Scalable Clustering

Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. In this dissertation, we develop a provably clustering algorithm namely Scalable Clustering by Robust Loss Minimization (SCRLM) that performs well on Gaussian Mixture Models with outliers. We derive theoretical guarantees that SCRLM obtains high accuracy with high probability under certain assumption. Moreover, it can also be used as an initialization strategy for k-means clustering. Experiments on real-world large-scale datasets demonstrate the effectiveness of SCRLM when clustering a large number of clusters, and a k-means algorithm initialized by SCRLM outperforms most classic clustering methods in both speed and accuracy, while scaling well to large datasets such as ImageNet. We further extend SCRLM to Hierarchical SCRLM (HSCRLM) to handle hierarchical structures while maintaining robustness and theoretical guarantees. These advancements contribute to addressing modern clustering challenges.