Positive Definite Kernels in Machine Learning

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.

💡 Research Summary

This survey paper provides a comprehensive introduction to positive definite kernels and the broad family of machine‑learning methods that have grown out of them, commonly referred to as kernel methods. It begins by defining a positive definite kernel as a symmetric function k(x, y) whose Gram matrix