针对核范数正则约束使得矩阵低秩性不足、奇异值分解对大规模数据计算代价大、传统优化算法需人为调试最优参数的问题,提出一种基于Schatten-p范数和近端交替线性最小化算法的深度可学习子空间聚类算法。首先,通过Schatten-p范数作为低...针对核范数正则约束使得矩阵低秩性不足、奇异值分解对大规模数据计算代价大、传统优化算法需人为调试最优参数的问题,提出一种基于Schatten-p范数和近端交替线性最小化算法的深度可学习子空间聚类算法。首先,通过Schatten-p范数作为低秩正则项,使得子空间聚类系数矩阵更好地满足低秩结构;其次,利用Schatten-p范数的矩阵分解格式,避免了SVD计算代价大的不足;最后,针对传统优化算法须人为调整参数的问题,根据激活函数和稀疏正则项的对应关系,建立深度学习网络框架,通过数据自适应学习得到最优参数集。在MNIST手写数字、Amsterdam Library of Object Images和ORL人脸三个数据集上进行聚类的数值实验,结果表明:提出的子空间聚类算法相比于谱聚类、低秩子空间聚类和稀疏子空间聚类算法有更好的聚类性能。展开更多
Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_...Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).展开更多
文摘针对核范数正则约束使得矩阵低秩性不足、奇异值分解对大规模数据计算代价大、传统优化算法需人为调试最优参数的问题,提出一种基于Schatten-p范数和近端交替线性最小化算法的深度可学习子空间聚类算法。首先,通过Schatten-p范数作为低秩正则项,使得子空间聚类系数矩阵更好地满足低秩结构;其次,利用Schatten-p范数的矩阵分解格式,避免了SVD计算代价大的不足;最后,针对传统优化算法须人为调整参数的问题,根据激活函数和稀疏正则项的对应关系,建立深度学习网络框架,通过数据自适应学习得到最优参数集。在MNIST手写数字、Amsterdam Library of Object Images和ORL人脸三个数据集上进行聚类的数值实验,结果表明:提出的子空间聚类算法相比于谱聚类、低秩子空间聚类和稀疏子空间聚类算法有更好的聚类性能。
文摘Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).
