Unsupervised Similarity Learning for Spectral Clustering

TMLR Paper3772 Authors

Abstract:

Spectral clustering is a widely adopted method capable of identifying non-convex cluster boundaries.
However, traditional spectral clustering requires the definition of a predefined similarity metric for constructing the Laplacian matrix, a requirement that limits flexibility and adaptability.
Instead of predefining this metric upfront as a fixed parametric function, we introduce a novel approach that learns the optimal parameters of a similarity function through parameter optimization.
This optimizes a similarity function to assign high similarity values to data pairs with shared discriminative features and low values to those without such features.
Previous methods, which also adapt similarity measures, often depend on hyperparameters or resort to non-convex optimization strategies, which are unsuitable in unsupervised scenarios due to their dependency on initial conditions and inability to validate using labels.
Our proposed method leverages convex optimization to learning
the parameters of the similarity metrics without relying on hyperparameters, thus ensuring robust and reliable unsupervised learning suitable for spectral clustering.
We demonstrate the effectiveness of our approach across multiple benchmark datasets, confirming its superiority in performance and adaptability.

Submission Length: Regular submission (no more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=xtgDcssHBP&referrer=%5BAuthor%20Console%5D(%2Fgroup%3Fid%3DTMLR%2FAuthors%23your-submissions)

Changes Since Last Submission: Fixed a typo in Corollar 1 from $2d^{2}(x,y)-3\sigma^{2}=2(u(x,y)+1)-3\sigma^{2}\to\textcolor{blue}{2d(x,y)}-3\sigma^{2}=2(u(x,y)+1)-3\sigma^{2}$ as suggested by the **Reviewer kuMq**.

Assigned Action Editor: ~Ofir_Lindenbaum1

Submission Number: 3772