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.

中文翻译：

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快速准确的显式内核映射

摘要

内核功能是强大的技术，已在许多机器学习算法中成功使用。为了克服标准内核功能的可扩展性问题，已经出现了明确的内核映射。诸如随机傅立叶特征（RFF）之类的显式内核映射是一种用于近似移动不变核的流行方法。但是，为了获得良好的精度，需要大量的运行时间。最近还提出了更快，更准确的变体。所有这些方法仍然是位移不变核的近似值。代替近似值，我们提出了一个快速，精确和显式的内核映射，称为显式余弦映射（ECM）。这种精确映射的优势体现在基于内核的算法中的性能改进形式。此外，它的显式特性使其可以在流应用程序中使用。还提出了另一种明确的内核映射，称为Euler内核映射。在流式异常检测（AD）的应用中评估了两个内核映射的有效性。AD结果表明，基于ECM的算法比以前的算法具有更高的AD精度，同时速度更快。