一般来说,令特征空间为希尔伯特空间较为常见。希尔伯特空间就是完备的内积空间。这里涉及到两个概念:(1)内积空间;(2)完备性。内积空间是具有内积的线性空间,通过内积可以定义范数、距离等概念。完备性是指空间中的任意柯西序列极限均存在,这是实数性质在高维上的推广。一个简单的反例就是Q或QN。完备性是希尔伯特空间许多分析性质的
Domain adaptionRKHSMaximum mean difference (MMD)Lagrange multiplier method (LMM) optimizationSubspace learning of Reproducing Kernel Hilbert Space (RKHS) is most popular among domain adaption applications. The key goal is to embed the source and target domain samples into a common RKHS subspace where ...
Ref[3]最后和MMD的关系也很有意思,值得过一段时间认真研究下(see also "Maximum Mean Discrepancy Gradient Flow")【话说MMD是non-parametric inference里比较常用的distance,在选test fn是Lipschitz时和W1-dist有关,Paul Dupuis有用它和KL mix起来设计新的distance的文章,更general的dist和flow在“KALE Flow: A ...
mmdregularizationsamplingrkhsgradient-flowsampling-methodsf-divergencewasserstein-gradient-flowsparticle-flowreproducing-kernel-hilbert-space UpdatedDec 20, 2024 Python Additive interaction modelling using I-priors kernelregressionrkhshilbert-spacesfisher-informationrkksempirical-bayeskrein-spacesreproducing-kernel ...
在支持向量机SVM中,通常使用核函数将样本输入空间转化为再生核Hilbert空间(Reproducing kernel Hilbert space,RKHS),提高算法处理非线性分类问题的性能。相比于Hilbert空间,RKHS有着很多优秀的性质。下面从RKHS的定义、RKHS刻画、RKHS与Hilbert空间关系等三个部分展开工作。
A reasonable method should be that the MMD of the source and target domain data with the same label should be as small as possible after RKHS subspace transformation. However, the labels of target domain data are unknown and there is no way to model according to this criterion. In this ...
And the experiments show the superiority of MSE criterion, which performs better than the common Maximum Mean Difference (MMD) and the Covariance Matrix (CovM) criteria. Furthermore, considering the robustness of the RKHS subspace learning framework to the data dimension, we propose the domain ...