A new regression algorithm of an adaptive reduced relevance vector machine is proposed to estimate the illumination chromaticity of an image for the purpose of color constancy. Within the framework of sparse Bayesian learning, the algorithm extends the relevance vector machine by combining global and local kernels adaptively in the form of multiple kernels, and the improved locality preserving projection （LLP） is then applied to reduce the column dimension of the multiple kernel input matrix to achieve less training time. To estimate the illumination chromaticity, the algorithm is trained by fuzzy central values of chromaticity histograms of a set of images and the corresponding illuminants. Experiments with real images indicate that the proposed algorithm performs better than the support vector machine and the relevance vector machine while requiring less training time than the relevance vector machine.
