Algorithms for sparsity constrained principal component analysis

buir.advisorPınar, Mustafa Çelebi
dc.contributor.authorAktaş, Fatih Selim
dc.date.accessioned2023-08-11T11:28:31Z
dc.date.available2023-08-11T11:28:31Z
dc.date.copyright2023-07
dc.date.issued2023-07
dc.date.submitted2023-08-09
dc.descriptionCataloged from PDF version of article.
dc.description Thesis (Master's): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2023.
dc.descriptionIncludes bibliographical references (leaves 74-82).
dc.description.abstractThe classical Principal Component Analysis problem consists of finding a linear transform that reduces the dimensionality of the original dataset while keeping most of the variation. Extra sparsity constraint sets most of the coefficients to zero which makes interpretation of the linear transform easier. We present two approaches to the sparsity constrained Principal Component Analysis. Firstly, we develop computationally cheap heuristics that can be deployed in very high-dimensional problems. Our heuristics are justified with linear algebra approximations and theoretical guarantees. Furthermore, we strengthen our algorithms by deploying the necessary conditions for the optimization model. Secondly, we use a non-convex log-sum penalty in the semidefinite space. We show a connection to the cardinality function and develop an algorithm, PCA Sparsified, to solve the problem locally via solving a sequence of convex optimization problems. We analyze the theoretical properties of this algorithm and comment on the numerical implementation. Moreover, we derive a pre-processing method that can be used with previous approaches. Finally, our findings from the numerical experiments we conducted show that our greedy algorithms scale to high dimensional problems easily while being highly competitive in many problems with state-of-art algorithms and even beating them uniformly in some cases. Additionally, we illustrate the effectiveness of PCA Sparsified on small dimensional problems in terms of variance explained. Although it is computationally very demanding, it consistently outperforms local and greedy approaches.
dc.description.provenanceMade available in DSpace on 2023-08-11T11:28:31Z (GMT). No. of bitstreams: 1 B162307.pdf: 1469738 bytes, checksum: 3dbf91d542f815c4a84535c8594c135f (MD5) Previous issue date: 2023-07en
dc.description.statementofresponsibilityby Fatih Selim Aktaş
dc.embargo.release2024-02-09
dc.format.extentxi, 92 leaves : charts ; 30 cm.
dc.identifier.itemidB162307
dc.identifier.urihttps://hdl.handle.net/11693/112649
dc.language.isoEnglish
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectSparse PCA
dc.subjectGreedy algorithms
dc.subjectSDP
dc.titleAlgorithms for sparsity constrained principal component analysis
dc.title.alternativeSeyrek kısıtlı temel bileşen analizi için algoritmalar
dc.typeThesis
thesis.degree.disciplineIndustrial Engineering
thesis.degree.levelMaster's
thesis.degree.nameMS (Master of Science)

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