Multiple kernel learning and feature space denoising

Abstract

We review a multiple kernel learning (MKL) technique called ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> regularised multiple kernel Fisher discriminant analysis (MK-FDA), and investigate the effect of feature space denoising on MKL. Experiments show that with both the original kernels or denoised kernels, ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> MK-FDA outperforms its fixed-norm counterparts. Experiments also show that feature space denoising boosts the performance of both single kernel FDA and ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> MK-FDA, and that there is a positive correlation between the learnt kernel weights and the amount of variance kept by feature space denoising. Based on these observations, we argue that in the case where the base feature spaces are noisy, linear combination of kernels cannot be optimal. An MKL objective function which can take care of feature space denoising automatically, and which can learn a truly optimal (non-linear) combination of the base kernels, is yet to be found.