A fast and accurate explicit kernel map

Abstract

Kernel functions are powerful techniques that have been used successfully in many machine learning algorithms. Explicit kernel maps have emerged as an alternative to standard kernel functions in order to overcome the latter’s scalability issues. An explicit kernel map such as Random Fourier Features (RFF) is a popular method for approximating shift invariant kernels. However, it requires large run time in order to achieve good accuracy. Faster and more accurate variants of it have also been proposed recently. All these methods are still approximations to a shift invariant kernel. Instead of an approximation, we propose a fast, exact and explicit kernel map called Explicit Cosine Map (ECM). The advantage of this exact map is manifested in the form of performance improvements in kernel based algorithms. Furthermore, its explicit nature enables it to be used in streaming applications. Another explicit kernel map called Euler kernel map is also proposed. The effectiveness of both kernel maps is evaluated in the application of streaming Anomaly Detection (AD). The AD results indicate that ECM based algorithm achieves better AD accuracy than previous algorithms, while being faster.