TSK-fuzzy modeling based on /spl epsiv/-insensitive learning

In this paper, new learning methods tolerant to imprecision are introduced and applied to fuzzy modeling based on the Takagi-Sugeno-Kang fuzzy system. The fuzzy modeling has an intrinsic inconsistency. It may perform thinking tolerant to imprecision, but learning methods are zero-tolerant to imprecision. The proposed methods make it possible to exclude this intrinsic inconsistency of a fuzzy modeling, where zero-tolerance learning is used to obtain fuzzy model tolerant to imprecision. These new methods can be called /spl epsiv/-insensitive learning or /spl epsiv/ learning, where, in order to fit the fuzzy model to real data, the /spl epsiv/-insensitive loss function is used. This leads to a weighted or "fuzzified" version of Vapnik's support vector regression machine. This paper introduces two approaches to solving the /spl epsiv/-insensitive learning problem. The first approach leads to the quadratic programming problem with bound constraints and one linear equality constraint. The second approach leads to a problem of solving a system of linear inequalities. Two computationally efficient numerical methods for the /spl epsiv/-insensitive learning are proposed. The /spl epsiv/-insensitive learning leads to a model with the minimal Vapnik-Chervonenkis dimension, which results in an improved generalization ability of this model and its outliers robustness. Finally, numerical examples are given to demonstrate the validity of the introduced methods.     

Discovery of a significant optical chromatographic difference between spores of Bacillus anthracis and its close relative, Bacillus thuringiensis

A significant difference between two closely related Bacillus spores has been discovered using optical chromatography. This difference can be harnessed for the separation of microscopic particles using opposing laser and fluid flow forces. Particles of different size, composition, and shape experience different optical and fluid forces and come to rest at unique equilibrium positions where the two forces balance. Separations in excess of 600 mum have been observed between Bacillus anthracis Sterne strain and its genetic relative, Bacillus thuringiensis. These findings open new possibilities for detection and characterization of the biological warfare agent, B. anthracis, the causative agent of anthrax, the deadly mammalian disease. The large optical separation between these species is surprising given their close genetic relationship but may be explained by differences in their shape and exosporium morphology, which may result in differences in fluid drag force. The observation of large differences due to less common variables indicates the complex nature of the force balance in optical chromatography, which may in the future be used to separate and characterize microbiological samples. In general, the discovery of such large differences between such closely related biological species suggests new possibilities for the separation and characterization of microorganisms using the full range of emerging techniques that employ radiation pressure (optical filtering, laser tweezers, optical chromatography, etc.).     

Computationally effective algorithm for robust weighted averaging

One of the greatest disadvantages of the weighted signal averaging method is its sensitivity to the presence of noise and outliers in data and the need to estimate the noise variance in all signal cycles. The robust weighted averaging method based on the epsilon-insensitive loss function is free of these disadvantages, but has a very high computational burden and requires a choice of the insensitivity parameter epsilon. In this study, a new computationally effective algorithm for robust weighted averaging with automatic adjustment of the insensitivity parameter is introduced.     

Trace elements in fruiting bodies of ectomycorrhizal fungi growing in Scots pine (Pinus sylvestris L.) stands in Poland

The trace metal contents in fruiting bodies of ectomycorrhizal (ECM) fungi, symbiotic partners of Scots pine, were studied on three sites situated in west-central Poland. Elements were determined by atomic absorption spectrometry in 123 samples of 16 species. The study explored the differences in metal accumulation in relation to site, fungal species, age and part of the fruiting body and results were related to metal content in soil and plant material (roots and needles). Soil analysis revealed that results were obtained under environmental conditions not subject to strong anthropogenic pressure. Median metal concentrations did not differ disparately between sites, although the concentrations of each of the tested metals in the individual species varied to a large extent. Extremely high levels of Al with a large bioconcentration factor (BCF) were found in sporocarps of Thelephora terrestris. The spread between the highest and the lowest concentration (max/min) was very wide in Al, Cd and Pb and these elements may be considered to be absorbed preferentially by fruiting bodies of some species whereas Fe, Mn and Zn, with relatively low values of max/min, are normally absorbed by the majority of fungi. There was no clear relationship between caps and stipes in metal content. However, a tendency to higher metal concentration in the caps was observed. The metal content in young and older fruiting bodies of five different fungi was species dependent. In order to estimate the degree of accumulation of each element by plant and mushrooms, bioconcentration factors (BCFs) were calculated. In plant material (roots and needles), highest values of BCFs were noted for essential metals, like Zn and Mn. Lead showed a definite exclusion pattern (BCF below 1). In fruiting bodies of tested fungi, especially in Amanita muscaria, cadmium was the most intensively accumulated metal. Lead was excluded by plants but was accumulated or excluded by fungi depending on the species. The significance of mycological observation and quantification of the metal content in monitoring of the forest ecosystem is discussed.     

