In this paper, the similarity-invariant subspaces of B(H), which is tile Banach algebra of all bounded linear operators on a separable infinite-dimensional Hilbert space H, are completely characterized and the represe...In this paper, the similarity-invariant subspaces of B(H), which is tile Banach algebra of all bounded linear operators on a separable infinite-dimensional Hilbert space H, are completely characterized and the representations of bounded linear maps on B(H) which preserve similarity in both directions are given.展开更多
LSPE(Locality and Similarity Preserving Embedding)特征选择算法首先基于KNN定义图结构来保持数据的局部性,再基于定义图学习数据的低维重构系数来保持数据的局部性和相似性。两个步骤独立进行,缺乏交互。由于近邻个数是人为定义的,...LSPE(Locality and Similarity Preserving Embedding)特征选择算法首先基于KNN定义图结构来保持数据的局部性,再基于定义图学习数据的低维重构系数来保持数据的局部性和相似性。两个步骤独立进行,缺乏交互。由于近邻个数是人为定义的,使得学习到的图结构不具备自适应的近邻,不是最优的,进而影响算法性能。为优化LSPE算法的性能,提出改进的局部和相似性保持特征选择算法,将图学习与稀疏重构、特征选择并入同一个框架,使得图学习和稀疏编码同时进行,其要求编码过程是稀疏的,自适应近邻的和非负的。所提算法旨在寻找一个能保持数据的局部性和相似性的投影,并对投影矩阵施加l(2,1)范数,进而选择能够保持局部性和相似性的相关特征。实验结果表明,改进后的算法减少了主观人为影响,消除了选择特征的不稳定性,对数据噪声鲁棒性更强,提高了图像分类的准确率。展开更多
基金This research is supported by the Excellent Young Teachers Program of MOE, P. R. C.by National Natural Science Foundation of China (No. 10071047)
文摘In this paper, the similarity-invariant subspaces of B(H), which is tile Banach algebra of all bounded linear operators on a separable infinite-dimensional Hilbert space H, are completely characterized and the representations of bounded linear maps on B(H) which preserve similarity in both directions are given.
文摘LSPE(Locality and Similarity Preserving Embedding)特征选择算法首先基于KNN定义图结构来保持数据的局部性,再基于定义图学习数据的低维重构系数来保持数据的局部性和相似性。两个步骤独立进行,缺乏交互。由于近邻个数是人为定义的,使得学习到的图结构不具备自适应的近邻,不是最优的,进而影响算法性能。为优化LSPE算法的性能,提出改进的局部和相似性保持特征选择算法,将图学习与稀疏重构、特征选择并入同一个框架,使得图学习和稀疏编码同时进行,其要求编码过程是稀疏的,自适应近邻的和非负的。所提算法旨在寻找一个能保持数据的局部性和相似性的投影,并对投影矩阵施加l(2,1)范数,进而选择能够保持局部性和相似性的相关特征。实验结果表明,改进后的算法减少了主观人为影响,消除了选择特征的不稳定性,对数据噪声鲁棒性更强,提高了图像分类的准确率。
