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In this study, we present a new sparse-representation-based face-classification algorithm that exploits dynamic dictionary optimization on an extended dictionary using synthesized faces. More specifically, given a dictionary consisting of face examples, we first augment the dictionary with a set of virtual faces generated by calculating the image difference of a pair of faces. This results in an extended dictionary with hybrid training samples, which enhances the capacity of the dictionary to represent new samples. Second, to reduce the redundancy of the extended dictionary and improve the classification accuracy, we use a dictionary-optimization method. We truncate the extended dictionary with a more compact structure by discarding the original samples with small contributions to represent a test sample. Finally, we perform sparse-representation-based face classification using the optimized dictionary. Experimental results obtained using the AR and FERRET face datasets demonstrate the superiority of the proposed method in terms of accuracy, especially for small-sample-size problems. [ABSTRACT FROM AUTHOR]

Abstract: Multigranulation rough set is an expansion of the classical rough set by using multiple granular structures. Presently, three important multigranulation rough sets have been proposed, they are optimistic, pessimistic and β-multigranulation approaches. However, such three multigranulation rough sets do not take the test cost into consideration, which is an important issue in both data mining and machine learning. To solve such problem, we propose a test cost sensitive multigranulation rough set model in this paper. We show that test cost sensitive multigranulation rough set is a generalization of optimistic, pessimistic and β-multigranulation rough sets. Furthermore, it is found that the traditional heuristic algorithm is not suitable for granular structure selection with lower test cost, we then propose a backtracking algorithm for granular structure selection with minimal test cost. The algorithms are tested on ten UCI (University of California–Irvine) data sets. Experimental results show the effectiveness of backtracking algorithm by comparing with heuristic algorithm. This study suggests potential application areas and new research trends concerning multigranulation rough set theory. [Copyright &y& Elsevier]