Yubo Zhuang, second-year Statistics-PhD student, was recently notified of being awarded a 2022 NeuIPS 2022 Scholar Award for his paper titled “Wasserstein K-means for clustering probability distributions.” The Thirty-Sixth Annual Conference on Neural Information Processing Systems (NeurIPS 2022) is an interdisciplinary conference that brings together researchers in machine learning, neuroscience, statistics, optimization, computer vision, natural language processing, life sciences, natural sciences, social sciences, and other adjacent fields. Recipients of the NeuIPS Scholar Award are invited to attend the 2022 NeuIPS conference, which will be held from November 28th through December 9th in a hybrid format in New Orleans, Louisianna.
Professor Xiaohui Chen and Professor Yun Yang co-advised Zhuang on his submission.
Paper abstract:
Clustering is an important exploratory data analysis technique to group objects based on their similarity. The widely used K-means clustering method relies on some notion of distance to partition data into a fewer number of groups. In the Euclidean space, centroid-based and distance-based formulations of the K-means are equivalent. In modern machine learning applications, data often arise as probability distributions and a natural generalization to handle measure-valued data is to use the optimal transport metric. Due to non-negative Alexandrov curvature of the Wasserstein space, barycenters suffer from regularity and non-robustness issues. The peculiar behaviors of Wasserstein barycenters may make the centroid-based formulation fail to represent the within-cluster data points, while the more direct distance-based K-means approach and its semidefinite program (SDP) relaxation are capable of recovering the true cluster labels. In the special case of clustering Gaussian distributions, we show that the SDP relaxed Wasserstein K-means can achieve exact recovery given the clusters are well-separated under the 2-Wasserstein metric. Our simulation and real data examples also demonstrate that distance-based K-means can achieve better classification performance over the standard centroid-based K-means for clustering probability distributions and images.