FROM FIXED TO ADAPTIVE BUDGET ROBUST KERNEL ADAPTIVE FILTERING By SONGLIN ZHAO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy FROM FIXED TO ADAPTIVE BUDGET ROBUST KERNEL ADAPTIVE FILTERING By Songlin Zhao December 2012 Chair: Jose C. Principe Major: Electrical and Computer Engineering Recently, owning to universal modeling capacity, convexity in performance surface and modest computational complexity, kernel adaptive filters have attracted more and more attention. Even though these methods achieve powerful classification and regression performance in complicated nonlinear problems, they have drawbacks. This work focuses on how to improve kernel adaptive filters performance both on accuracy and computational complexity. After reviewing some existing adaptive filters cost functions, we introduce an information theoretic objective function, Maximal Correntropy Criterion (MCC), that contains high order statistical information. Here we propose to adopt this objective function for kernel adaptive filters to improve system accuracy performance in nonlinear and non-Gaussian scenario. To determine the free parameter, kernel width in correntropy, an adaptive method based on the statistical property of the prediction error is proposed. After that we propose a growing and pruning method to realize a fixed-budget kernel least mean square (KLMS) algorithm based on improvements of the quantized kernel least mean square algorithm and a new significance measure. The end result is to control the computational complexity and memory requirement of kernel adaptive filters while preserving the accuracy as much as possible. This balance between accuracy and filter model order is explored from the perspective of information learning. Indeed the issue is how to deal with the trade-off between system complexity and