Year: 2014
Type: dissertation
Abstract: With the advent of the internet and advances in computing power, the collection of very large high-dimensional datasets has become feasible -understanding and modelling high-dimensional data has thus become a crucial activity, especially in the field of pattern recognition.Since non-parametric density estimators are data-driven and do not require or impose a pre-defined probability density function on data, they are very powerful tools for probabilistic data modelling and analysis.Conventional non-parametric density estimation methods, however, originated from the field of statistics and were not originally intended to perform density estimation in high-dimensional features spaces -as is often encountered in real-world pattern recognition tasks.Therefore we address the fundamental problem of non-parametric density estimation in high-dimensional feature spaces in this study.Recent advances in maximum-likelihood (ML) kernel density estimation have shown that kernel density estimators hold much promise for estimating nonparametric probability density functions in high-dimensional feature spaces.We therefore derive two new iterative kernel bandwidth estimators from the maximum-likelihood (ML) leaveone-out objective function and also introduce a new non-iterative kernel bandwidth estimator (based on the theoretical bounds of the ML bandwidths) for the purpose OpsommingMaksimumwaarskynlikheid-kerndigtheidskatting in Hoë-dimensionele Ruimtes deur
Authors: Van der Walt, Christiaan Maarten
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W629575809