Scalable Model-Based Gaussian Process Clustering

Gaussian process is an indispensable tool in clustering functional data, owing to it's flexibility and inherent uncertainty quantification. However, when the functional data is observed over a large grid (say, of length p), Gaussian process clustering quickly renders itself infeasible, incurring O(p 2 ) space complexity and O(p 3 ) time complexity per iteration; and thus prohibiting it's natural adaptation to large environmental applications [1], [2]. To ensure scalability of Gaussian process clustering in such applications, we propose to embed the popular Vecchia approximation [3] for Gaussian processes at the heart of the clustering task, provide crucial theoretical insights towards algorithmic design, and finally develop a computationally efficient expectation maximization (EM) algorithm. Empirical evidence of the utility of our proposal is provided via simulations and analysis of polar temperature anomaly (noaa.gov) data-sets.