 2.28 (Mann-Whitney U test, corrected p value = 0.008). In the log-rank analysis, high expression levels of hsa-miR-375 correlated with a significantly higher risk of local relapse (p = 0.003). In a multivariate analysis (forward stepwise regression) including established predictors and prognosticators, hsa-miR-375 was the only variable that was able to distinguish the statistical significance between relapse and control groups (raw p value = 0.000195 HR = 0.76, 95 % CI 0.66-0.88;corrected p value = 0.005). Conclusions: Hsa-miR-375 predicts local control in patient with early stage breast cancer, especially in estrogen receptor alpha (ER-alpha)-positive patients. It can therefore serve as an additional molecular marker for treatment choice independently from known predictors and prognosticators. Validation in larger prospective studies is warranted

cn.MOPS: mixture of Poissons for discovering copy number variations in next-generation sequencing data with a low false discovery rate

Quantitative analyses of next-generation sequencing (NGS) data, such as the detection of copy number variations (CNVs), remain challenging. Current methods detect CNVs as changes in the depth of coverage along chromosomes. Technological or genomic variations in the depth of coverage thus lead to a high false discovery rate (FDR), even upon correction for GC content. In the context of association studies between CNVs and disease, a high FDR means many false CNVs, thereby decreasing the discovery power of the study after correction for multiple testing. We propose ‘Copy Number estimation by a Mixture Of PoissonS’ (cn.MOPS), a data processing pipeline for CNV detection in NGS data. In contrast to previous approaches, cn.MOPS incorporates modeling of depths of coverage across samples at each genomic position. Therefore, cn.MOPS is not affected by read count variations along chromosomes. Using a Bayesian approach, cn.MOPS decomposes variations in the depth of coverage across samples into integer copy numbers and noise by means of its mixture components and Poisson distributions, respectively. The noise estimate allows for reducing the FDR by filtering out detections having high noise that are likely to be false detections. We compared cn.MOPS with the five most popular methods for CNV detection in NGS data using four benchmark datasets: (i) simulated data, (ii) NGS data from a male HapMap individual with implanted CNVs from the X chromosome, (iii) data from HapMap individuals with known CNVs, (iv) high coverage data from the 1000 Genomes Project. cn.MOPS outperformed its five competitors in terms of precision (1–FDR) and recall for both gains and losses in all benchmark data sets. The software cn.MOPS is publicly available as an R package at http://www.bioinf.jku.at/software/cnmops/ and at Bioconductor

FABIA: factor analysis for bicluster acquisition

Motivation: Biclustering of transcriptomic data groups genes and samples simultaneously. It is emerging as a standard tool for extracting knowledge from gene expression measurements. We propose a novel generative approach for biclustering called ‘FABIA: Factor Analysis for Bicluster Acquisition’. FABIA is based on a multiplicative model, which accounts for linear dependencies between gene expression and conditions, and also captures heavy-tailed distributions as observed in real-world transcriptomic data. The generative framework allows to utilize well-founded model selection methods and to apply Bayesian techniques

Orderings of fuzzy sets based on fuzzy orderings. part I: the basic approach.

Abstract In Part I of this series of papers, a general approach for ordering fuzzy sets with respect to fuzzy orderings was presented. Part I also highlighted three limitations of this approach. The present paper addresses these limitations and proposes solutions for overcoming them. We first consider a fuzzification of the ordering relation, then ways to compare fuzzy sets with different heights, and finally we introduce how to refine the ordering relation by lexicographic hybridization with a different ordering method. II.1 Introduction In the first part of this series of paper