Non-isomorphic two dimensional indecomposable modules over infinite dimensional hereditary path algebras are described. We infer that none of them can be determined by their dimension vectors.
Dimensionality reduction （DR） methods based on sparse representation as one of the hottest research topics have achieved remarkable performance in many applications in recent years. However, it＇s a challenge for ex...Dimensionality reduction （DR） methods based on sparse representation as one of the hottest research topics have achieved remarkable performance in many applications in recent years. However, it＇s a challenge for existing sparse representation based methods to solve nonlinear problem due to the limitations of seeking sparse representation of data in the original space. Motivated by kernel tricks, we proposed a new framework called empirical kernel sparse representation （EKSR） to solve nonlinear problem. In this framework, non- linear separable data are mapped into kernel space in which the nonlinear similarity can be captured, and then the data in kernel space is reconstructed by sparse representation to preserve the sparse structure, which is obtained by minimiz- ing a ~1 regularization-related objective function. EKSR pro- vides new insights into dimensionality reduction and extends two models： 1） empirical kernel sparsity preserving projec- tion （EKSPP）, which is a feature extraction method based on sparsity preserving projection （SPP）; 2） empirical kernel sparsity score （EKSS）, which is a feature selection method based on sparsity score （SS）. Both of the two methods can choose neighborhood automatically as the natural discrimi- native power of sparse representation. Compared with sev- eral existing approaches, the proposed framework can reduce computational complexity and be more convenient in prac- tice.展开更多
A new adaptive learning algorithm for constructing and training wavelet networks is proposed based on the time-frequency localization properties of wavelet frames and the adaptive projection algorithm. The exponential...A new adaptive learning algorithm for constructing and training wavelet networks is proposed based on the time-frequency localization properties of wavelet frames and the adaptive projection algorithm. The exponential convergence of the adaptive projection algorithm in finite-dimensional Hilbert spaces is constructively proved, with exponential decay ratios given with high accuracy. The learning algorithm can sufficiently utilize the time-frequency information contained in the training data, iteratively determines the number of the hidden layer nodes and the weights of wavelet networks, and solves the problem of structure optimization of wavelet networks. The algorithm is simple and efficient, as illustrated by examples of signal representation and denoising.展开更多
This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors de...This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors derive the strong convergence with rate,strong representation as well as asymptotic normality of the conditional quantile estimator.Also,a Berry-Esseen-type bound for the estimator is established.In addition,the finite sample behavior of the estimator is investigated via simulations.展开更多
基金The NSF(11371307)of ChinaResearch Culture Funds(2014xmpy11)of Anhui Normal University
文摘Non-isomorphic two dimensional indecomposable modules over infinite dimensional hereditary path algebras are described. We infer that none of them can be determined by their dimension vectors.
文摘Dimensionality reduction （DR） methods based on sparse representation as one of the hottest research topics have achieved remarkable performance in many applications in recent years. However, it＇s a challenge for existing sparse representation based methods to solve nonlinear problem due to the limitations of seeking sparse representation of data in the original space. Motivated by kernel tricks, we proposed a new framework called empirical kernel sparse representation （EKSR） to solve nonlinear problem. In this framework, non- linear separable data are mapped into kernel space in which the nonlinear similarity can be captured, and then the data in kernel space is reconstructed by sparse representation to preserve the sparse structure, which is obtained by minimiz- ing a ~1 regularization-related objective function. EKSR pro- vides new insights into dimensionality reduction and extends two models： 1） empirical kernel sparsity preserving projec- tion （EKSPP）, which is a feature extraction method based on sparsity preserving projection （SPP）; 2） empirical kernel sparsity score （EKSS）, which is a feature selection method based on sparsity score （SS）. Both of the two methods can choose neighborhood automatically as the natural discrimi- native power of sparse representation. Compared with sev- eral existing approaches, the proposed framework can reduce computational complexity and be more convenient in prac- tice.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 69872030) the Natural Science Foundation of Shaanxi Province (Grant No. 98 × 08) Elite Young Teacher Foundation of Ministry of China (1997).
文摘A new adaptive learning algorithm for constructing and training wavelet networks is proposed based on the time-frequency localization properties of wavelet frames and the adaptive projection algorithm. The exponential convergence of the adaptive projection algorithm in finite-dimensional Hilbert spaces is constructively proved, with exponential decay ratios given with high accuracy. The learning algorithm can sufficiently utilize the time-frequency information contained in the training data, iteratively determines the number of the hidden layer nodes and the weights of wavelet networks, and solves the problem of structure optimization of wavelet networks. The algorithm is simple and efficient, as illustrated by examples of signal representation and denoising.
基金supported by the National Natural Science Foundation of China(No.11271286)the Specialized Research Fund for the Doctor Program of Higher Education of China(No.20120072110007)a grant from the Natural Sciences and Engineering Research Council of Canada
文摘This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors derive the strong convergence with rate,strong representation as well as asymptotic normality of the conditional quantile estimator.Also,a Berry-Esseen-type bound for the estimator is established.In addition,the finite sample behavior of the estimator is investigated via simulations.
