Class-dependent rough-fuzzy granular space, dispersion index and classification

Abstract

A new rough-fuzzy model for pattern classification based on granular computing is described in the present article. In this model, we propose the formulation of class-dependent granules in fuzzy environment. Fuzzy membership functions are used to represent the feature-wise belonging to different classes, thereby producing fuzzy granulation of the feature space. The fuzzy granules thus generated possess better class discriminatory information that is useful in pattern classification with overlapping classes. Neighborhood rough sets are used in the selection of a subset of granulated features that explore the local/contextual information from neighbor granules. The model thus explores mutually the advantages of class-dependent fuzzy granulation and neighborhood rough set. The superiority of the proposed model to other similar methods is established with seven completely labeled data sets, including a synthetic remote sensing image, and two partially labeled real remote sensing images collected from satellites. Various performance measures, including a new method of dispersion estimation, are used for comparative analysis. The new measure called “dispersion score” quantifies the nature of distribution of the classified patterns among different classes so that lower is the dispersion, better is the classifier. The proposed model learns well even with a lower percentage of training set that makes the system fast. The model is seen to have lowest dispersion measure (i.e., misclassified patterns are confined to minimum number of classes) compared to others; thereby reflecting well the overlapping characteristics of a class with others, and providing a strong clue for the class-wise performance improvement with available higher-level information. The statistical significance of the proposed model is also supported by the χ² test.