Novel histograms kernels with structural properties

•We study the space where histograms lie.•We introduce some intuitive and desirable structural properties for measures.•A new similarity measure for comparing histograms is proposed.•We show that the proposed similarity is a conditionally positive definite kernel.•Experiments on face recognition and image retrieval were done. This paper introduces a new similarity measure for comparing histograms, named Weighted Distribution Matching, which bases the comparison not only in the specific bin values but also in the shape of the histograms. It is proved that the proposed similarity is a conditionally positive definite kernel. The space where histograms lie is studied, and some intuitively desirable structural properties are introduced. The most representative measures of the state of art were compared on the basis of these properties. Experiments conducted on face recognition and image retrieval validate the proposal.