Generalized weighted conditional fuzzy clustering

Fuzzy clustering helps to find natural vague boundaries in data. The fuzzy c-means method is one of the most popular clustering methods based on minimization of a criterion function. Among many existing modifications of this method, conditional or context-dependent c-means is the most interesting one. In this method, data vectors are clustered under conditions based on linguistic terms represented by fuzzy sets. This paper introduces a family of generalized weighted conditional fuzzy c-means clustering algorithms. This family include both the well-known fuzzy c-means method and the conditional fuzzy c-means method. Performance of the new clustering algorithm is experimentally compared with fuzzy c-means using synthetic data with outliers and the Box-Jenkins database.     

/spl epsiv/-insensitive fuzzy c-regression models: introduction to /spl epsiv/-insensitive fuzzy modeling

This paper introduces a new epsilon-insensitive fuzzy c-regression models (epsilonFCRM), that can be used in fuzzy modeling. To fit these regression models to real data, a weighted epsilon-insensitive loss function is used. The proposed method make it possible to exclude an intrinsic inconsistency of fuzzy modeling, where crisp loss function (usually quadratic) is used to match real data and the fuzzy model. The epsilon-insensitive fuzzy modeling is based on human thinking and learning. This method allows easy control of generalization ability and outliers robustness. This approach leads to c simultaneous quadratic programming problems with bound constraints and one linear equality constraint. To solve this problem, computationally efficient numerical method, called incremental learning, is proposed. Finally, examples are given to demonstrate the validity of introduced approach to fuzzy modeling.     

An /spl epsiv/-margin nonlinear classifier based on fuzzy if-then rules

This paper introduces a new classifier design methods that are based on a modification of the classical Ho-Kashyap procedure. First, it proposes a method to design a linear classifier using the absolute loss rather than the squared loss that results in a better approximation of the misclassification error and robustness of outliers. Additionally, easy control of the generalization ability is obtained by minimization of the Vapnik-Chervonenkis dimension. Next, an extension to a nonlinear classifier by an ensemble averaging technique is presented. Each classifier is represented by a fuzzy if-then rule in the Takagi-Sugeno-Kang form. Two approaches to the estimation of parameters value are used: local, where each of the if-then rule parameters are determined independently and global where all rules are obtained simultaneously. Finally, examples are given to demonstrate the validity of the introduced methods.     

Robust weighted averaging

Signal averaging is often used to extract a useful signal embedded in noise. This method is especially useful for biomedical signals, where the spectra of the signal and noise significantly overlap. In this case, traditional filtering techniques introduce unacceptable signal distortion. In averaging methods, constancy of the noise power is usually assumed, but in reality noise features a variable power. In this case, it is more appropriate to use a weighted averaging. The main problem in this method is the estimation of the noise power in order to obtain the weight values. Additionally, biomedical signals often contain outliers. This requires robust averaging methods. This paper shows that signal averaging can be formulated as a problem of minimization of a criterion function. Based on this formulation new weighted averaging methods are introduced, including weighted averaging based on criterion function minimization (WACFM) and robust epsilon-insensitive WACFM. Performances of these new methods are experimentally compared with the traditional averaging and other weighted averaging methods using electrocardiographic signal with the muscle noise, impulsive noise, and time-misalignment of cycles. Finally, an application to the late potentials extraction is shown.