Major advancements in kernel function approximation

• Published in: The Artificial intelligence review Vol. 54; no. 2; pp. 843 - 876
• Main Authors: Francis, Deena P., Raimond, Kumudha
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2021; Springer; Springer Nature B.V
• Subjects: Approximation; Artificial Intelligence; Cognitive tasks; Computer Science; Feature maps; Kernel functions; Machine learning; Mathematical analysis; Kernel function; Random Fourier features; Approximation; Explicit feature maps; Classification; Theoretical guarantees; Kernel
• ISSN: 0269-2821; 1573-7462
• DOI: 10.1007/s10462-020-09880-z

Kernel based methods have become popular in a wide variety of machine learning tasks. They rely on the computation of kernel functions, which implicitly transform the data in its input space to data in a very high dimensional space. Efficient application of these functions have been subject to study in the last 10 years. The main focus was on improving the scalability of kernel based methods. In this regard, kernel function approximation using explicit feature maps have emerged as a substitute for traditional kernel based methods. Over the years, various advancements from the theoretical perspective have been made to explicit kernel maps, especially to the method of random Fourier features (RFF), which is the main focus of our work. In this work, the major developments in the theory of kernel function approximation are reviewed in a systematic manner and the practical applications are discussed. Furthermore, we identify the shortcomings of the current research, and discuss possible avenues for future work.