Novel Optimization Methods for Temporal and Predictive Clustering

Abstract

Clustering, an unsupervised learning method, aims to group unlabeled samples based on similarity, but modern datasets introduce challenges. First, data often extends beyond static features to temporal sequences. Second, clustering may move beyond the geometric similarity between samples in feature space. Traditional clustering methods struggle with these complexities, as they largely assume static, geometrically separable samples. To address this limitation, this thesis introduces several new clustering approaches formulated as Mixed-Integer Linear Programs (MILP) to guarantee global optimization. Specifically, a Temporal Clustering framework addresses time-dependent data and considers temporal dynamism in cluster assignments and definition. A scalable Linear Predictive Clustering formulation groups samples by shared predictive structures in a non-separable feature space. A novel Granger-causal Clustering integrates temporal dynamics with predictive relationships and provides an interoperable definition via Bounded Box constraints. Collectively, these methods advance clustering by incorporating temporal, predictive, and causal structures in a principled optimization framework.