最近邻特征空间嵌入(nearest feature space embedding,NFSE)方法选取最近邻特征空间时使用欧氏距离度量,导致样本的类内离散度和类间离散度同步变化,无法准确反映样本在高维空间的分布;选取每个样本最近邻特征空间都要遍历所有类,导致...最近邻特征空间嵌入(nearest feature space embedding,NFSE)方法选取最近邻特征空间时使用欧氏距离度量,导致样本的类内离散度和类间离散度同步变化,无法准确反映样本在高维空间的分布;选取每个样本最近邻特征空间都要遍历所有类,导致训练时间长。针对以上问题,提出非线性距离的最近邻特征空间嵌入改进方法(nearest feature space embedding method based on nonlinear distance metric,NDNFSE),引入非线性距离公式选取最近邻特征空间,并使用结合夹角度量的最近邻分类器,提高了识别率;仅在样本的近邻类中选取最近邻特征空间,有效减少了训练时间。实验表明,NDNFSE的训练时间明显低于NFSE,识别率总体高于各对比算法。展开更多
Let X be a metric space with an ordering structure,A: X→X is a operator and x≤Ax for any x∈X. In this paper we prove a new fixed point theorem, which generalizes famous caristi fixed point theorem.
In this paper, we present a new ear-following model, i.e. comprehensive optimal velocity model （COVM）, whose optimal velocity function not only depends on the following distance of the preceding vehicle, but also de...In this paper, we present a new ear-following model, i.e. comprehensive optimal velocity model （COVM）, whose optimal velocity function not only depends on the following distance of the preceding vehicle, but also depends on the velocity difference with preceding vehicle. Simulation results show that COVM is an improvement over the previous ones theoretically. Then, the stability condition of the model is obtained by the linear stability analysis, which has shown that the model could obtain a bigger stable region than previous models in the phase diagram. Through the nonlinear analysis, the Burgers, Korteweg-de Vries （KdV） and modified KdV （mKdV） equations are derived for the triangular shock wave, the soliton wave, and the kink-antikink soliton wave. At the same time, numerical simulations are also carried out to show that the model could simulate these density waves.展开更多
In this paper,the distance-sability of nonlinear discrete system is investigated by means of the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov fu...In this paper,the distance-sability of nonlinear discrete system is investigated by means of the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov function is avoided.展开更多
In this paper,we study the very weak solutions to some nonlinear elliptic systems with righthand side integrable data with respect to the distance to the boundary.Firstly,we study the existence of the approximate solu...In this paper,we study the very weak solutions to some nonlinear elliptic systems with righthand side integrable data with respect to the distance to the boundary.Firstly,we study the existence of the approximate solutions.Secondly,a priori estimates are given in the framework of weighted spaces.Finally,we prove the existence,uniqueness and regularity of the very weak solutions.展开更多
The authors establish several estimates showing that the distance in W^(1,p),1 < p < ∞,between two immersions from a domain of R^n into R^(n+1) is bounded by the distance in L^p between two matrix fields define...The authors establish several estimates showing that the distance in W^(1,p),1 < p < ∞,between two immersions from a domain of R^n into R^(n+1) is bounded by the distance in L^p between two matrix fields defined in terms of the first two fundamental forms associated with each immersion. These estimates generalize previous estimates obtained by the authors and P. G. Ciarlet and weaken the assumptions on the fundamental forms at the expense of replacing them by two different matrix fields.展开更多
文摘最近邻特征空间嵌入(nearest feature space embedding,NFSE)方法选取最近邻特征空间时使用欧氏距离度量,导致样本的类内离散度和类间离散度同步变化,无法准确反映样本在高维空间的分布;选取每个样本最近邻特征空间都要遍历所有类,导致训练时间长。针对以上问题,提出非线性距离的最近邻特征空间嵌入改进方法(nearest feature space embedding method based on nonlinear distance metric,NDNFSE),引入非线性距离公式选取最近邻特征空间,并使用结合夹角度量的最近邻分类器,提高了识别率;仅在样本的近邻类中选取最近邻特征空间,有效减少了训练时间。实验表明,NDNFSE的训练时间明显低于NFSE,识别率总体高于各对比算法。
文摘Let X be a metric space with an ordering structure,A: X→X is a operator and x≤Ax for any x∈X. In this paper we prove a new fixed point theorem, which generalizes famous caristi fixed point theorem.
基金Supported by the National Natural Science Foundation of China under Grant Nos.71071013,71001004,and 71071012Foundation of Beijing Jiaotong University under Grant No.2009JBZ012-2
文摘In this paper, we present a new ear-following model, i.e. comprehensive optimal velocity model （COVM）, whose optimal velocity function not only depends on the following distance of the preceding vehicle, but also depends on the velocity difference with preceding vehicle. Simulation results show that COVM is an improvement over the previous ones theoretically. Then, the stability condition of the model is obtained by the linear stability analysis, which has shown that the model could obtain a bigger stable region than previous models in the phase diagram. Through the nonlinear analysis, the Burgers, Korteweg-de Vries （KdV） and modified KdV （mKdV） equations are derived for the triangular shock wave, the soliton wave, and the kink-antikink soliton wave. At the same time, numerical simulations are also carried out to show that the model could simulate these density waves.
基金The project is supported by Henan Province Natural Science Fund
文摘In this paper,the distance-sability of nonlinear discrete system is investigated by means of the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov function is avoided.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.DUT13JS05)
文摘In this paper,we study the very weak solutions to some nonlinear elliptic systems with righthand side integrable data with respect to the distance to the boundary.Firstly,we study the existence of the approximate solutions.Secondly,a priori estimates are given in the framework of weighted spaces.Finally,we prove the existence,uniqueness and regularity of the very weak solutions.
基金supported by the Research Grants Council of the Hong Kong Special Administration Region,China(No.9042388,CityU 11305716)
文摘The authors establish several estimates showing that the distance in W^(1,p),1 < p < ∞,between two immersions from a domain of R^n into R^(n+1) is bounded by the distance in L^p between two matrix fields defined in terms of the first two fundamental forms associated with each immersion. These estimates generalize previous estimates obtained by the authors and P. G. Ciarlet and weaken the assumptions on the fundamental forms at the expense of replacing them by two different matrix fields.
