This paper describes a method for performing kernel smoothing regression in an incremental, adaptive manner. A simple and fast combination of incremental vector quantization with kernel smoothing regression using adaptive bandwidth is shown to be effective for online modeling of environmental datasets. The method is illustrated on openly available datasets corresponding to the Tropical Atmosphe...

We review heat kernel smoothing techniques for denoising and regressing data in irregularly shaped domains embedded in Euclidean spaces. This is a problem often encountered in functional data analysis and medical imaging. In this chapter, we present a unified mathematical framework based on the eigenfunctions of the Laplace-Beltrami operators defined on irregular domains. Numerical implementati...

This study evaluates the effects of spatial smoothing on inter-subject correlation (ISC) analysis for FMRI data using the traditional model based analysis as a reference. So far within ISC analysis the effects of smoothing have not been studied systematically and linear Gaussian filters with varying kernel widths have been used without better knowledge about the effects of filtering. Instead, w...

The trend-renewal-process (TRP) is defined to be a time-transformed renewal process, where the time transformation is given by a trend function λ(·) which is similar to the intensity of a nonhomogeneous Poisson process (NHPP). A nonparametric maximum likelihood estimator of the trend function of a TRP can be obtained much in the same manner as for the NHPP using kernel smoothing. But for a TRP ...

Iowa State University, The University of Western Australia and Iowa State University We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing bandwidth, which is effectively a studentized L2-distance between the kernel t...

Regression analysis when the underlying regression function has jumps is a research problem with many applications. In practice, jumps often represent structure changes of a related process. Hence, it is important to detect them accurately from observed noisy data. In the literature, there are some jump detectors proposed, most of which are based on local constant or local linear kernel smoothi...

Recent proposals for implementation of kernel based nonparametric curve estimators are seen to be faster than naive direct implementations by factors up into the hundreds. The main ideas behind two different approaches of this type are made clear. Careful speed comparisons in a variety of settings, and using a variety of machines and software is done. Various issues on computational accuracy an...

Kernel based learning has already found wide applications to solve several data mining problems. In this paper, we proposed an improved linear kernel with automatic smoothing parameter (Sp) selection compared to the classical approach. Experiment results using some classification related benchmark datasets reveal that the improved linear kernel performed better than some existing kernel techniq...