A study on positive-definite and efficient kernels for structured data

核方法是机器学习研究的一个重要领域，它使我们能够利用大数据等信息资产在各种应用中做出有用的预测。除了矢量数据外，还有大量具有结构的数据。例如，DNA是一组核苷酸；蛋白质、解析树和XML文档的结构自然是树；用图结构表示各种网络。在这方面，本项目旨在建立结构化数据的核理论和将核应用于实际应用的结构化数据的实用技术。具体来说，我们已经开发了一种数学理论来研究核的正确定性和处理各种结构化数据的各种类型的核。此外，我们已经开发了一个计算内核的实用程序，并通过互联网向机器学习领域的研究人员发布了它。

Kernel method is an important field of machine learning research and allows us to leverage information assets like big data to make useful predictions in various applications. In addition to vector data,there exist huge amount of data that have structures. For example, DNA is an array of nucleotides; Protein, parse trees and XML documents are naturally structured as trees; Various kinds of networks are represented using the graph structure. In this regard, this project aims to establish a theory of kernels for structured data and practical techniques to apply kernels to structured data of the real applications. Specifically, we have developed a mathematical theory to investigate positive definiteness of kernels and various types of kernels that deal with a wide variety of structured data. Furthermore, we have developed a utility to compute kernels and have publicized it to researchers in the field of machine learning over the Internet.