Granular computing: perspectives and challenges

Rule-Based Modeling With DBSCAN-Based Information Granules

Rule-based models are applicable to model the behavior of complex and nonlinear systems. Due to limited experience and randomness involving constructing information granules, an insufficient credible rules division could reduce the model's accuracy. This paper proposes a new rule-based modeling approach, which utilizes density-based spatial clustering of applications with noise (DBSCAN)-based information granules to construct the rules. First, bear in mind the advantages of density-based clustering, DBSCAN is proposed to generate data structures. Based on these data structures, two rule-based models are constructed: 1) models using DBSCAN clusters to construct granules and rules directly and 2) models generating subgranules in each DBSCAN cluster for rule formation. Experiments involving these two models are completed, and obtained results are compared with those generated with a traditional model involving fuzzy C -means-based granules. Numerical results show that the rule-based model, which builds rules from subgranules of DBSCAN structures, performs the best in analyzing system behaviors.

Granular Fuzzy Modeling Guided Through the Synergy of Granulating Output Space and Clustering Input Subspaces

As an augmentation of classic fuzzy models, granular fuzzy models (GFMs) have been applied to many fields being in rapport with experimental data, models, and users. However, most of the existing methods used to construct GFMs are based on the principle of optimal allocation of information granularity, which requires that a numeric model be provided in advance. In this paper, a straightforward and convincing modeling method is proposed to directly construct GFM on a basis of experimental data. The method first granulates the output space to form some interval information granules with distinct semantics and then uses them to partition the entire input space into a series of input subspaces. Subsequently, an initial GFM is emerged by using "If-Then" rules to relate with those interval information granules positioned in the output space and structures expressed in prototypes that are produced by clustering individual input subspaces. Further, the initial GFM is also refined by continuously migrating prototypes in individual input subspaces. The experimental studies using the synthetic dataset and several real-world datasets are reported. They offer a useful insight into the feasibility and effectiveness of the proposed modeling method and reveal the impact of parameters on the performance of the ensuing GFMs. An application example is also presented to exhibit the advantages of the resulting GFM.

Data-driven sequential three-way decisions for unlabeled information system

Based on the granular computing and three-way decisions theory, the sequential three-way decisions (S3WD) model implements the idea of progressive computing. However, almost S3WD models are established based on labeled information system, and there is still a lack of S3WD model for processing unlabeled information system (UIS). In this paper, to solve the issue of given accepted number for UIS, a data-driven sequential three-way decisions (DDS3WD) model is proposed. Firstly, from the perspective of similarity computed by TOPSIS, a general three-way decisions model for UIS based on decision risk is presented and its shortcomings are analyzed. Then, a concept of optimal density difference is defined to establish the DDS3WD model for UIS by updating attributes. Finally, the related experiments show that DDS3WD is feasible and effective for dealing with UIS under the condition of given accepted number of objects.

Multicriteria Decision Making With Incomplete Weights Based on 2-D Uncertain Linguistic Choquet Integral Operators

In regard to multicriteria decision making (MCDM) problems where the values of the criteria are expressed by 2-D uncertain linguistic variables (2DULVs), where the criteria are interactive and the criteria weights are incompletely known, two novel MCDM methods are proposed in this paper. First, we offer some novel operational laws of 2DULVs, which can avoid the operational results exceeding the boundary of linguistic term sets. Then, we propose four operators to capture the interactions over the criteria, namely, the 2-D uncertain linguistic Choquet averaging (2DULCA) operator, the 2-D uncertain linguistic Choquet geometric (2DULCG) operator, the Shapley 2DULCA (S2DULCA) operator, and the Shapley 2DULCG (S2DULCG) operator. In addition, we establish the models based on the maximization deviation approach and the Shapley function to get the criteria weights. Finally, we propose two novel MCDM methods under 2-D uncertain linguistic environments, where four examples are used to explain the created MCDM methods. Comparative experimental results are presented to highlight the superiorities of the created approaches.

