Abstrac Khmelnitskaya et al.have recently proposed the average covering tree value as a new solution concept for cooperative transferable utility games with directed graph structure.The average covering tree value is...Abstrac Khmelnitskaya et al.have recently proposed the average covering tree value as a new solution concept for cooperative transferable utility games with directed graph structure.The average covering tree value is defined as the average of marginal contribution vectors corresponding to the specific set of rooted trees,and coincides with the Shapley value when the game has complete communication structure.In this paper,we discuss the computational complexity of the average covering tree value.We show that computation of the average covering tree value is#P-complete even if the characteristic function of the game is{0,1}-valued.We prove this by a reduction from counting the number of all linear extensions of a partial order,which has been shown by Brightwell et al.to be a#P-complete counting problem.The implication of this result is that an efficient algorithm to calculate the average covering tree value is unlikely to exist.展开更多
Improved local tangent space alignment (ILTSA) is a recent nonlinear dimensionality reduction method which can efficiently recover the geometrical structure of sparse or non-uniformly distributed data manifold. In thi...Improved local tangent space alignment (ILTSA) is a recent nonlinear dimensionality reduction method which can efficiently recover the geometrical structure of sparse or non-uniformly distributed data manifold. In this paper, based on combination of modified maximum margin criterion and ILTSA, a novel feature extraction method named orthogonal discriminant improved local tangent space alignment (ODILTSA) is proposed. ODILTSA can preserve local geometry structure and maximize the margin between different classes simultaneously. Based on ODILTSA, a novel face recognition method which combines augmented complex wavelet features and original image features is developed. Experimental results on Yale, AR and PIE face databases demonstrate the effectiveness of ODILTSA and the feature fusion method.展开更多
基金This work was partially supported by the Okawa Foundation for Information and TelecommunicationWe wish to thank the two anonymous reviewers for their constructive suggestions and comments.The comments have helped us significantly improve the paper.
文摘Abstrac Khmelnitskaya et al.have recently proposed the average covering tree value as a new solution concept for cooperative transferable utility games with directed graph structure.The average covering tree value is defined as the average of marginal contribution vectors corresponding to the specific set of rooted trees,and coincides with the Shapley value when the game has complete communication structure.In this paper,we discuss the computational complexity of the average covering tree value.We show that computation of the average covering tree value is#P-complete even if the characteristic function of the game is{0,1}-valued.We prove this by a reduction from counting the number of all linear extensions of a partial order,which has been shown by Brightwell et al.to be a#P-complete counting problem.The implication of this result is that an efficient algorithm to calculate the average covering tree value is unlikely to exist.
基金the National Natural Science Foundation of China(No.61004088)the Key Basic Research Foundation of Shanghai Municipal Science and Technology Commission(No.09JC1408000)
文摘Improved local tangent space alignment (ILTSA) is a recent nonlinear dimensionality reduction method which can efficiently recover the geometrical structure of sparse or non-uniformly distributed data manifold. In this paper, based on combination of modified maximum margin criterion and ILTSA, a novel feature extraction method named orthogonal discriminant improved local tangent space alignment (ODILTSA) is proposed. ODILTSA can preserve local geometry structure and maximize the margin between different classes simultaneously. Based on ODILTSA, a novel face recognition method which combines augmented complex wavelet features and original image features is developed. Experimental results on Yale, AR and PIE face databases demonstrate the effectiveness of ODILTSA and the feature fusion method.
