RI: Small: Hard Clustering via Bayesian Nonparametrics

RI：小：通过贝叶斯非参数进行硬聚类

• 批准号: 1217433
• 负责人: Mikhail Belkin
• 金额: $ 43.97万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1217433&HistoricalAwards=false
• 关键词: RI; Small; Hard; Clustering; via

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.

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，在实践中往往是首选。 第一步是将Dirichlet过程高斯混合模型与不预先固定聚类数的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，共同证明这种渐近方法的实用性：（1）将分析扩展到分层贝叶斯模型，从而在多个数据集上实现可扩展的硬聚类方法;（2）与谱方法和图聚类的联系，从而实现新颖灵活的图聚类方法;（3）高斯设置之外的扩展，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了大量的实验。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、社交网络分析和许多其他领域。 此外，该研究将通过发布的软件和融入俄亥俄州州立大学的课程工作，使更广泛的社区受益。