  Transfer learning aims to faciliate learning tasks in a label-scarce target
domain by leveraging knowledge from a related source domain with plenty of
labeled data. Often times we may have multiple domains with little or no
labeled data as targets waiting to be solved. Most existing efforts tackle
target domains separately by modeling the `source-target' pairs without
exploring the relatedness between them, which would cause loss of crucial
information, thus failing to achieve optimal capability of knowledge transfer.
In this paper, we propose a novel and effective approach called Multi-Relevance
Transfer Learning (MRTL) for this purpose, which can simultaneously transfer
different knowledge from the source and exploits the shared common latent
factors between target domains. Specifically, we formulate the problem as an
optimization task based on a collective nonnegative matrix tri-factorization
framework. The proposed approach achieves both source-target transfer and
target-target leveraging by sharing multiple decomposed latent subspaces.
Further, an alternative minimization learning algorithm is developed with
convergence guarantee. Empirical study validates the performance and
effectiveness of MRTL compared to the state-of-the-art methods.
