Affiliations: [a] School of Automation, Southeast University, Nanjing 210096, Jiangsu, China | [b] Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Nanjing 210096, Jiangsu, China | [c] College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, Jiangsu, China
Abstract: In practical application, the performances of face recognition are always affected by variations of expression, illumination and so on. To address this problem, an interval type-2 fuzzy linear discriminant analysis (IT2FLDA) method is proposed. In this paper, we first propose the supervised interval type-2 fuzzy C-Means (IT2FCM) algorithm. Moreover, the supervised IT2FCM is incorporated into linear discriminant analysis (LDA). In this method, the membership degree matrix of training samples belonging to each class and means of each class are firstly calculated by the supervised IT2FCM algorithm. They are then applied to the definition of fuzzy within-class scatter matrix and fuzzy between-class scatter matrix, respectively. In doing so, means of each class that are estimated by the supervised IT2FCM can converge to a more desirable location than ones obtained by class sample average and fuzzy k-nearest neighbor (FKNN) method. Furthermore, the IT2FLDA is able to minimize the effects of uncertainties, find the optimal projective directions and make the feature subspace discriminating and robust, which inherits the benefits of the supervised IT2FCM and LDA. The experiment results show that the IT2FLDA improves the recognition rate and reduces sensitivity to variations when compared to results from the previous techniques.
Keywords: Type-2 fuzzy set, linear discriminant analysis, the supervised interval type-2 fuzzy C-Means, membership degree matrix