Attribute-Driven Granular Model for EMG-Based Pinch and Fingertip Force Grand Recognition

Fine multifunctional prosthetic hand manipulation requires precise control on the pinch-type and the corresponding force, and it is a challenge to decode both aspects from myoelectric signals. This paper proposes an attribute-driven granular model (AGrM) under a machine-learning scheme to solve this problem. The model utilizes the additionally captured attribute as the latent variable for a supervised granulation procedure. It was fulfilled for EMG-based pinch-type classification and the fingertip force grand prediction. In the experiments, 16 channels of surface electromyographic signals (i.e., main attribute) and continuous fingertip force (i.e., subattribute) were simultaneously collected while subjects performing eight types of hand pinches. The use of AGrM improved the pinch-type recognition accuracy to around 97.2% by 1.8% when constructing eight granules for each grasping type and received more than 90% force grand prediction accuracy at any granular level greater than six. Further, sensitivity analysis verified its robustness with respect to different channel combination and interferences. In comparison with other clustering-based granulation methods, AGrM achieved comparable pinch recognition accuracy but was of lowest computational cost and highest force grand prediction accuracy.

Similarity measure for multi-granularity rough approximations of vague sets

Vague sets are a further extension of fuzzy sets. In rough set theory, target concept can be characterized by different rough approximation spaces when it is a vague concept. The uncertainty measure of vague sets in rough approximation spaces is an important issue. If the uncertainty measure is not accurate enough, different rough approximation spaces of a vague concept may possess the same result, which makes it impossible to distinguish these approximation spaces for charactering a vague concept strictly. In this paper, this problem will be solved from the perspective of similarity. Firstly, based on the similarity between vague information granules(VIGs), we proposed an uncertainty measure with strong distinguishing ability called rough vague similarity (RVS). Furthermore, by studying the multi-granularity rough approximations of a vague concept, we reveal the change rules of RVS with the changing granularities and conclude that the RVS between any two rough approximation spaces can degenerate to granularity measure and information measure. Finally, a case study and related experiments are listed to verify that RVS possesses a better performance for reflecting differences among rough approximation spaces for describing a vague concept.

Boosting Granular Support Vector Machines for the Accurate Prediction of Protein-Nucleotide Binding Sites

AIM AND OBJECTIVE

The accurate identification of protein-ligand binding sites helps elucidate protein function and facilitate the design of new drugs. Machine-learning-based methods have been widely used for the prediction of protein-ligand binding sites. Nevertheless, the severe class imbalance phenomenon, where the number of nonbinding (majority) residues is far greater than that of binding (minority) residues, has a negative impact on the performance of such machine-learning-based predictors.

MATERIALS AND METHODS

In this study, we aim to relieve the negative impact of class imbalance by Boosting Multiple Granular Support Vector Machines (BGSVM). In BGSVM, each base SVM is trained on a granular training subset consisting of all minority samples and some reasonably selected majority samples. The efficacy of BGSVM for dealing with class imbalance was validated by benchmarking it with several typical imbalance learning algorithms. We further implemented a protein-nucleotide binding site predictor, called BGSVM-NUC, with the BGSVM algorithm.

RESULTS

Rigorous cross-validation and independent validation tests for five types of proteinnucleotide interactions demonstrated that the proposed BGSVM-NUC achieves promising prediction performance and outperforms several popular sequence-based protein-nucleotide binding site predictors. The BGSVM-NUC web server is freely available at http://csbio.njust.edu.cn/bioinf/BGSVM-NUC/ for academic use.

Development and Analysis of Neural Networks Realized in the Presence of Granular Data

In this article, we propose a design and evaluation framework of granular neural networks realized in the presence of information granules. Neural networks realized in this manner are able to process both nonnumerical data, such as information granules as well as numerical data. Information granules are meaningful and semantically sound entities formed by organizing existing knowledge and available experimental data. The directional nature of mapping between the input and output data needs to be considered when building information granules. The development of neural networks advocated in this article is realized as a two-phase process. First, a collection of information granules is formed through granulation of numeric data in the input and output spaces. Second, neural networks are constructed on the basis of information granules rather than original (numeric) data. The proposed method leads to the construction of neural networks in a completely new way. In comparison with traditional (numeric) neural networks, the networks developed in the presence of granular data require shorter learning time. They also produce the results (outputs) that are information granules rather than numeric entities. The quality of granular outputs generated by our neural networks is evaluated in terms of the coverage and specificity criteria that are pertinent to the characterization of the information granules.

