The kernel recursive least-squares algorithm
The kernel recursive least-squares algorithm
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DOI：
10.1109/tsp.2004.830985
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发表时间：
2004-08-01
影响因子：
5.4
通讯作者：
Meir, R
中科院分区：
文献类型：
--
作者：
Engel, Y;Mannor, S;Meir, R
我们提出了递归最小二乘（RLS）算法的非线性版本。我们的。算法在由Mercer内核引起的高维特征空间中执行线性回归，因此可用于递归构造最小于点的求解解决方案，以针对信号处理应用中经常遇到的非线性最小二乘问题。为了使解决方案正规化并保持算法的复杂性，我们使用顺序稀疏过程，仅当将其特征空间图像无法充分近似地结合到以前接收的样品的图像时，才能在内核表示中允许新的输入样本。这种稀疏过程允许算法通常实时在线运行。我们分析了算法的行为，将其比例属性与支持向量机的缩放属性进行比较，并证明了其在求解两个信号处理问题时间序列预测和通道均衡方面的效用。
We present a nonlinear version of the recursive least squares (RLS) algorithm. Our. algorithm performs linear regression in a high-dimensional feature space induced by a Mercer kernel and can therefore be used to recursively construct minimum mean-squared-error solutions to nonlinear least-squares problems that are frequently encountered in signal processing applications. In order to regularize solutions and keep the complexity of the algorithm bounded, we use a sequential sparsification process that admits into the kernel representation a new input sample only if its feature space image cannot be sufficiently well approximated by combining the images of previously admitted samples. This sparsification procedure allows the algorithm to operate online, often in real time. We analyze the behavior of the algorithm, compare its scaling properties to those of support vector machines, and demonstrate its utility in solving two signal processing problems-time-series prediction and channel equalization.