[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117442-en":3,"doc-seo-117442-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},117442,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Graphs in Unsupervised Machine Learning - Dissertation","Graphs represent data points and their complex relationships, enabling modeling of intricate real-world systems across many tasks. By combining graph-structured data with suitable algorithms, unsupervised machine learning benefits from discovering patterns without labeled examples. This dissertation introduces unsupervised learning on graphs, emphasizing clustering and representation learning while weighing strengths and challenges of graph-based approaches. It proposes a new clustering method inspired by tangles to obtain interpretable soft hierarchies with theoretical guarantees and extensive empirical validation. It also studies graph autoencoders by linking non-linear architectures to linear models, showing linear baselines can match or exceed performance when node features are effectively exploited, supported by theory and experiments.","Graphs in Unsupervised Machine Learning  \nDissertation  \nder Mathematisch-Naturwissenschaftlichen Fakult¨at der Eberhard Karls Universit¨at T¨ubingen zur Erlangung des Grades eines  \nDoktors der Naturwissenschaften  \n(Dr. rer. nat.)  \nvorgelegt von  \nM. Sc. Solveig Peter  \naus Ditzingen  \nT¨ubingen  \n2024  \nGedruckt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakult¨at der Eberhard Karls Universit¨at T¨ubingen.  \nTag der m¨undlichen Qualifikation: 21.01.2025  \nDekan: Prof. Dr. Thilo Stehle  \n1. Berichterstatterin: Prof. Dr. Ulrike von Luxburg  \n2. Berichterstatter: Prof. Dr. Robert Williamson  \nAbstract  \nGraphs are versatile data structures that represent individual data points and the intricate relationships between them, making them invaluable for modeling complex real-world systems. Their flexibility allows them to be applied to a wide range of problems, and with appropriate algorithms, they have become crucial in many domains. In particular, unsupervised machine learning – where patterns are discovered without labeled data – has greatly benefited from integrating graphs. This thesis presents an introduction to unsupervised machine learning on graphs, focusing on clustering and representation learning. We explore the strengths and challenges of applying graphs to machine learning, emphasizing these two specific tasks. Our contributions span two distinct perspectives within unsupervised learning on graphs. In the first part, we propose a novel clustering method inspired by the concept of tangles from mathematical graph theory. Tangles are used to detect densely connected subsets within a graph, and we adapt this idea to cluster data across various domains. Our approach yields a soft clustering hierarchy that is often inherently interpretable. We provide theoretical performance guarantees across different data types and validate the method’s effectiveness through extensive empirical evaluations. The second part of this thesis delves into representation learning on graphs. We investigate the inductive biases of graph autoencoders, connecting their non-linear architecture to a linear model. Our empirical findings show that linear models can match or surpass the performance of non-linear graph auto-encoders when node features are effectively leveraged. Additionally, we analyze the constraints imposed by features on the solution space, offering theoretical and empirical evidence that these features are the key to achieving strong performance in this setting.  \nii  \nZusammenfassung  \nGraphen sind vielseitige Datenstrukturen, die einzelne Datenpunkte sowie die komplexen Beziehungen zwischen jenen abbilden. Durch ihre Vielseitigkeit sind sie f¨ur die Modellierung komplexer realer Systeme unverzichtbar geworden und dank ihrer Flexibilit¨at k¨onnen sie auf eine Vielzahl von Problemen angewendet werden. Sie sind, kombiniert mit geeigneten Algorithmen, in vielen Bereichen von entscheidender Bedeutung. Insbesondere profitiert das un¨uberwachte maschinelle Lernen – bei welchem Muster ohne gelabelte Daten detektiert werden – erheblich von der Integration von Graphen. Diese Arbeit bietet eine Einf¨uhrung in das un¨uberwachte maschinelle Lernen auf Graphen, mit dem Schwerpunkt auf Clustering und Repr¨asentationslernen. Wir elaborieren die positiven und negativen Aspekte der Verwendung von Graphen im maschinellen Lernen und konzentrieren uns dabei auf die beiden eben genannten Aufgaben. Unser Beitrag umfasst zwei unterschiedliche Perspektiven auf das un¨uberwachte Lernen auf Graphen. Im ersten Teil stellen wir eine neuartige Clustering-Methode vor, die vom Konzept eines “Tangles” aus der mathematischen Graphentheorie inspiriert ist. Tangles dienen dazu, dicht verbundene Teilmengen innerhalb eines Graphen zu identifizieren, und wir adaptieren diese Idee, um Daten aus verschiedenen Dom¨anen zu clustern. Unser Ansatz f¨uhrt zu einer weichen Clustering-Hierarchie, die oft von Natur aus interpretierbar ist. Wir pr¨asentieren theoreti","cbCaisO1DSxjKcw7","https://ap.wps.com/l/cbCaisO1DSxjKcw7","pdf",7093937,1,108,"English","en",105,"# Abstract\n# Zusammenfassung\n# Acknowledgements","[{\"question\":\"What tasks does the thesis focus on in unsupervised learning on graphs?\",\"answer\":\"The thesis centers on clustering and representation learning on graphs, discussing both the strengths and challenges of using graphs for these tasks.\"},{\"question\":\"How does the thesis approach clustering using the idea of tangles?\",\"answer\":\"It introduces a clustering method inspired by tangles from mathematical graph theory, using them to detect densely connected subsets and producing a soft clustering hierarchy.\"},{\"question\":\"What do the findings say about graph autoencoders versus linear models?\",\"answer\":\"The work shows that linear models can match or surpass non-linear graph autoencoders when node features are effectively leveraged, and it analyzes feature-induced constraints on the solution space.\"}]","Graphs in Unsupervised Machine Learning - 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