Journal ArticleDOI
Extended Kernel Recursive Least Squares Algorithm
TLDR
A kernelized version of the extended recursive least squares (EX-KRLS) algorithm which implements for the first time a general linear state model in reproducing kernel Hilbert spaces (RKHS) which only requires inner product operations between input vectors, thus enabling the application of the kernel property.Abstract:
This paper presents a kernelized version of the extended recursive least squares (EX-KRLS) algorithm which implements for the first time a general linear state model in reproducing kernel Hilbert spaces (RKHS), or equivalently a general nonlinear state model in the input space. The center piece of this development is a reformulation of the well known extended recursive least squares (EX-RLS) algorithm in RKHS which only requires inner product operations between input vectors, thus enabling the application of the kernel property (commonly known as the kernel trick). The first part of the paper presents a set of theorems that shows the generality of the approach. The EX-KRLS is preferable to 1) a standard kernel recursive least squares (KRLS) in applications that require tracking the state-vector of general linear state-space models in the kernel space, or 2) an EX-RLS when the application requires a nonlinear observation and state models. The second part of the paper compares the EX-KRLS in nonlinear Rayleigh multipath channel tracking and in Lorenz system modeling problem. We show that the proposed algorithm is able to outperform the standard KRLS and EX-RLS in both simulations.read more
Citations
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Journal ArticleDOI
Quantized Kernel Least Mean Square Algorithm
TL;DR: A quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method, and a lower and upper bound on the theoretical value of the steady-state excess mean square error is established.
Journal ArticleDOI
Spatiotemporal Learning via Infinite-Dimensional Bayesian Filtering and Smoothing: A Look at Gaussian Process Regression Through Kalman Filtering
TL;DR: Methods for converting spatiotemporal Gaussian process regression problems into infinite-dimensional state-space models are presented and the use of machine-learning models in signal processing becomes computationally feasible, and it opens the possibility to combine machine- learning techniques with signal processing methods.
Journal ArticleDOI
An Information Theoretic Approach of Designing Sparse Kernel Adaptive Filters
TL;DR: A systematic sparsification scheme is proposed, which can drastically reduce the time and space complexity without harming the performance of kernel adaptive filters.
Journal ArticleDOI
Quantized Kernel Recursive Least Squares Algorithm
TL;DR: By incorporating a simple online vector quantization method, a recursive algorithm is derived to update the solution, namely the quantized kernel recursive least squares algorithm.
Journal ArticleDOI
Kernel Recursive Least-Squares Tracker for Time-Varying Regression
TL;DR: This paper derives the standard KRLS equations from a Bayesian perspective and takes advantage of this framework to incorporate forgetting in a consistent way, thus enabling the algorithm to perform tracking in nonstationary scenarios and is the first kernel adaptive filtering algorithm that includes a forgetting factor in a principled and numerically stable manner.
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Maximum likelihood from incomplete data via the EM algorithm
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Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.