Name
Title | ||
|---|---|---|
On Kernel design for online model selection by Gaussian multikernel adaptive filtering |
Abstract | ||
|---|---|---|
In this paper, we highlight a design of Gaussian kernels for online model selection by the multikernel adaptive filtering approach. In the typical multikernel adaptive filtering, the maximum value that each kernel function can take is one. This means that, if one employs multiple Gaussian kernels with multiple variances, the one with the largest variance would become dominant in the kernelized input vector (or matrix). This makes the autocorrelation matrix of the the kernelized input vector be ill-conditioned, causing significant deterioration in convergence speed. To avoid this ill-conditioned problem, we consider the normalization of the Gaussian kernels. Because of the normalization, the condition number of the autocorrelation matrix is improved, and hence the convergence behavior is improved considerably. As a possible alternative to the original multikernel-based online model selection approach using the Moreau-envelope approximation, we also study an adaptive extension of the generalized forward-backward splitting (GFBS) method to suppress the cost function without any approximation. Numerical examples show that the original approximate method tends to select the correct center points of the Gaussian kernels and thus outperforms the exact method. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/APSIPA.2014.7041802 | Asia-Pacific Signal and Information Processing Association, 2014 Annual Summit and Conference |
Keywords | Field | DocType |
Gaussian processes,adaptive filters,approximation theory,convergence of numerical methods,correlation theory,matrix algebra,GFBS method,Gaussian kernel normalization,Gaussian multikernel adaptive filtering,Moreau-envelope approximation,adaptive extension,autocorrelation matrix,convergence speed,correct center points,cost function suppression,generalized forward-backward splitting,ill-conditioned problem,kernel design,kernelized input vector,multikernel-based online model selection approach,multiple variances,online model selection | Kernel (linear algebra),Condition number,Mathematical optimization,Normalization (statistics),Autocorrelation matrix,Algorithm,Multikernel,Gaussian,Adaptive filter,Mathematics,Kernel (statistics) | Conference |
ISSN | Citations | PageRank |
2309-9402 | 2 | 0.37 |
References | Authors | |
9 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Osamu Toda | 1 | 2 | 0.37 |
| Masahiro Yukawa | 2 | 272 | 30.44 |