Multi-View Cluster Analysis with Incomplete Data to Understand Treatment Effects

Multi-view cluster analysis, as a popular granular computing method, aims to partition sample subjects into consistent clusters across different views in which the subjects are characterized. Frequently, data entries can be missing from some of the views. The latest multi-view co-clustering methods cannot effectively deal with incomplete data, especially when there are mixed patterns of missing values. We propose an enhanced formulation for a family of multi-view co-clustering methods to cope with the missing data problem by introducing an indicator matrix whose elements indicate which data entries are observed and assessing cluster validity only on observed entries. In comparison with the simple strategy of removing subjects with missing values, our approach can use all available data in cluster analysis. In comparison with common methods that impute missing data in order to use regular multi-view analytics, our approach is less sensitive to imputation uncertainty. In comparison with other state-of-the-art multi-view incomplete clustering methods, our approach is sensible in the cases of missing any value in a view or missing the entire view, the most common scenario in practice. We first validated the proposed strategy in simulations, and then applied it to a treatment study of heroin dependence which would have been impossible with previous methods due to a number of missing-data patterns. Patients in a treatment study were naturally assessed in different feature spaces such as in the pre-, during-and post-treatment time windows. Our algorithm was able to identify subgroups where patients in each group showed similarities in all of the three time windows, thus leading to the recognition of pre-treatment (baseline) features predictive of post-treatment outcomes.

Reduced Dilation-Erosion Perceptron for Binary Classification

Dilation and erosion are two elementary operations from mathematical morphology, a non-linear lattice computing methodology widely used for image processing and analysis. The dilation-erosion perceptron (DEP) is a morphological neural network obtained by a convex combination of a dilation and an erosion followed by the application of a hard-limiter function for binary classification tasks. A DEP classifier can be trained using a convex-concave procedure along with the minimization of the hinge loss function. As a lattice computing model, the DEP classifier assumes the feature and class spaces are partially ordered sets. In many practical situations, however, there is no natural ordering for the feature patterns. Using concepts from multi-valued mathematical morphology, this paper introduces the reduced dilation-erosion (r-DEP) classifier. An r-DEP classifier is obtained by endowing the feature space with an appropriate reduced ordering. Such reduced ordering can be determined using two approaches: one based on an ensemble of support vector classifiers (SVCs) with different kernels and the other based on a bagging of similar SVCs trained using different samples of the training set. Using several binary classification datasets from the OpenML repository, the ensemble and bagging r-DEP classifiers yielded mean higher balanced accuracy scores than the linear, polynomial, and radial basis function (RBF) SVCs as well as their ensemble and a bagging of RBF SVCs.

Aggregation of Classifiers: A Justifiable Information Granularity Approach

In this paper, we introduced a new approach of combining multiple classifiers in a heterogeneous ensemble system. Instead of using numerical membership values when combining, we constructed interval membership values for each class prediction from the meta-data of observation by using the concept of information granule. In the proposed method, the uncertainty (diversity) of the predictions produced by the base classifiers is quantified by the interval-based information granules. The decision model is then generated by considering both bound and length of the intervals. Extensive experimentation using the UCI datasets has demonstrated the superior performance of our algorithm over other algorithms including six fixed combining methods, one trainable combining method, AdaBoost, bagging, and random subspace.

Resilience Analysis of Critical Infrastructures: A Cognitive Approach Based on Granular Computing

A great impetus for the study of resilience in critical infrastructures (CIs) is found in the large number of initiatives and international research programmes from U.S., EU, and Asia. Politicians, decision makers, and citizens are now aware of the drastic consequences that can have the cascading effects of an adverse event in these large scale infrastructures. However, the study of resilience in CIs is challenging for several reasons, among which their large scale and interdependencies. We have to consider also that adverse events, e.g., attacks, natural hazards, or man-made disasters, suddenly occur and evolve rapidly, giving us little time to take decisions and react to them. Approximate reasoning and rapid decision making have to be considered requirements for resilience analysis of CIs. The main result presented in this paper relates to a systemic integration of granular computing (GrC) and resilience analysis for CIs. Each phase of our approach presents distinctive aspects but, overall, we argue the merit of this paper consists in the originality of the study, being this the first work that combines GrC and resilience analysis of CIs. This paper reports an illustrative example that shows how to apply our results, and a discussion on the necessary contextualizations and extensions of the GrC results to be better adapted for CIs resilience.