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The study is concerned with a granular data description in which we propose a characterization of numeric data by a collection of information granules so that the key structure of the data, their topology and essential relationships are described in the form of a family of fuzzy sets – information granules. A comprehensive design process is introduced in which we show a two-phase development strategy: first, numeric prototypes are built with the use of Fuzzy C-Means (FCM) that is followed by their augmentation resulting in a collection of information granules. In the design of information granules we engage the fundamental ideas of Granular Computing, especially the principle of justifiable granularity. A series of experiments is presented to visualize the key steps of the construction of information granules. [ABSTRACT FROM AUTHOR]

Granular Computing (GrC) is a human-centric way to discover the fundamental structure of data sets. The resulting information granules can be efficiently exploited to organize knowledge and reveal data descriptions, which can play a pivotal role in the classification problems. Furthermore, information granules are abstract collections of data entities and exhibit flexibility and tolerance when it comes to the representation of incomplete data. However, most of the existing methods focused on the data imputation and classification separately. They also require better interpretability. The crux of this study is to develop a novel information granule-based classification method for incomplete data and a way of representing missing entities and regarding them as information granules in a unified framework. The first aspect focuses on revealing the structural backbone of multiple labeled subspaces of data by fuzzy clustering of missing values. It emerges a classifier with interpretable "IF-THEN" rules by the refinement of fuzzy prototypes in a supervised mode to capture the critical relationship of the multi-class incomplete data. The second aspect concerns the construction of some information granules to impute and represent missing values according to the refined prototypes and classification findings. The experimental studies involved synthetic and publicly available datasets in quantifying the advantages of the classification and representation abilities of the proposed methods on incomplete data. • We proposed a novel information granule-based classifier to reveal the structural of the subspaces of data, which is easier to be interpreted. • We considered incomplete data among classification modeling, so that this classifier can deal with the incomplete data straightforwardly. • We present a refinement mechanism for the information granule-based classifier to optimize the prototypes of the classification rules. • As a byproduct of the classification, the imputed information granules are distinguished from present data and have more tolerance to the imputation error. [ABSTRACT FROM AUTHOR]

Abstract Rule-based modeling has been one of the key directions in fuzzy modeling since its inception. Nowadays it exhibits a number of conceptual development and algorithmic pursuits. Fuzzy clustering, especially Fuzzy C-Means (FCM), is a commonly used algorithmic tool to construct rules, in particular building fuzzy sets forming conditions of the rules. While being efficient with this regard and transforming data into a collection of fuzzy sets, one should note that the agenda of fuzzy clustering (and clustering, in general) does not fully align with the agenda of system modeling and because of this, it requires some attention and calls for further refinements. Clustering is a direction-free (relational) process and developed constructs (clusters) are optimized in light of the direction-free criterion (say, a commonly used objective function). In contrast, in fuzzy models the rules are direction-sensitive artifacts, which implies that the clusters themselves need to be reflective of this directionality requirement. This paper contributes to this direction of studies by bringing a collection of augmentations of the generic FCM algorithm along this line. There are three original enhancements considered in the study: (i) an accommodation of extreme (minimal and maximal) values encountered in the output variable, (ii) a reduction of spurious impact of rules being the result of variable overlap existing among fuzzy sets forming the condition parts of the rules, and (iii) a development of the core (granular) structure of rules and analysis of their features. The motivation behind these augmentations is presented followed by the detailed algorithms along with a series of illustrative examples. In the sequel, a number of numeric studies are conducted demonstrating in a quantitative manner the contributions delivered by the refinements. [ABSTRACT FROM AUTHOR]

Deoxyribonucleic acid (DNA) microarray is an important technology, which supports a simultaneous measurement of thousands of genes for biological analysis. With the rapid development of the gene expression data characterized by uncertainty and being of high dimensionality, there is a genuine need for advanced processing techniques. With this regard, Fuzzy Possibilistic C-Means Clustering (FPCM) and Granular Computing (GrC) are introduced with the aim to solve problems of feature selection and outlier detection. In this study, by taking advantage of the FPCM and GrC, an Advanced Fuzzy Possibilistic C-Means Clustering based on Granular Computing (GrFPCM) is proposed to select features as a preprocessing phase for clustering problems while the developed granular space is used to cope with uncertainty. Experiments were completed for various gene expression datasets and a comparative analysis is reported. [ABSTRACT FROM AUTHOR]

Data clustering is aimed at discovering a structure in data. The revealed structure is usually represented in terms of prototypes and partition matrices. In some cases, the prototypes are simultaneously formed using data and features by running a co-clustering (bi-clustering) algorithm. Interval valued fuzzy clustering exhibits advantages when handling uncertainty. This study introduces a novel clustering technique by combining fuzzy co-clustering approach and interval-valued fuzzy sets in which two values of the fuzzifier of the fuzzy clustering algorithm are used to form the footprint of uncertainty (FOU). The study demonstrates the performance of the proposed method through a series of experiments completed for various datasets (including color segmentation, multi-spectral image classification, and document categorization). The experiments quantify the quality of results with the aid of validity indices and visual inspection. Some comparative analysis is also covered. [ABSTRACT FROM AUTHOR]

Missing values are a common phenomenon when dealing with real-world data sets. Analysis of incomplete data sets has become an active area of research. In this paper, we focus on the problem of clustering incomplete data, which is intended to introduce some prior distribution information of the missing values into the algorithm of fuzzy clustering. First, non-parametric hypothesis testing is employed to describe the missing values adhering to a certain Gaussian distribution as probabilistic information granules based on the nearest neighbors of incomplete data. Second, we propose a novel clustering model, in which probabilistic information granules of missing values are incorporated into the Fuzzy C-Means clustering of incomplete data by involving the maximum likelihood criterion. Third, the clustering model is optimized by using a tri-level alternating optimization utilizing the method of Lagrange multipliers. The convergence and the time complexity of the clustering algorithm are also discussed. The experiments reported both on synthetic and real-world data sets demonstrate that the proposed approach can effectively realize clustering of incomplete data. [ABSTRACT FROM AUTHOR]