000000332 001__ 332 000000332 005__ 20260311152000.0 000000332 0247_ $$2DOI$$a10.6083/M4ZG6Q60 000000332 037__ $$aETD 000000332 245__ $$aLocally defined principal curves and surfaces 000000332 260__ $$bOregon Health and Science University 000000332 269__ $$a2008 000000332 336__ $$aDissertation 000000332 502__ $$bPh.D. 000000332 520__ $$aPrincipal curves are smooth, self‑consistent curves that pass through the center of a data distribution and are widely used for dimensionality reduction and feature extraction. However, their traditional definitions are ill‑posed and lead to practical difficulties in algorithm design. This dissertation introduces a novel framework that redefines principal curves, surfaces, and manifolds using the gradient and Hessian of the probability density function, providing a clear geometric interpretation and a unified view of clustering, principal curves, and manifold learning. The approach supports multiple density estimation methods and leads to practical algorithms, which are demonstrated across diverse applications including image processing, signal analysis, and manifold learning. 000000332 540__ $$fCC BY 000000332 542__ $$fIn copyright - single owner 000000332 650__ $$aCluster Analysis$$028809 000000332 6531_ $$aprincipal curves and manifolds 000000332 6531_ $$anonparametric dimensionality reduction 000000332 6531_ $$aunsupervised learning 000000332 6531_ $$agaussian distribution 000000332 6531_ $$aalgebraic curves 000000332 691__ $$aSchool of Medicine$$041369 000000332 692__ $$aDepartment of Science and Engineering$$041447 000000332 7001_ $$aOzertem, Umut$$uOregon Health and Science University$$041354 000000332 7201_ $$aErdogmus, Deniz$$uOregon Health and Science University$$041354$$7Personal$$eAdvisor 000000332 8564_ $$9d17b5f1b-ba13-4da7-9019-13e20ccc4a00$$s8194064$$uhttps://digitalcollections.ohsu.edu/record/332/files/333_etd.pdf$$ePublic$$24ea22ce23a5b98d84e2c1139c4afe009$$31 000000332 905__ $$a/rest/prod/jm/21/4p/16/jm214p16v 000000332 909CO $$ooai:digitalcollections.ohsu.edu:332$$pstudent-work 000000332 956__ $$aGet Accessible Copy$$uhttps://ohsu.libwizard.com/f/requestaccessibledocument 000000332 980__ $$aTheses and Dissertations