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dc.contributor.advisorJenssen, Robert
dc.contributor.authorMyhre, Jonas Nordhaug
dc.date.accessioned2016-11-02T12:58:31Z
dc.date.available2016-11-02T12:58:31Z
dc.date.issued2016-10-14
dc.description.abstractA wide range of machine learning methods have taken advantage of density estimates and their derivatives, including methodology related to principal manifolds and mode seeking, finding use in a number of real applications. However, research concerned with improving density derivative estimation and its practical use have received relatively limited attention. Also, the fact that the derivatives of a distribution over a point set can provide a statistical framework for manifold learning has not yet been used to its full potential. The aim of this thesis is to help fill these gaps, and to provide novel machine learning algorithms and tools based on principal manifolds using density derivatives. We present three different lines of works aiming towards this goal. The first work presents a fast and exact kernel density derivative estimator. The method takes advantage of the fact that the derivatives of a multivariate product kernel can be decomposed into a product of univariate differentiations. By cutting redundant multiplications we obtain significant speedup while retaining an exact estimator. Next, we present a novel algorithm for manifold unwrapping based on tracing the gradient flow along a manifold estimated using density derivatives. This allows a direct and geometrically intuitive approach consistent with theory from differential geometry. Promising results are shown on both real and synthetic data sets. Finally, we provide a novel framework for robust mode seeking. It is based on ensemble clustering and resampling techniques. This allows a clustering algorithm that is both robust with respect to parameter choices as well as being capable of handling data sets of very high dimension. Concretely, we build the ensemble by running multiple instances of a k nearest neighbor mode seeking algorithm. We show good results on benchmark tests, as well as a case study involving medical health records.en_US
dc.description.doctoraltypeph.d.en_US
dc.description.popularabstractI dette arbeidet presenterer vi nye algoritmer for ulineær maskinlæring. Veldig mange målinger ute i den virkelige verden kan tilskrives ulineær struktur. For i eksempel medisinske bilder hvor pasienten beveger seg etterhvert som bildene taes slik at bildene i utgangspunktet ser like ut, men den underliggende strukturen endrer seg. Vi har i dette arbeidet tatt utganspunkt i såkalte prinsipalkurver og prinsipale overflater. Disse metodene er spesielt egnede til å takle datasett med vanskelig geometri, samtidig som de er robuste overfor støy. Vi har utviklet algoritmer innenfor nye områder og raskere og mer robuste algoritmer på mere kjente områder.en_US
dc.descriptionThe papers of this thesis are not available in Munin. <br> Paper I: Shaker, M. Myhre, J. N., Erdogmus, D.: “Computationally Efficient Exact Calculation of Kernel Density Derivatives". Available in <a href=http://dx.doi.org/10.1007/s11265-014-0904-1> Journal of Signal Processing Systems 2015, 81(3):321-332. </a> <br> Paper 2: Myhre, J. N., Shaker, M., Kaba, M. D., Erdogmus, D.: “Manifold unwrapping using density ridges". (Manuscript). <br> Paper 3: Shaker, M., Myhre, J. N., Kaba, M. D., Erdogmus, D.: “Invertible nonlinear cluster unwrapping". Available in <a href=http://dx.doi.org/10.1109/MLSP.2014.6958878> 2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP). ISBN: 978-1-4799-3694-6. </a> <br> Paper 4: Myhre, J. N., Mikalsen, K., Løkse, S., Jenssen, R.: «A robust clustering using a kNN mode seeking ensemble". (Manuscript).en_US
dc.identifier.isbn978-82-8236-230-6 (trykt) og 978-82-8236-231-3 (pdf)
dc.identifier.urihttps://hdl.handle.net/10037/9921
dc.language.isoengen_US
dc.publisherUiT Norges arktiske universiteten_US
dc.publisherUiT The Arctic University of Norwayen_US
dc.rights.accessRightsopenAccessen_US
dc.subject.courseIDDOKTOR-004
dc.subjectMachine Learningen_US
dc.titleMachine Learning using Principal Manifolds and Mode Seekingen_US
dc.typeDoctoral thesisen_US
dc.typeDoktorgradsavhandlingen_US


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