Random Fourier Approximations for Skewed Multiplicative Histogram Kernels

Abstract. Approximations based on random Fourier features have recently emerged as an efficient and elegant methodology for designing large-scale kernel machines [4]. By expressing the kernel as a Fourier expansion, features are generated based on a finite set of random basis projections with inner products that are Monte Carlo approximations to the original kernel. However, the original Fourier features are only applicable to translation-invariant kernels and are not suitable for histograms that are always non-negative. This paper extends the concept of translation-invariance and the random Fourier feature methodology to arbitrary, locally compact Abelian groups. Based on empirical observations drawn from the exponentiated 2 kernel, the state-of-the-art for histogram descriptors, we propose a new group called the skewedmultiplicative group and design translation-invariant kernels on it. Experiments show that the proposed kernels outperform other kernels that can be similarly approxima...

• Type: Conference
• Year: 2010
• Where: DAGM
• Authors: Fuxin Li, Catalin Ionescu, Cristian Sminchisescu
• Keywords: DAGM 2010, Fourier Feature, Image Processing, Random Fourier Feature, Translation-invariant Kernels