A stochastic behavior analysis of stochastic restricted-gradient descent   algorithm in reproducing kernel Hilbert spaces
  This paper presents a stochastic behavior analysis of a kernel-based stochastic restricted-gradient descent method. The restricted gradient gives a steepest ascent direction within the so-called dictionary subspace. The analysis provides the transient and steady state performance in the mean squared error criterion. It also includes stability conditions in the mean and mean-square sense. The present study is based on the analysis of the kernel normalized least mean square (KNLMS) algorithm initially proposed by Chen et al. Simulation results validate the analysis. 
Masa-aki Takizawa, Masahiro Yukawa, and Cedric Richard
cs.LG stat.ML