Adaptive Learning in Cartesian Product of Reproducing Kernel Hilbert Spaces
Adaptive Learning in Cartesian Product of Reproducing Kernel Hilbert Spaces
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DOI：
10.1109/tsp.2015.2463261
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发表时间：
2014-08
影响因子：
5.4
通讯作者：
M. Yukawa
中科院分区：
文献类型：
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作者：
M. Yukawa
提出了一种新的基于多再生核Hilbert空间笛卡尔积上的迭代正交投影的自适应学习算法。目标是估计或跟踪假定包含多个分量的非线性函数，诸如i）线性和非线性分量以及ii）高频和低频分量。在这种情况下，使用多个RKHS允许多分量函数的紧凑表示。该算法是作者提出的两种不同方法的结合：多核自适应滤波和超平面沿着仿射子空间投影算法（HYPASS）。在特定情况下，RKHS的“和”空间是同构的，在一个直接的对应关系下，到产品空间，因此所提出的算法也可以被视为一个迭代投影方法在和空间。数值算例表明了该算法的有效性。
We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The objective is to estimate or track nonlinear functions that are supposed to contain multiple components such as i) linear and nonlinear components and ii) high- and low- frequency components. In this case, the use of multiple RKHSs permits a compact representation of multicomponent functions. The proposed algorithm is where two different methods of the author meet: multikernel adaptive filtering and the algorithm of hyperplane projection along affine subspace (HYPASS). In a particular case, the “sum” space of the RKHSs is isomorphic, under a straightforward correspondence, to the product space, and hence the proposed algorithm can also be regarded as an iterative projection method in the sum space. The efficacy of the proposed algorithm is shown by numerical examples.