Fuzzy Modeling for Uncertain Nonlinear Systems Using Fuzzy Equations and Z-Numbers

In this paper, the uncertainty property is represented by Z-number as the coefficients and variables of the fuzzy equation. This modification for the fuzzy equation is suitable for nonlinear system modeling with uncertain parameters. Here, we use fuzzy equations as the models for the uncertain nonlinear systems. The modeling of the uncertain nonlinear systems is to find the coefficients of the fuzzy equation. However, it is very difficult to obtain Z-number coefficients of the fuzzy equations. Taking into consideration the modeling case at par with uncertain nonlinear systems, the implementation of neural network technique is contributed in the complex way of dealing the appropriate coefficients of the fuzzy equations. We use the neural network method to approximate Z-number coefficients of the fuzzy equations

Explaining Support Vector Machines: A Color Based Nomogram.

PROBLEM SETTING: Support vector machines (SVMs) are very popular tools for classification, regression and other problems. Due to the large choice of kernels they can be applied with, a large variety of data can be analysed using these tools. Machine learning thanks its popularity to the good performance of the resulting models. However, interpreting the models is far from obvious, especially when non-linear kernels are used. Hence, the methods are used as black boxes. As a consequence, the use of SVMs is less supported in areas where interpretability is important and where people are held responsible for the decisions made by models. OBJECTIVE: In this work, we investigate whether SVMs using linear, polynomial and RBF kernels can be explained such that interpretations for model-based decisions can be provided. We further indicate when SVMs can be explained and in which situations interpretation of SVMs is (hitherto) not possible. Here, explainability is defined as the ability to produce the final decision based on a sum of contributions which depend on one single or at most two input variables. RESULTS: Our experiments on simulated and real-life data show that explainability of an SVM depends on the chosen parameter values (degree of polynomial kernel, width of RBF kernel and regularization constant). When several combinations of parameter values yield the same cross-validation performance, combinations with a lower polynomial degree or a larger kernel width have a higher chance of being explainable. CONCLUSIONS: This work summarizes SVM classifiers obtained with linear, polynomial and RBF kernels in a single plot. Linear and polynomial kernels up to the second degree are represented exactly. For other kernels an indication of the reliability of the approximation is presented. The complete methodology is available as an R package and two apps and a movie are provided to illustrate the possibilities offered by the method

Effect of Biodiversity Changes in Disease Risk: Exploring Disease Emergence in a Plant-Virus System

The effect of biodiversity on the ability of parasites to infect their host and cause disease (i.e. disease risk) is a major question in pathology, which is central to understand the emergence of infectious diseases, and to develop strategies for their management. Two hypotheses, which can be considered as extremes of a continuum, relate biodiversity to disease risk: One states that biodiversity is positively correlated with disease risk (Amplification Effect), and the second predicts a negative correlation between biodiversity and disease risk (Dilution Effect). Which of them applies better to different host-parasite systems is still a source of debate, due to limited experimental or empirical data. This is especially the case for viral diseases of plants. To address this subject, we have monitored for three years the prevalence of several viruses, and virus-associated symptoms, in populations of wild pepper (chiltepin) under different levels of human management. For each population, we also measured the habitat species diversity, host plant genetic diversity and host plant density. Results indicate that disease and infection risk increased with the level of human management, which was associated with decreased species diversity and host genetic diversity, and with increased host plant density. Importantly, species diversity of the habitat was the primary predictor of disease risk for wild chiltepin populations. This changed in managed populations where host genetic diversity was the primary predictor. Host density was generally a poorer predictor of disease and infection risk. These results support the dilution effect hypothesis, and underline the relevance of different ecological factors in determining disease/infection risk in host plant populations under different levels of anthropic influence. These results are relevant for managing plant diseases and for establishing conservation policies for endangered plant species

It’s not the size, it’s the relationship: from ‘small states’ to asymmetry

Debate about the definition of “small state” has produced more fragmentation than consensus, even as the literature has demonstrated its subjects’ roles in joining international organizations propagating norms, executing creative diplomacy, influencing allies, avoiding and joining conflicts, and building peace. However, work on small states has struggled to identify commonalities in these states’ international relations, to cumulate knowledge, or to impact broader IR theory. This paper advocates a changed conceptual and definitional framework. Analysis of “small states” should pivot to examine the dynamics of the asymmetrical relationships in which these states are engaged. Instead of seeking an overall metric for size as the relevant variable—falling victim in a different way Dahl’s “lump-of-power fallacy,” we can recognize the multifaceted, variegated nature of power, whether in war or peacetime

