Tang Yi, Li Luoqing, Li Xuelong
Key Laboratory of Applied Mathematics, Hubei Province, and Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, China.
IEEE Trans Syst Man Cybern B Cybern. 2011 Feb;41(1):131-8. doi: 10.1109/TSMCB.2010.2048312. Epub 2010 Jun 1.
In the field of machine learning, it is a key issue to learn and represent similarity. This paper focuses on the problem of learning similarity with a multikernel method. Motivated by geometric intuition and computability, similarity between patterns is proposed to be measured by their included angle in a kernel-induced Hilbert space. Having noticed that the cosine of such an included angle can be represented by a normalized kernel, it can be said that the task of learning similarity is equivalent to learning an appropriate normalized kernel. In addition, an error bound is also established for learning similarity with the multikernel method. Based on this bound, a boosting-style algorithm is developed. The preliminary experiments validate the effectiveness of the algorithm for learning similarity.
在机器学习领域，学习和表示相似度是一个关键问题。本文聚焦于使用多核方法学习相似度的问题。受几何直观性和可计算性的启发，提出在核诱导的希尔伯特空间中通过模式之间的夹角来度量模式间的相似度。注意到这样一个夹角的余弦可以由一个归一化核表示，因此可以说学习相似度的任务等同于学习一个合适的归一化核。此外，还为使用多核方法学习相似度建立了一个误差界。基于这个界，开发了一种提升风格的算法。初步实验验证了该算法在学习相似度方面的有效性。
