  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).
