Stochastic limited memory bundle algorithm for clustering in big data

Clustering is a crucial task in data mining and machine learning. In this paper, we propose an efficient algorithm, BIG-CLuST, for solving minimum sum-of-squares clustering problems in large and big datasets. We first develop a novel stochastic limited memory bundle algorithm (SLMBA) for large-scale nonsmooth finite-sum optimization problems and then formulate the clustering problem accordingly. The BIG-CLuST algorithm - a stochastic adaptation of the incremental clustering methodology - aims to find the global or a high-quality local solution for the clustering problem. It detects good starting points, i.e., initial cluster centers, for the SLMBA, applied as an underlying solver. We evaluate BIG-CLuST on several real-world datasets with numerous data points and features, comparing its performance with other clustering algorithms designed for large and big data. Numerical results demonstrate the efficiency of the proposed algorithm and the high quality of the found solutions on par with the best existing methods.