A Graph-Theoretic Framework for Understanding Open-World Semi-Supervised Learning

• URL: http://arxiv.org/abs/2311.03524v1
• Date: Mon, 6 Nov 2023 21:15:09 GMT
• Title: A Graph-Theoretic Framework for Understanding Open-World Semi-Supervised Learning
• Authors: Yiyou Sun and Zhenmei Shi and Yixuan Li
• Abstract summary: Open-world semi-supervised learning aims at inferring both known and novel classes in unlabeled data. This paper formalizes a graph-theoretic framework tailored for the open-world setting. Our graph-theoretic framework illuminates practical algorithms and provides guarantees.
• Score: 33.05104609131764
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Open-world semi-supervised learning aims at inferring both known and novel classes in unlabeled data, by harnessing prior knowledge from a labeled set with known classes. Despite its importance, there is a lack of theoretical foundations for this problem. This paper bridges the gap by formalizing a graph-theoretic framework tailored for the open-world setting, where the clustering can be theoretically characterized by graph factorization. Our graph-theoretic framework illuminates practical algorithms and provides guarantees. In particular, based on our graph formulation, we apply the algorithm called Spectral Open-world Representation Learning (SORL), and show that minimizing our loss is equivalent to performing spectral decomposition on the graph. Such equivalence allows us to derive a provable error bound on the clustering performance for both known and novel classes, and analyze rigorously when labeled data helps. Empirically, SORL can match or outperform several strong baselines on common benchmark datasets, which is appealing for practical usage while enjoying theoretical guarantees.

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