Spectral Clustering in Convex and Constrained Settings

TL;DR

The paper addresses the challenge of incorporating pairwise constraints into semidefinite spectral clustering (SDSC) by introducing three frameworks: Constrained, Active, and Self-Taught Semidefinite Spectral Clustering (CSDSC, ASDSC, STSDSC). Each framework leverages a feasible matrix $Y^*$ from projected semidefinite relaxation to guide clustering, with CSDSC embedding constraints directly, ASDSC enabling active constraint acquisition, and STSDSC employing self-teaching to expand the constraint set. Empirical results on datasets such as Hepatitis, Iris, Wine, and Twomoon show that the constrained variants outperform baselines, with STSDSC delivering the strongest performance under limited supervision. The work highlights the practical value of constrained SDSC for real-world clustering tasks and provides public code to facilitate adoption and further research.

Abstract

Spectral clustering methods have gained widespread recognition for their effectiveness in clustering high-dimensional data. Among these techniques, constrained spectral clustering has emerged as a prominent approach, demonstrating enhanced performance by integrating pairwise constraints. However, the application of such constraints to semidefinite spectral clustering, a variant that leverages semidefinite programming to optimize clustering objectives, remains largely unexplored. In this paper, we introduce a novel framework for seamlessly integrating pairwise constraints into semidefinite spectral clustering. Our methodology systematically extends the capabilities of semidefinite spectral clustering to capture complex data structures, thereby addressing real-world clustering challenges more effectively. Additionally, we extend this framework to encompass both active and self-taught learning scenarios, further enhancing its versatility and applicability. Empirical studies conducted on well-known datasets demonstrate the superiority of our proposed framework over existing spectral clustering methods, showcasing its robustness and scalability across diverse datasets and learning settings. By bridging the gap between constrained learning and semidefinite spectral clustering, our work contributes to the advancement of spectral clustering techniques, offering researchers and practitioners a versatile tool for addressing complex clustering challenges in various real-world applications. Access to the data, code, and experimental results is provided for further exploration (https://github.com/swarupbehera/SCCCS).

Figures (3)

• Figure 1: Overview of data clustering methods.
• Figure 2: Overview of the proposed frameworks.
• Figure 3: Comparison of Average Rand Index among algorithms with varying constraint rates.