Histogram Matching for Kernel based Feature Combination

Kernel-based feature combination techniques such as Multiple Kernel Learning (MKL) use arithmetical operations to linearly combine different kernels (Lanckriet et al., 2004) (Orabona et al., 2010). We have discovered that the histograms of routinely used kernels are usually very different (see Fig.2 for example). This means that their units of measure are not the same, it is therefore necessary to standardize the kernel of individual feature channels before they are arithmetically combined together. Whilst previous methods advocate to make the mean or the variance of different kernels (similarity measures) the same (Lee et al., 2011), we suggest that their histogram should be calibrated to a canonical histogram (Fu et al., 2011). We have developed a simple and robust histogram matching based method for standardizing kernels and show that histogram matching can always boost the performance of state of the art MKL algorithms. Our method can be considered as imposing a stronger constraint on normalizing the data than mean and variance calibrations. We advocate that histogram matching should be considered as a new baseline, besides mean and variance calibration, for feature combination.