L2-norm multiple kernel learning and its application to biomedical data fusion

<p>Abstract</p> <p>Background</p> <p>This paper introduces the notion of optimizing different norms in the dual problem of support vector machines with multiple kernels. The selection of norms yields different extensions of multiple kernel learning (MKL) such as <it>L</it>_∞, <it>L</it>₁, and <it>L</it>₂MKL. In particular, <it>L</it>₂MKL is a novel method that leads to non-sparse optimal kernel coefficients, which is different from the sparse kernel coefficients optimized by the existing <it>L</it>_∞MKL method. In real biomedical applications, <it>L</it>₂MKL may have more advantages over sparse integration method for thoroughly combining complementary information in heterogeneous data sources.</p> <p>Results</p> <p>We provide a theoretical analysis of the relationship between the <it>L</it>₂optimization of kernels in the dual problem with the <it>L</it>₂coefficient regularization in the primal problem. Understanding the dual <it>L</it>₂problem grants a unified view on MKL and enables us to extend the <it>L</it>₂method to a wide range of machine learning problems. We implement <it>L</it>₂MKL for ranking and classification problems and compare its performance with the sparse <it>L</it>_∞and the averaging <it>L</it>₁MKL methods. The experiments are carried out on six real biomedical data sets and two large scale UCI data sets. <it>L</it>₂MKL yields better performance on most of the benchmark data sets. In particular, we propose a novel <it>L</it>₂MKL least squares support vector machine (LSSVM) algorithm, which is shown to be an efficient and promising classifier for large scale data sets processing.</p> <p>Conclusions</p> <p>This paper extends the statistical framework of genomic data fusion based on MKL. Allowing non-sparse weights on the data sources is an attractive option in settings where we believe most data sources to be relevant to the problem at hand and want to avoid a "winner-takes-all" effect seen in <it>L</it>_∞MKL, which can be detrimental to the performance in prospective studies. The notion of optimizing <it>L</it>₂kernels can be straightforwardly extended to ranking, classification, regression, and clustering algorithms. To tackle the computational burden of MKL, this paper proposes several novel LSSVM based MKL algorithms. Systematic comparison on real data sets shows that LSSVM MKL has comparable performance as the conventional SVM MKL algorithms. Moreover, large scale numerical experiments indicate that when cast as semi-infinite programming, LSSVM MKL can be solved more efficiently than SVM MKL.</p> <p>Availability</p> <p>The MATLAB code of algorithms implemented in this paper is downloadable from <url>http://homes.esat.kuleuven.be/~sistawww/bioi/syu/l2lssvm.html</url>.</p

Multiproject–multicenter evaluation of automatic brain tumor classification by magnetic resonance spectroscopy

Contains fulltext : 75361.pdf (publisher's version ) (Open Access)14 p

Clinimetric evaluation of active range of motion measures in patients with non-specific neck pain: a systematic review

The study is to provide a critical analysis of the research literature on clinimetric properties of instruments that can be used in daily practice to measure active cervical range of motion (ACROM) in patients with non-specific neck pain. A computerized literature search was performed in Medline, Cinahl and Embase from 1982 to January 2007. Two reviewers independently assessed the clinimetric properties of identified instruments using a criteria list. The search identified a total of 33 studies, investigating three different types of measurement instruments to determine ACROM. These instruments were: (1) different types of goniometers/inclinometers, (2) visual estimation, and (3) tape measurements. Intra- and inter-observer reliability was demonstrated for the cervical range of motion instrument (CROM), Cybex electronic digital instrument (EDI-320) and a single inclinometer. The presence of agreement was assessed for the EDI-320 and a single inclinometer. The CROM received a positive rating for construct validity. When clinical acceptability is taken into account both the CROM and the single inclinometer can be considered appropriate instruments for measuring the active range of motion in patients with non-specific neck pain in daily practice. Reliability is the aspect most frequently evaluated. Agreement, validity and responsiveness are documented less frequently