Publications

Revealing a structure in data is of paramount importance in a broad range of problems of information processing. In spite of the specificity of the problem in which such analysis is realized, there is an evident commonality of all these pursuits worth emphasizing. One can distinguish between a core and a residual of the data structure. In this study, we propose a formal environment supporting these concepts and develop its algorithmic fabric. The algorithms leading to the development of information granules lend themselves to the Fuzzy C-Means (FCM) equipped with the Tchebyschev (1<sub>∞</sub>) metric. The paper offers a novel contribution of a gradient-based learning of the prototypes developed in this form of clustering. The 1<sub>∞</sub> metric promotes a design of easily interpretable hyperboxes. In this setting, we quantify the notion of the core and residual part of the data. An interaction between information granules is discussed as well

The conventional fuzzy C-means (FCM) algorithm is not robust to noise and its rate of convergence is generally impacted by data distribution. Consequently, it is challenging to develop FCM-related algorithms that have good performance and require less computing time. In this article, we elaborate on a comprehensive FCM-related algorithm for image segmentation. To make FCM robust, we first utilize a morphological grayscale reconstruction (MGR) operation to filter observed images before clustering, which guarantees noise-immunity and image detail-preservation. Since real images can generally be approximated by sparse coefficients in a tight wavelet frame system, feature spaces of observed and filtered images can be obtained. Taking such features to be clustered, we investigate an improved FCM model in which a sparse regularization term is introduced into the objective function of FCM. We design a three-step iterative algorithm to solve the sparse regularization-based FCM model, which is constructed by the Lagrangian multiplier method, hard-threshold operator, and normalization operator, respectively. Such an algorithm can not only perform well for image segmentation, but also come with high computational efficiency. To further enhance the segmentation accuracy, we use MGR to filter the label set generated by clustering. Finally, a large number of supporting experiments and comparative studies with other FCM-related algorithms available in the literature are provided. The obtained results for synthetic, medical and color images indicate that the proposed algorithm has good ability for multiphase image segmentation, and performs better than other alternative FCM-related algorithms. Moreover, the proposed algorithm requires less time than most of the existing algorithms.

In this paper, the fundamental idea of Incremental Granular Models (IGM) introduced by Pedrycz and Kwak (2007) is followed and their comprehensive design framework is developed. In contrast to typical rule-based systems encountered in fuzzy modeling, the underlying principle of IGM is to consider a two-phase development. First, we build a Linear Regression (LR) model which could be treated as a global model. Next, all modeling errors are compensated by a collection of fuzzy rules that capture more localized nonlinearities of the system as a local model. Here we expand local granular models into Radial Basis Function Networks (RBFN) or Adaptive Neuro-Fuzzy Networks (ANFN) with the use of information granules through Context-based Fuzzy C-Means (CFCM) clustering in the design of incremental model. Numerical studies concern two datasets coming from the machine learning repository. The experimental results revealed that both Incremental RBFN (IRBFN) and Incremental ANFN (IANFN) showed good performance in comparison to the previous works.

In this paper we present a comparative analysis of the predictive power of two different sets of metrics for defect prediction. We choose one set of product related and one set of process related software metrics and use them for classifying Java files of the Eclipse project as defective respective defect-free. Classification models are built using three common machine learners: logistic regression, Naïve Bayes, and decision trees. To allow different costs for prediction errors we perform cost-sensitive classification, which proves to be very successful: >75% percentage of correctly classified files, a recall of >80%, and a false positive rate <30%. Results indicate that for the Eclipse data, process metrics are more efficient defect predictors than code metrics.

Aiming at the previously-proposed entropy-based differently implicational algorithm of fuzzy inference, this study analyzes its continuity.To begin with, for the FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) problems, the continuous as well as uniformly continuous properties of the entropy-based differently implicational algorithm are demonstrated for the Tchebyshev and Hamming metrics, in which the R-implications derived from left-continuous tnorms are employed.Furthermore, four numerical fuzzy inference examples are provided, and it is found that the entropy-based differently implicational algorithm can obtain more reasonable solution in contrast with the fuzzy entropy full implication algorithm.Finally, in the entropybased differently implicational algorithm, we point out that the first fuzzy implication reflects the effect of rule base, and that the second fuzzy implication embodies the inference mechanism.