Εξηγήσιμη ομαδοποίηση σε ευσταθή στιγμιότυπα

Παπανικολάου, Ηλίας; Papanikolaou, Ilias

dc.contributor.author	Παπανικολάου, Ηλίας	el
dc.contributor.author	Papanikolaou, Ilias	en
dc.date.accessioned	2023-05-24T07:00:14Z
dc.date.available	2023-05-24T07:00:14Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/57751
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.25448
dc.rights	Default License
dc.subject	Ερμηνεύσιμη Μηχανική Μάθηση	el
dc.subject	Interpretable Machine Learning	en
dc.subject	Εξηγήσιμη Ομαδοποίηση	el
dc.subject	Ανάλυση πέρα από τη χειρότερη περίπτωση	el
dc.subject	Ευστάθεια σε διαταραχές	el
dc.subject	Μετρικοί Χώροι	el
dc.subject	Explainable Clustering	en
dc.subject	Beyond the worst-case analysis	en
dc.subject	Perturbation stability	en
dc.subject	Metric Spaces	en
dc.title	Εξηγήσιμη ομαδοποίηση σε ευσταθή στιγμιότυπα	el
heal.type	bachelorThesis
heal.classification	Algorithms	en
heal.language	el
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2023-04-04
heal.abstract	This thesis is concerned with the explainable clustering problem under stability assumptions. Explainable Clustering is an interpretation method developed by Dasgupta et al. that aims to provide concise explanations for the inclusion of each data point in a cluster. The question that we try to answer is whether the Price of Explainability, i.e. the inherent cost due to the restricted solution format that guarantees explainability, can be reduced if we assume that the input clustering instances satisfy either the proximity or the perturbation stability property. After we introduce several stability notions in the context of clustering and analyze the most important algorithms for explainable clustering, we show that under $a$-center stability, with $a = \Omega(k d^{\frac{1}{p}})$ there are explainable algorithms with constant approximation ratio. Next, we study the stability of several hard explainable clustering instances and prove that this dependence on the number of dimensions $d$ and clusters $k$ is necessary. More specifically, we manage to show that there are some hard clustering instances with the $\mathcal{l}_p$ objective that satisfy the $a$-proximity with $a = \Omega\left(kd^{\frac{1}{p}}\right)$ and there exist $\Omega(\sqrt{d})$-(metric) perturbation stable instances in the $k$-median case ($p = 1$), where $d$ is the number of the dimensions of the dataset. To prove the second result, we show that if a clustering instance satisfies the $a$-proximity property along with a property that ensures that all clusters in the optimal clustering have roughly the same cost, then this instance is $\Omega(\sqrt{a})$-metric perturbation stable. We conclude that it is not reasonable to assume that practical instances are stable enough for the Price of Explainability to reduce, under these stability assumptions.	en
heal.advisorName	Φωτάκης, Δημήτριος	el
heal.committeeMemberName	Παγουρτζής, Αριστείδης	el
heal.committeeMemberName	Χατζηαφράτης, Ευάγγελος	el
heal.committeeMemberName	Φωτάκης, Δημήτριος	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών. Τομέας Τεχνολογίας Πληροφορικής και Υπολογιστών	el
heal.academicPublisherID	ntua
heal.numberOfPages	84 σ.	el
heal.fullTextAvailability	false