Statistical, Computational and Algorithmic Aspects of Kernel Clustering

核聚类的统计、计算和算法方面

• 批准号: 499522214
• 负责人: Professor Debarghya Ghoshdastidar, Ph.D.
• 金额: --
• 依托单位: Lehrstuhl für Informatik VII: Theoretische Informatik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/499522214?language=en
• 关键词: Statistical; Computational; Algorithmic; Aspects; Kernel

Clustering is one of the fundamental problems in data analysis, and kernel clustering algorithms are among the most popular clustering techniques. Kernel clustering algorithms can find latent groups in complex data from pairwise similarities among the data, computed using a pre-defined kernel function. Kernel methods are based on the mathematical theory of reproducing kernels, which helps in theoretically analysing the statistical performance of these methods, particularly in the context of supervised machine learning. In comparison, there is little mathematical understanding of the role of kernels in clustering. This project addresses the deficit of understanding of kernel clustering. In particular, this project combines mathematical and numerical research to answer three key questions on kernel clustering: (1) What kind of underlying cluster structures can be statistically recovered by kernel clustering? (2) How do efficient kernel clustering algorithms perform on large datasets? (3) What is the connection between kernel clustering and other clustering approaches? To answer these questions, the project will provide theoretical research on the statistical guarantees of kernel clustering for planted cluster recovery, statistical-computational tradeoff of kernel clustering, and connections between kernel clustering and distribution based clustering. As a consequence of the theoretical study, the project will also develop new computationally efficient and interpretable clustering algorithms. Furthermore, given the recently established role of kernel theory in the analysis of supervised machine learning and deep learning, this project provides a building block for a deeper understanding of modern clustering and unsupervised learning algorithms.

聚类是数据分析中的基本问题之一，内核聚类算法是最受欢迎的聚类技术之一。内核聚类算法可以从数据之间的成对相似性中找到复杂数据中的潜在组，并使用预定义的内核函数计算。内核方法基于复制核的数学理论，该理论有助于从理论上分析这些方法的统计性能，尤其是在监督机器学习的背景下。相比之下，对核在聚类中的作用几乎没有数学理解。该项目解决了对内核聚类的理解的不足。特别是，该项目结合了数学和数值研究，以回答有关内核聚类的三个关键问题：（1）可以通过内核聚类在统计上恢复哪种基础群集结构？ （2）有效的内核聚类算法如何在大型数据集上执行？ （3）内核聚类与其他聚类方法之间有什么联系？为了回答这些问题，该项目将提供有关内核聚类的统计保证的理论研究，用于种植集群恢复，内核聚类的统计计算折衷以及内核聚类与基于分布的聚类之间的连接。 由于理论研究的结果，该项目还将开发新的计算高效且可解释的聚类算法。此外，鉴于内核理论在监督机器学习和深度学习分析中的最近确定的作用，该项目为对现代聚类和无监督学习算法的更深入了解提供了一个基础。