Construction Of Information Granules Research Articles

Multi-association evidential feature selection and its application to identifying schizophrenia

Granular Computing (GrC)-based feature selection can remove redundant features from a massive amount of data and improve the efficiency of information processing. However, the existing method of neighborhood-based information granule only considers the distance between samples, ignoring other significant relationships existing between them. To fill this gap, this paper proposes a novel feature selection approach based on two-step multi-association neighborhood evidence entropy. This approach is constructed in three phases. Firstly, adaptive k value corresponding to each sample in sparse representation method is determined. Sparse correlation and distance measure are fused to form a multi-association information granule. Then, the samples in the multi-association information granule are estimated and weak-related information is removed to constitute a two-step multi-association information granule. Secondly, sparse correlation information is processed using Dempster-Shafer evidence theory, and a new credibility-based function is developed. In addition, the credibility is used to construct a novel neighborhood evidence entropy, which can effectively reflect the uncertainty of data. Thirdly, the proposed neighborhood evidence entropy is applied to assess the importance of features. As a result, several vital features are selected. The experimental results on twelve datasets demonstrate that the effectiveness of the proposed method is superior to other algorithms in construction of information granules and classification accuracy, respectively. Finally, the proposed method is applied to the selection of brain regions in schizophrenia. It can effectively analyze the lesions of schizophrenia and improve the prediction of the disorder. The code is available at https://github.com/fxx-Aurora/TMAE-FS/tree/main.

Synergistic Mechanism of Designing Information Granules with the Use of the Principle of Justifiable Granularity

The construction of information granules is a significant and interesting topic of Granular Computing (GrC) in which information granules play a vital role in representing and describing data, and it has become one of the most effective frameworks for solving complex problems. In this study, we are interested in the collaborative impacts of several different characteristics on constructing information granules, and a novel synergistic mechanism of the principle of justifiable granularity is utilized in developing information granules. The synergistic mechanism is finalized with a two-phase process—to start with, the principle of justifiable granularity and Fuzzy C-Means Clustering method are combined to develop a collection of information granules. First, the available experimental data is transformed (normalized) into fuzzy sets following the standard Fuzzy C-Means Clustering method. Then, information granules are developed based on the elements located in different clusters with the use of the principle of justifiable granularity. In the sequel, the positions of information granules are updated by considering the collaborative impacts of the other information granules with the parameters of specifying the level of influence. Experimental studies are conducted to illustrate the nature and feasibility of the proposed framework based on the synthetic data as well as a series of publicly available datasets coming from KEEL machine learning repositories.

Development and evaluation of M + 1-way classification mechanism realized through identifying foreign patterns

In this study, we are concerned with a new design methodology of M + 1-way classification mechanism. The intent is to reduce the cost of error prediction caused by insufficient evidence. The study is motivated by the notion of three-way decisions, which has been successfully used in various application areas to build human-centric systems. In contrast to traditional multiple classifications, one additional class is added into the proposed architecture to represent the reject decision made on foreign patterns, which exhibit significant differences compared to the patterns used for constructing the classification models. A collection of information granules is constructed on the basis of available experimental evidence to form a compact and interpretable representation of the feature space occupied by the native patterns. The patterns located outside the regions occupied by these information granules are identified and filtered out prior to classification while only the native patterns are subject to classification. The proposed methodology leads to a human-centric and human-interactive construct in which the rejected patterns need further processing. Different distance functions are utilized in the construction of information granules. The performance of the proposed architecture is evaluated involving one synthetic dataset and a collection of publicly available datasets.

Construction and Evaluation of Information Granules: From the Perspective of Clustering

While granular computing has experienced rapid growth in the past decades and some milestones have been reached, a comprehensive study of the representation capabilities delivered by numeric prototypes and granular prototypes produced by different techniques still calls for comprehensive research and a comparative analysis. Well-constructed information granules are reflective of the nature of the numeric evidence and serve as backbones of granular classifiers and granular models. The objective of this study is to review a number of clustering paradigms aimed at the construction of information granules, discuss the development of granular prototypes, and conduct a comprehensive evaluation of quality of numeric prototypes and their corresponding augmentations coming in the form of granular prototypes. We have been witnessing many studies devoted to the construction of information granules, but a comparative analysis of the quality of information granules constructed on a basis of prototypes produced by different clustering algorithms is still lacking. In this regard, the review of the clustering algorithms supporting the formation of information granules and the comprehensive comparative study of their usefulness in classification and modeling tasks offered in this study make sense. This will promote the usage of information granules in various future works, especially classification problem and system modeling.

A Two-Stage Approach for Constructing Type-2 Information Granules.

