RI: Small: Hard Clustering via Bayesian Nonparametrics

现代机器学习算法经常遇到可扩展性和建模能力之间的权衡。对于数据聚类问题，贝叶斯方法比经典方法具有许多建模优势，但硬聚类方法（如k-means）由于其简单性和可扩展性，在实践中通常更受欢迎。本项目旨在弥合经典硬聚类方法与基于贝叶斯非参数的聚类模型之间的差距。第一步是将Dirichlet过程高斯混合模型与不预先固定簇数的k-means类算法连接起来的渐近结果。利用这一关键结果，PI和他的团队将探索四个相关的研究方向，这些方向共同展示了这种渐近方法的实用性：(1)将分析扩展到分层贝叶斯模型，从而导致在多个数据集上可扩展的硬聚类方法；(2)结合谱方法和图聚类，提出新颖灵活的图聚类方法；(3)超越高斯设置的扩展，导致主题建模和其他离散数据聚类问题的新方法；(4)在计算机视觉和文本领域进行广泛的实验。鉴于k-means确实是机器学习的主力，这四个方向有可能影响广泛的大规模应用，包括计算机视觉、生物信息学、社会网络分析和许多其他领域。此外，这项研究将通过发布软件和集成到俄亥俄州立大学的课程中，从而使更广泛的社区受益。

Modern machine learning algorithms often encounter a trade off between scalability and modeling power. For the problem of data clustering, Bayesian approaches enjoy numerous modeling advantages over classical methods, but hard clustering methods such as k-means are often preferred in practice due to their simplicity and scalability.This project explores bridging the gap between classical hard clustering methods and clustering models based on Bayesian nonparametrics. The first step is an asymptotic result connecting the Dirichlet process Gaussian mixture model with a k-means-like algorithm that does not fix the number of clusters in advance. Using this key result, the PI and his team will explore four related research directions which collectively demonstrate the utility of this asymptotic approach: (1) extensions of the analysis to hierarchical Bayesian models, leading to scalable hard clustering methods over multiple data sets; (2) connections to spectral methods and graph clustering, leading to novel and flexible graph clustering methods; (3) extensions beyond the Gaussian setting, leading to new approaches to topic modeling and other discrete-data clustering problems; and (4) extensive experiments in both the computer vision and text domains.Given that k-means is truly a workhorse of machine learning, these four directions have the potential to impact a wide array of large-scale applications including computer vision, bioinformatics, social network analysis, and many other domains. Furthermore, the research will benefit the broader community through released software and integration into coursework at Ohio State University.