Data granulation by the principles of uncertainty

Researches in granular modeling produced a variety of mathematical models, such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets, which are all suitable to characterize the so-called information granules. Modeling of the input data uncertainty is recognized as a crucial aspect in information granulation. Moreover, the uncertainty is a well-studied concept in many mathematical settings, such as those of probability theory, fuzzy set theory, and possibility theory. This fact suggests that an appropriate quantification of the uncertainty expressed by the information granule model could be used to define an invariant property, to be exploited in practical situations of information granulation. In this perspective, a procedure of information granulation is effective if the uncertainty conveyed by the synthesized information granule is in a monotonically increasing relation with the uncertainty of the input data. In this paper, we present a data granulation framework that elaborates over the principles of uncertainty introduced by Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is possible to apply such principles regardless of the input data type and the specific mathematical setting adopted for the information granules. The proposed framework is conceived (i) to offer a guideline for the synthesis of information granules and (ii) to build a groundwork to compare and quantitatively judge over different data granulation procedures. To provide a suitable case study, we introduce a new data granulation technique based on the minimum sum of distances, which is designed to generate type-2 fuzzy sets. We analyze the procedure by performing different experiments on two distinct data types: feature vectors and labeled graphs. Results show that the uncertainty of the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference

Segmentation of articular cartilage and early osteoarthritis based on the fuzzy soft thresholding approach driven by modified evolutionary ABC optimization and local statistical aggregation

Articular cartilage assessment, with the aim of the cartilage loss identification, is a crucial task for the clinical practice of orthopedics. Conventional software (SW) instruments allow for just a visualization of the knee structure, without post processing, offering objective cartilage modeling. In this paper, we propose the multiregional segmentation method, having ambitions to bring a mathematical model reflecting the physiological cartilage morphological structure and spots, corresponding with the early cartilage loss, which is poorly recognizable by the naked eye from magnetic resonance imaging (MRI). The proposed segmentation model is composed from two pixel's classification parts. Firstly, the image histogram is decomposed by using a sequence of the triangular fuzzy membership functions, when their localization is driven by the modified artificial bee colony (ABC) optimization algorithm, utilizing a random sequence of considered solutions based on the real cartilage features. In the second part of the segmentation model, the original pixel's membership in a respective segmentation class may be modified by using the local statistical aggregation, taking into account the spatial relationships regarding adjacent pixels. By this way, the image noise and artefacts, which are commonly presented in the MR images, may be identified and eliminated. This fact makes the model robust and sensitive with regards to distorting signals. We analyzed the proposed model on the 2D spatial MR image records. We show different MR clinical cases for the articular cartilage segmentation, with identification of the cartilage loss. In the final part of the analysis, we compared our model performance against the selected conventional methods in application on the MR image records being corrupted by additive image noise.Web of Science117art. no. 86

Semi-supervised cross-entropy clustering with information bottleneck constraint

In this paper, we propose a semi-supervised clustering method, CEC-IB, that models data with a set of Gaussian distributions and that retrieves clusters based on a partial labeling provided by the user (partition-level side information). By combining the ideas from cross-entropy clustering (CEC) with those from the information bottleneck method (IB), our method trades between three conflicting goals: the accuracy with which the data set is modeled, the simplicity of the model, and the consistency of the clustering with side information. Experiments demonstrate that CEC-IB has a performance comparable to Gaussian mixture models (GMM) in a classical semi-supervised scenario, but is faster, more robust to noisy labels, automatically determines the optimal number of clusters, and performs well when not all classes are present in the side information. Moreover, in contrast to other semi-supervised models, it can be successfully applied in discovering natural subgroups if the partition-level side information is derived from the top levels of a hierarchical clustering

Modeling and Recognition of Smart Grid Faults by a Combined Approach of Dissimilarity Learning and One-Class Classification

Detecting faults in electrical power grids is of paramount importance, either from the electricity operator and consumer viewpoints. Modern electric power grids (smart grids) are equipped with smart sensors that allow to gather real-time information regarding the physical status of all the component elements belonging to the whole infrastructure (e.g., cables and related insulation, transformers, breakers and so on). In real-world smart grid systems, usually, additional information that are related to the operational status of the grid itself are collected such as meteorological information. Designing a suitable recognition (discrimination) model of faults in a real-world smart grid system is hence a challenging task. This follows from the heterogeneity of the information that actually determine a typical fault condition. The second point is that, for synthesizing a recognition model, in practice only the conditions of observed faults are usually meaningful. Therefore, a suitable recognition model should be synthesized by making use of the observed fault conditions only. In this paper, we deal with the problem of modeling and recognizing faults in a real-world smart grid system, which supplies the entire city of Rome, Italy. Recognition of faults is addressed by following a combined approach of multiple dissimilarity measures customization and one-class classification techniques. We provide here an in-depth study related to the available data and to the models synthesized by the proposed one-class classifier. We offer also a comprehensive analysis of the fault recognition results by exploiting a fuzzy set based reliability decision rule

Graph ambiguity

In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved

Gray Image extraction using Fuzzy Logic

Fuzzy systems concern fundamental methodology to represent and process uncertainty and imprecision in the linguistic information. The fuzzy systems that use fuzzy rules to represent the domain knowledge of the problem are known as Fuzzy Rule Base Systems (FRBS). On the other hand image segmentation and subsequent extraction from a noise-affected background, with the help of various soft computing methods, are relatively new and quite popular due to various reasons. These methods include various Artificial Neural Network (ANN) models (primarily supervised in nature), Genetic Algorithm (GA) based techniques, intensity histogram based methods etc. providing an extraction solution working in unsupervised mode happens to be even more interesting problem. Literature suggests that effort in this respect appears to be quite rudimentary. In the present article, we propose a fuzzy rule guided novel technique that is functional devoid of any external intervention during execution. Experimental results suggest that this approach is an efficient one in comparison to different other techniques extensively addressed in literature. In order to justify the supremacy of performance of our proposed technique in respect of its competitors, we take recourse to effective metrics like Mean Squared Error (MSE), Mean Absolute Error (MAE), Peak Signal to Noise Ratio (PSNR).Comment: 8 pages, 5 figures, Fuzzy Rule Base, Image Extraction, Fuzzy Inference System (FIS), Membership Functions, Membership values,Image coding and Processing, Soft Computing, Computer Vision Accepted and published in IEEE. arXiv admin note: text overlap with arXiv:1206.363