Scalable Support Vector Clustering Using Budget

Owing to its application in solving the difficult and diverse clustering or outlier detection problem, support-based clustering has recently drawn plenty of attention. Support-based clustering method always undergoes two phases: finding the domain of novelty and performing clustering assignment. To find the domain of novelty, the training time given by the current solvers is typically over-quadratic in the training size, and hence precluding the usage of support-based clustering method for large-scale datasets. In this paper, we propose applying Stochastic Gradient Descent (SGD) framework to the first phase of support-based clustering for finding the domain of novelty and a new strategy to perform the clustering assignment. However, the direct application of SGD to the first phase of support-based clustering is vulnerable to the curse of kernelization, that is, the model size linearly grows up with the data size accumulated overtime. To address this issue, we invoke the budget approach which allows us to restrict the model size to a small budget. Our new strategy for clustering assignment enables a fast computation by means of reducing the task of clustering assignment on the full training set to the same task on a significantly smaller set. We also provide a rigorous theoretical analysis about the convergence rate for the proposed method. Finally, we validate our proposed method on the well-known datasets for clustering to show that the proposed method offers a comparable clustering quality while simultaneously achieving significant speedup in comparison with the baselines.