Universal Clustering Bounds
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Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Keywords: nonnegative matrix factorization, orthogonal, subspace, k-means, clustering
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TL;DR: Unifies Euclidean clustering and ONMF under the umbrella of subspace clustering, with a universal bound
Abstract: This paper seamlessly integrates several fundamental learning tasks under the umbrella of subspace clustering, namely orthogonal nonnegative matrix factorization, and K-means clustering. Within this framework, we unveil a unified, closed-form solution that elegantly addresses these tasks. Our main theoretical contribution establishes that our deterministic solution achieves perfect accuracy when the data exhibits sufficiently well-defined clusters. Furthermore, the immediate relaxation of our solution yields practical algorithms that not only rival but also surpass the current state-of-the-art in these complex problem domains. This achievement is corroborated by a comprehensive array of experiments conducted on synthetic datasets, as well as on a diverse set of five real-world datasets.
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Submission Number: 2105
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