  Very often for the same scientific question, there may exist different
techniques or experiments that measure the same numerical quantity.
Historically, various methods have been developed to exploit the information
within each type of data independently. However, statistical data fusion
methods that could effectively integrate multi-source data under a unified
framework are lacking. In this paper, we propose a novel data fusion method,
called B-scaling, for integrating multi-source data. Consider $K$ measurements
that are generated from different sources but measure the same latent variable
through some linear or nonlinear ways. We seek to find a representation of the
latent variable, named B-mean, which captures the common information contained
in the $K$ measurements while takes into account the nonlinear mappings between
them and the latent variable. We also establish the asymptotic property of the
B-mean and apply the proposed method to integrate multiple histone
modifications and DNA methylation levels for characterizing epigenomic
landscape. Both numerical and empirical studies show that B-scaling is a
powerful data fusion method with broad applications.
