机器学习中的正定核
Positive Definite Kernels in Machine Learning
摘要：
本综述介绍了正定核以及它们在机器学习文献中启发的一组方法，即核方法。我们首先讨论了正定核的一些性质以及再生核希尔伯特空间，自然扩展的功能集$\{k(x,\cdot),x\in\mathcal{X}\}$与核$k$定义在空间$\mathcal{X}$。我们将详细讨论利用著名的统计模型构建核函数。我们提供了许多数据分析方法的概述，这些方法利用再生核希尔伯特空间，并讨论了结合几个内核来提高某些任务的性能的想法。我们还提供了不同内核的简短食谱，这些内核对某些数据类型特别有用，例如图像，图形或语音片段。
英文摘要：
This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as reproducing kernel Hibert spaces, the natural extension of the set of functions $\{k(x,\cdot),x\in\mathcal{X}\}$ associated with a kernel $k$ defined on a space $\mathcal{X}$. We discuss at length the construction of kernel functions that take advantage of well-known statistical models. We provide an overview of numerous data-analysis methods which take advantage of reproducing kernel Hilbert spaces and discuss the idea of combining several kernels to improve the performance on certain tasks. We also provide a short cookbook of different kernels which are particularly useful for certain data-types such as images, graphs or speech segments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
