Generalised density function estimation using moments and the characteristic function

Esterhuizen, Gerhard (Stellenbosch : University of Stellenbosch, 2003-03)

Thesis

ENGLISH ABSTRACT: Probability density functions (PDFs) and cumulative distribution functions (CDFs) play a central role in statistical pattern recognition and verification systems. They allow observations that do not occur according to deterministic rules to be quantified and modelled. An example of such observations would be the voice patterns of a person that is used as input to a biometric security device. In order to model such non-deterministic observations, a density function estimator is employed to estimate a PDF or CDF from sample data. Although numerous density function estimation techniques exist, all the techniques can be classified into one of two groups, parametric and non-parametric, each with its own characteristic advantages and disadvantages. In this research, we introduce a novel approach to density function estimation that attempts to combine some of the advantages of both the parametric and non-parametric estimators. This is done by considering density estimation using an abstract approach in which the density function is modelled entirely in terms of its moments or characteristic function. New density function estimation techniques are first developed in theory, after which a number of practical density function estimators are presented. Experiments are performed in which the performance of the new estimators are compared to two established estimators, namely the Parzen estimator and the Gaussian mixture model (GMM). The comparison is performed in terms of the accuracy, computational requirements and ease of use of the estimators and it is found that the new estimators does combine some of the advantages of the established estimators without the corresponding disadvantages.

AFRIKAANSE OPSOMMING: Waarskynlikheids digtheidsfunksies (WDFs) en Kumulatiewe distribusiefunksies (KDFs) speel 'n sentrale rol in statistiese patroonherkenning en verifikasie stelsels. Hulle maak dit moontlik om nie-deterministiese observasies te kwantifiseer en te modelleer. Die stempatrone van 'n spreker wat as intree tot 'n biometriese sekuriteits stelsel gegee word, is 'n voorbeeld van so 'n observasie. Ten einde sulke observasies te modelleer, word 'n digtheidsfunksie afskatter gebruik om die WDF of KDF vanaf data monsters af te skat. Alhoewel daar talryke digtheidsfunksie afskatters bestaan, kan almal in een van twee katagoriee geplaas word, parametries en nie-parametries, elk met hul eie kenmerkende voordele en nadele. Hierdie werk Ie 'n nuwe benadering tot digtheidsfunksie afskatting voor wat die voordele van beide die parametriese sowel as die nie-parametriese tegnieke probeer kombineer. Dit word gedoen deur digtheidsfunksie afskatting vanuit 'n abstrakte oogpunt te benader waar die digtheidsfunksie uitsluitlik in terme van sy momente en karakteristieke funksie gemodelleer word. Nuwe metodes word eers in teorie ondersoek en ontwikkel waarna praktiese tegnieke voorgele word. Hierdie afskatters het die vermoe om 'n wye verskeidenheid digtheidsfunksies af te skat en is nie net ontwerp om slegs sekere families van digtheidsfunksies optimaal voor te stel nie. Eksperimente is uitgevoer wat die werkverrigting van die nuwe tegnieke met twee gevestigde tegnieke, naamlik die Parzen afskatter en die Gaussiese mengsel model (GMM), te vergelyk. Die werkverrigting word gemeet in terme van akkuraatheid, vereiste numeriese verwerkingsvermoe en die gemak van gebruik. Daar word bevind dat die nuwe afskatters weI voordele van die gevestigde afskatters kombineer sonder die gepaardgaande nadele.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/1001
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