Jacek M. Leski

Towards a robust fuzzy clustering

Fuzzy clustering helps to find natural vague boundaries in data. The Fuzzy C-Means method (FCM) is one of the most popular clustering methods based on minimization of a criterion function. However, one of the greatest disadvantages of this method is its sensitivity to presence of noise and outliers in data. This paper introduces a new e-insensitive Fuzzy C-Means (eFCM) clustering algorithm. As a special case, this algorithm includes the well-known Fuzzy C-Medians method (FCMED). Also, methods with insensitivity control named αFCM and βFCM are introduced. Performance of the new clustering algorithm is experimentally compared with the FCM method using synthetic data with outliers and heavy-tailed and overlapped groups of data in background noise.

Robust weighted averaging [of biomedical signals]

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 /spl epsi/-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.

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 /spl epsiv/-insensitive fuzzy c-regression models (/spl epsiv/FCRM), that can be used in fuzzy modeling. To fit these regression models to real data, a weighted /spl epsiv/-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 /spl epsiv/-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.

Some Practical Remarks on Neural Networks Approach to Fetal Cardiotocograms Classification

Cardiotocographic monitoring is a primary biophysical method for assessment of a fetal state based on quantitative analysis of the biophysical signals. Although the computerized fetal monitoring systems have become a standard in clinical centres, the effective methods, which could enable conclusion generation, are still being searched. In the proposed work the attempts have been made to answer some important questions, which occurred during application of neural network for classification of the fetal state as being normal or abnormal. These questions are particularly important for medical applications and concern the influence of data set organization, inputs representation and the networks architecture. The networks of MLP and RBF types were developed and tested using 50 trials, with randomly mixed data contents in learning, validating and testing subsets. Additionally, the influence of numerical and categorical representation of the input quantitative parameters describing fetal cardiotocograms on the efficiency of the learning process was tested.

Fuzzy c-ordered-means 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. However, one of the greatest disadvantages of this method is its sensitivity to the presence of noise and outliers in data. This paper introduces a new robust fuzzy clustering method named Fuzzy C-Ordered-Means (FCOM) clustering. This method uses both the Hubers M-estimators and the Yagers OWA operators to obtain its robustness. The proposed method is compared to many other ones, e.g.: the Fuzzy C-Means (FCM), the Possibilistic Clustering (PC), the fuzzy Noise Clustering Method (NCM), the L p norm clustering ( L p FCM) ( 0 < p < 1 ), the L 1 norm clustering ( L 1 FCM), the Fuzzy Clustering with Polynomial Fuzzifier (PFCM) and the e-insensitive Fuzzy C-Means (βFCM). To this end experiments on synthetic data with outliers have been performed as well as on data with heavy-tailed and overlapping groups of points in background noise.

The Prediction of Fetal Outcome by Applying Neural Network for Evaluation of CTG Records

Cardiotocography (CTG) as a simultaneous recording of fetal heart rate, uterine contractions and fetal movement activity is a primary method for the assessment of fetal condition. At present, computerized fetal monitoring systems for on-line automated signal analysis are widely used. But effective techniques enabling conclusion generation are still being searched, and neural networks (NN) seem to be particularly attractive. In the presented work a number of investigations were carried out concerning application of NN when quantitative parameters describing fetal CTG signal — input variables - were used for prediction of fetal outcome (normal or abnormal). We tested how the efficiency of NN classification could be influenced by different modification of inputs, by interpretation of fetal outcome definition (output) as well as by various modifications of learning data sets. The obtained results gave a good background for application of the proposed classification tool within computer-aided fetal surveillance systems.

Fuzzy

This paper introduces a new classifier design method based on a modification of the classical fuzzy c-means clustering. First, a new fuzzy c-means clustering with p constant prototypes is proposed. This method can be considered a generalization of the concept of the conditional fuzzy clustering with some prototypes a priori known. A special initialization of the prototypes is introduced. Next, the proposed clustering method is used to construct the premises of an IF-THEN rule-based classifier. The conclusions of these rules are obtained by minimization of a criterion function with various approximations of a misclassification error (e.g., based on the quadratic, the linear, the sigmoidal or the Hubers loss function). The conjugate gradient algorithm is used to minimize the proposed criterion function. Each IF-THEN rule is represented in the Mamdani-Assilan form, which has good interpretability. Finally, an extensive experimental analysis on 14 benchmark datasets is performed to demonstrate the validity of the classifier introduced. Its competitiveness to the state-of-the-art classifiers, with respect to both performance and interpretability, is also shown.

(c+p)

Abstract Averaging of nonlinearly aligned (time-warped) signal cycles is an important method for suppressing noise of quasi-periodical or event related signals. However, in the paper we show that the operation of time warping introduces unfavorable violation of the requirements that should be satisfied for effective averaging and, as a result, it causes poor suppression of noise. To limit these effects, we redefine the matrix of the alignment costs. To improve results of averaging in cases of variable energy noise, we apply weighting of the summed signal samples. The derived formula gives smaller weights for more noisy signal cycles and this way limits their influence on the constructed template. The proposed modifications caused a significant increase of the Noise Reduction Factor (NRF) in the experiments on the simulated evoked potentials. Whereas the greatest NRF obtained by the reference methods in nonstationary white noise environment was equal to 1.55, for the new method proposed we achieved a value of 4.44. For non-stationary colored noise, the corresponding values were 1.44 and 2.99. Moreover, application of the developed method to ECG signal processing, prior to the measurements of the QT interval, significantly improved the measurements immunity to noise.