Fuzzy Sets and Systems - Special issue: fuzzy sets: where do we stand? Where do we go?
Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stacking with Multi-response Model Trees
MCS '02 Proceedings of the Third International Workshop on Multiple Classifier Systems
A Probabilistic Formulation for Hausdorff Matching
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Reducing multiclass to binary: a unifying approach for margin classifiers
The Journal of Machine Learning Research
Using Discriminant Analysis for Multi-class Classification
ICDM '03 Proceedings of the Third IEEE International Conference on Data Mining
Efficient Density-Based Clustering of Complex Objects
ICDM '04 Proceedings of the Fourth IEEE International Conference on Data Mining
IEEE Transactions on Knowledge and Data Engineering
Dynamic Cluster Formation Using Level Set Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Simultaneous evolution of neural network topologies and weights for classification and regression
IWANN'05 Proceedings of the 8th international conference on Artificial Neural Networks: computational Intelligence and Bioinspired Systems
Feature selection by analyzing class regions approximated byellipsoids
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Granular clustering: a granular signature of data
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Rough–Fuzzy Collaborative Clustering
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Linguistic models as a framework of user-centric system modeling
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
IEEE Transactions on Fuzzy Systems
Fuzzy min-max neural networks -- Part 2: Clustering
IEEE Transactions on Fuzzy Systems
General fuzzy min-max neural network for clustering and classification
IEEE Transactions on Neural Networks
Adaptive resolution min-max classifiers
IEEE Transactions on Neural Networks
A Fuzzy Min-Max Neural Network Classifier With Compensatory Neuron Architecture
IEEE Transactions on Neural Networks
Fuzzy min-max neural networks. I. Classification
IEEE Transactions on Neural Networks
Rough-wavelet granular space and classification of multispectral remote sensing image
Applied Soft Computing
Class-dependent rough-fuzzy granular space, dispersion index and classification
Pattern Recognition
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In this study, we are concerned with a development of a certain category of granular classifiers referred here to as hyperbox-driven classifiers (HDC). The approach fully capitalizes on the two key technologies of granular computing, namely set (interval) calculus and fuzzy sets in dealing with a description of geometry of patterns (data) belonging to a certain category. We take advantage of the capabilities of sets (intervals and their Cartesian products) when describing a core structure of classes of patterns in the form of some hyperboxes. Their combinations are referred to as a core structure of the feature space. Next, we refine the geometry of the classifier by bringing forward the concepts of regions of the feature space characterized by fuzzy sets. They are sought as a secondary structure. The construction of the core structure is realized by means of the supervised version of DBSCAN-one of the popular clustering algorithms of data mining. The secondary structure is described by fuzzy sets whose membership functions are a solution to some optimization problem of allocation of degrees of belongingness. In the formation of the secondary structure we exploit a concept of the Hausdorff distance that determines a distance between some information granule (of a well defined geometry) and a numeric pattern (a point in the highly dimensional feature space). The two-stage description of the granular classifier is also beneficial in the characterization of the classification error. By virtue of the design of the core structure, the classification error occurring there assumes very small, almost zero values. On the other hand, the secondary structure coming with a substantial level of overlap between classes is characterized by relatively higher values of the classification error. Being cognizant of that, we suggest a way of forming a synthetic measure built on the membership values and named a separability index that helps quantify the classification error in this setting. A series of numeric examples are used to demonstrate the effectiveness of the proposed granular classifiers.