  Domain Adaptation (DA) aims to generalize the classifier learned from the
source domain to the target domain. Existing DA methods usually assume that
rich labels could be available in the source domain. However, there are usually
a large number of unlabeled data but only a few labeled data in the source
domain, and how to transfer knowledge from this sparsely-labeled source domain
to the target domain is still a challenge, which greatly limits their
application in the wild. This paper proposes a novel Sparsely-Labeled Source
Assisted Domain Adaptation (SLSA-DA) algorithm to address the challenge with
limited labeled source domain samples. Specifically, due to the label scarcity
problem, the projected clustering is conducted on both the source and target
domains, so that the discriminative structures of data could be leveraged
elegantly. Then the label propagation is adopted to propagate the labels from
those limited labeled source samples to the whole unlabeled data progressively,
so that the cluster labels are revealed correctly. Finally, we jointly align
the marginal and conditional distributions to mitigate the cross-domain
mismatch problem, and optimize those three procedures iteratively. However, it
is nontrivial to incorporate those three procedures into a unified optimization
framework seamlessly since some variables to be optimized are implicitly
involved in their formulas, thus they could not promote to each other.
Remarkably, we prove that the projected clustering and conditional distribution
alignment could be reformulated as different expressions, thus the implicit
variables are revealed in different optimization steps. As such, the variables
related to those three quantities could be optimized in a unified optimization
framework and facilitate to each other, to improve the recognition performance
obviously.