In this article, we are concerned with the formation of type-2 information granules in a two-stage approach. We present a comprehensive algorithmic framework which gives rise to information granules of a higher type (type-2, to be specific) such that the key structure of the local granular data, their topologies, and their diversities become fully reflected and quantified. In contrast to traditional collaborative clustering where local structures (information granules) are obtained by running algorithms on the local datasets and communicating findings across sites, we propose a way of characterizing granular data (formed) by forming a suite of higher type information granules to reveal an overall structure of a collection of locally available datasets. Information granules built at the lower level on a basis of local sources of data are weighted by the number of data they represent while the information granules formed at the higher level of hierarchy are more abstract and general, thus facilitating a formation of a hierarchical description of data realized at different levels of detail. The construction of information granules is completed by resorting to fuzzy clustering algorithms (more specifically, the well-known Fuzzy C-Means). In the formation of information granules, we follow the fundamental principle of granular computing, viz., the principle of justifiable granularity. Experimental studies concerning selected publicly available machine-learning datasets are reported.

Design of Fuzzy Cognitive Maps for Modeling Time Series

This study elaborates on a comprehensive design methodology of fuzzy cognitive maps (FCMs). Here, the maps are regarded as a modeling vehicle of time series. It is apparent that whereas time series are predominantly numeric, FCMs are abstract constructs operating at the level of abstract entities referred to as concepts and represented by the individual nodes of the map. We introduce a mechanism to represent a numeric time series in terms of information granules constructed in the space of amplitude and change of amplitude of the time series, which, in turn, gives rise to a collection of concepts forming the corresponding nodes of the FCMs. Each information granule is mapped onto a node (concept) of the map. We identify two fundamental design phases of FCMs, namely 1) formation of information granules mapping numeric data (time series) into activation levels of information granules (viz., the nodes of the map), and 2) optimization of information granules at the parametric level, viz., learning (estimating) the weights between the nodes of the map. The learning is typically realized in a supervised mode on a basis of some experimental data. A construction of information granules is realized with the aid of fuzzy clustering, namely fuzzy C-means. The optimization is realized with the use of particle swarm optimization. The proposed approach is illustrated in detail by a series of experiments using a collection of publicly available data.

Granular fuzzy models: Analysis, design, and evaluation

The study is concerned with a design of granular fuzzy models. We exploit a concept of information granularity by developing a model coming as a network of intuitively structured collection of interval information granules described in the output space and a family of induced information granules (in the form of fuzzy sets) formed in the input space. In contrast to most fuzzy models encountered in the literature, the results produced by granular models are information granules rather than plain numeric entities. The design of the model concentrates on a construction of information granules that form a backbone of the overall construct. Interval information granules positioned in the output space are built by considering intervals of equal length, equal probability, and developing an optimized version of the intervals. The induced fuzzy information granules localized in the input space are realized by running a conditional Fuzzy C-Means (FCM). The performance of the model is assessed by considering criteria of coverage and information specificity (information granularity). Further optimization of the model is proposed along the line of an optimal re-distribution of input information granules induced by the individual interval information granules located in the output space. Experimental results involve some synthetic low-dimensional data and publicly available benchmark data sets.

Data description: A general framework of information granules

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.

Granular fuzzy models: a study in knowledge management in fuzzy modeling

In system modeling, knowledge management comes vividly into the picture when dealing with a collection of individual models. These models being considered as sources of knowledge, are engaged in some collective pursuits of a collaborative development to establish modeling outcomes of global character. The result comes in the form of a so-called granular fuzzy model, which directly reflects upon and quantifies the diversity of the available sources of knowledge (local models) involved in knowledge management. In this study, several detailed algorithmic schemes are presented along with related computational aspects associated with Granular Computing. It is also shown how the construction of information granules completed through the use of the principle of justifiable granularity becomes advantageous in the realization of granular fuzzy models and a quantification of the quality (specificity) of the results of modeling. We focus on the design of granular fuzzy models considering that the locally available models are those fuzzy rule-based. It is shown that the model quantified in terms of two conflicting criteria, that is (a) a coverage criterion expressing to which extent the resulting information granules “cover” include data and (b) specificity criterion articulating how detailed (specific) the obtained information granules are. The overall quality of the granular model is also assessed by determining an area under curve (AUC) where the curve is formed in the coverage-specificity coordinates. Numeric results are discussed with intent of displaying the most essential features of the proposed methodology and algorithmic developments.

