  In this paper, we attempts to learn a single metric across two heterogeneous
domains where source domain is fully labeled and has many samples while target
domain has only a few labeled samples but abundant unlabeled samples. To the
best of our knowledge, this task is seldom touched. The proposed learning model
has a simple underlying motivation: all the samples in both the source and the
target domains are mapped into a common space, where both their priors
P(sample)s and their posteriors P(label|sample)s are forced to be respectively
aligned as much as possible. We show that the two mappings, from both the
source domain and the target domain to the common space, can be reparameterized
into a single positive semi-definite(PSD) matrix. Then we develop an efficient
Bregman Projection algorithm to optimize the PDS matrix over which a LogDet
function is used to regularize. Furthermore, we also show that this model can
be easily kernelized and verify its effectiveness in crosslanguage retrieval
task and cross-domain object recognition task.
