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This paper mainly focuses on how to construct concept lattice effectively and efficiently based on improved variable precision rough set. On the basis of preprocessing formal concept, one algorithm that can determine the value range of variable precision parameter β according to the approximate classification quality is proposed. An improved β -upper and lower distribution attribute reduction algorithm is also proposed based on the improved variable precision rough set, the algorithm can be used for attribute reduction on the original data of the concept lattice, and to eliminate the redundant knowledge or noises of the formal context. For the reduced formal context, the paper combines the concept construction algorithm with an improved rule acquisition algorithm seamlessly, and proposes a novel approach of concept lattice construction based on improved variable precision rough set. Finally, a concept lattice generation prototype system is developed, this paper also performs comprehensive experiments, and the effectiveness of the improved algorithm is proved through the experimental results. [ABSTRACT FROM AUTHOR]

Noise is common in any real-world data set and may adversely affect classifiers built under the effect of such type of disturbance. Some of these classifiers are widely recognized for their good performance when dealing with imperfect data. However, the noise robustness of the classifiers is an important issue in noisy environments and it must be carefully studied. Both performance and robustness are two independent concepts that are usually considered separately, but the conclusions reached with one of these metrics do not necessarily imply the same conclusions with the other. Therefore, involving both concepts seems to be crucial in order determine the expected behavior of the classifiers against noise. Existing measures fail to properly integrate these two concepts, and they are also not well suited to compare different techniques over the same data. This paper proposes a new measure to establish the expected behavior of a classifier with noisy data trying to minimize the problems of considering performance and robustness individually: the Equalized Loss of Accuracy (ELA). The advantages of ELA against other robustness metrics are studied and all of them are also compared. Both the analysis of the distinct measures and the empirical results show that ELA is able to overcome the aforementioned problems that the rest of the robustness metrics may produce, having a better behavior when comparing different classifiers over the same data set. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an efficient feature extraction method, named local structure preserving discriminant analysis (LSPDA), is presented. LSPDA constructs the local scatter and the between-class scatter to characterize the sub- and multi-manifold information respectively. More specifically, the local structure is constructed according to a certain kind of similarity between data points which takes special consideration of both the local information and the class information based on a parameter-free neighborhood decision rule, and the between-class structure is constructed according to the importance degrees of the not-same-class points measured by a strictly monotonically decreasing function. After the local scatter and the between-class scatter have been characterized, the novel feature extraction criterion is derived via maximizing the difference between the between-class scatter and the local scatter. Experimental results on the Wine dataset, AR, FERET, CMU PIE, ORL and LFW face databases show the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: Traditionally unsupervised dimensionality reduction methods may not necessarily improve the separability of the data resided in different clusters due to ignorance of the inherent relationship between subspace selection and clustering. It is known that soft clustering using fuzzy c-means or its variants can provide a better and more meaningful data partition than hard clustering, which motivates us to develop a novel entropy regularized soft K-means algorithm for discriminant analysis (ResKmeans) in this paper. ResKmeans performs soft clustering and subspace selection simultaneously and thus gives rise to a generalized linear discriminant analysis (GELDA) which captures both the intra-cluster compactness and the inter-cluster separability. Furthermore, we clarify both the relationship between GELDA and conventional LDA and the inherent relationship between subspace selection and soft clustering. Experimental results on real-world data sets show ResKmeans is superior to other popular clustering algorithms. [Copyright &y& Elsevier]

Abstract: This paper proposes a regularized locality preserving discriminant analysis (RLPDA) approach for facial feature extraction and recognition. The RLPDA approach decomposes the eigenspace of the locality preserving within-class scatter matrix into three subspaces, i.e., the face space, the noise space and the null space, and then regularizes the three subspaces differently according to their predicted eigenvalues. As a result, the proposed approach integrates discriminative information in all of the three subspaces, de-emphasizes the effect of the eigenvectors corresponding to the small eigenvalues, and meanwhile suppresses the small sample size problem. Extensive experiments on ORL face database, FERET face subset and UMIST face database illustrate the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Abstract: To address two problems, namely nonlinear problem and singularity problem, of linear discriminant analysis (LDA) approach in face recognition, this paper proposes a novel kernel machine-based rank-lifting regularized discriminant analysis (KRLRDA) method. A rank-lifting theorem is first proven using linear algebraic theory. Combining the rank-lifting strategy with three-to-one regularization technique, the complete regularized methodology is developed on the within-class scatter matrix. The proposed regularized scheme not only adjusts the projection directions but tunes their corresponding weights as well. Moreover, it is shown that the final regularized within-class scatter matrix approaches to the original one as the regularized parameter tends to zero. Two public available databases, namely FERET and CMU PIE face databases, are selected for evaluations. Compared with some existing kernel-based LDA methods, the proposed KRLRDA approach gives superior performance. [Copyright &y& Elsevier]