Human Centricity and Perception-Based Perspective and Their Centrality to the Agenda of Granular Computing

In spite of their striking diversity, numerous tasks and architectures of intelligent systems such as those permeating multivariable data analysis, decision-making processes along with their underlying models, recommender systems and others exhibit two evident commonalities. They promote (a) human centricity and (b) vigorously engage perceptions (rather than plain numeric entities) in the realization of the systems and their further usage. Information granules play a pivotal role in such settings. Granular Computing delivers a cohesive framework supporting a formation of information granules and facilitating their processing. The author exploits two essential concepts of Granular Computing. The first one deals with the construction of information granules. The second one helps endow constructs of intelligent systems with a much needed conceptual and modeling flexibility. The study elaborates in detail on the three representative studies. In the first study being focused on the Analytic Hierarchy Process (AHP) used in decision-making, the author shows how an optimal allocation of granularity helps improve the quality of the solution and facilitate collaborative activities in models of group decision-making. The second study is concerned with a granular interpretation of temporal data where the role of information granularity is profoundly visible when effectively supporting human centric description of relationships existing in data. The third study concerns a formation of granular logic descriptors on a basis of a family of logic descriptors.

Information granules and their use in schemes of knowledge management

In system modeling, knowledge management comes vividly into the picture when dealing with a collection of models. These models, being considered as sources of knowledge, are engaged in some collective pursuits of collaboration and consensus formation. We show the use of information granules in these processes by elaborating on their conceptual role. It is revealed that information granules are used to facilitate processes of collaboration and consensus building. Such granular constructs, referred to as granular models, can also emerge as a part of higher order models to reflect and quantify the diversity of the sources of knowledge involved in knowledge management. Several detailed algorithmic schemes are presented, along with related computational aspects associated with Granular Computing. It is also shown how the construction of information granules, through the use of the principle of justifiable granularity, becomes advantageous in the realization of granular models. This study builds upon seminal concepts established in L.A. Zadeh’s Rosetta Stone paper devoted to information granulation.

The development of fuzzy radial basis function neural networks based on the concept of information ambiguity

There is a remarkably rich landscape of fuzzy clustering and ensuing design procedures of information granules. In a nutshell, fuzzy clustering (and clustering, in general) leads to direction-free constructs meaning that there is no clear distinction between input and output variables. In the framework of fuzzy modeling, information granules are used in the development of input–output mapping and from this perspective it becomes beneficial to consider the aspect of directionality in the construction of information granules (fuzzy sets) in the input space. Conditional fuzzy C-means clustering comes as one of the algorithmically viable alternatives using which we construct fuzzy sets over the input space in presence of supervision coming in the form of structure of data distributed over the output space. In this paper, presented is a new clustering method in which we use the ambiguity index to express the boundaries of the clusters. The design is illustrated with the aid of several numeric examples that provide a detailed insight into the performance of the fuzzy models formed in this manner and also highlight several crucial design issues.

Relational and directional aspects in the construction of information granules

In this study, we are concerned with a two-objective development of information granules completed on a basis of numeric data. The first goal of this design concerns revealing and representing a structure in a data set. As such, it is oriented toward coping with the underlying relational aspects of the experimental data. The second goal deals with the formation of a mapping between information granules constructed in two spaces (thus, it concentrates on the directional aspect of information granulation). The quality of the mapping is directly affected by the information granules over which it operates, so in essence, we are interested in the granules that not only reflect the data, but also contribute to the performance of such mapping. The optimization of information granules is realized through a collaboration occurring at the level of data and the mapping between the data sets. The operational facet of the problem is cast in the realm of fuzzy clustering. As the standard techniques of fuzzy clustering (including a well-known approach of FCM) are aimed exclusively at the first objective identified above, we augment them in order to accomplish sound mapping properties between the granules. This leads to a generalized version of the FCM (and any other clustering technique for this matter). We propose a generalized version of the objective function that includes an additional collaboration component to make the formed information granules in rapport with the mapping requirements (that comes with a directional component captured by the information granules). The additive form of the objective function with a modifiable component of collaborative activities makes it possible to express a suitable level of collaboration and avoid a phenomenon of potential competition in the case of incompatible structures and the associated mapping. The logic-based type of the mapping (that invokes the use of fuzzy relational equations) comes as a consequence of the logic framework of information granules. A complete optimization method is provided and illustrated with several numeral studies.

Information granules: Towards foundations of granular computing

We introduce basic notions related to granular computing, namely the information granule syntax and semantics as well as the inclusion and closeness (similarity) relations of granules. Different information sources (units, agents) are equipped with two kinds of operations on information granules: operations transforming tuples of information granules definable by a given agent into information granules definable by this agent and approximation operations for computing by agents approximations of information granules delivered by other agents. More complex granules are constructed by means of these operations and approximation operations from some input information granules. The construction of information granules is described by expressions called terms. We discuss a problem of synthesis of robust terms, i.e., descriptions of information granules, satisfying a given specification. This is an important problem for granular computing and its applications for spatial reasoning or knowledge discovery and data mining. © 2001 John Wiley & Sons, Inc.