Recent researches on transfer learning exploit deep structures for discriminative feature representation to tackle cross-domain disparity. However, few of them are able to joint feature learning and knowledge transfer in a unified deep framework. In this paper, we develop a novel approach, called Deep Low-Rank Coding (DLRC), for transfer learning. Specifically, discriminative low-rank coding is achieved in the guidance of an iterative supervised structure term for each single layer. In this way, both marginal and conditional distributions between two domains intend to be mitigated. In addition, a marginalized denoising feature transformation is employed to guarantee the learned single-layer low-rank coding to be robust despite of corruptions or noises. Finally, by stacking multiple layers of low-rank codings, we manage to learn robust cross-domain features from coarse to fine. Experimental results on several benchmarks have demonstrated the effectiveness of our proposed algorithm on facilitating the recognition performance for the target domain.

Graph based semi-supervised learning (GSSL) plays an important role in machine learning systems. The most crucial step in GSSL is graph construction. Although several interesting graph construction methods have been proposed in recent years, how to construct an effective graph is still an open problem. In this paper, we develop a novel approach to constructing graph, which is based on low-rank coding and $b$-matching constraint. By virtue of recent advances in low-rank subspace recovery theory, compact encoding using low-rank representation coefficients allows us to obtain a robust similarity metric between all pairs of samples. Meanwhile, the $b$-matching constraint helps in obtaining a sparse and balanced graph, which benefits label propagation in GSSL. We build a joint optimization model to learn low-rank codes and balanced graph simultaneously. After using a graph re-weighting strategy, we present a semi-supervised learning algorithm by incorporating our sparse and balanced graph with Gaussian harmonic function (GHF). Experimental results on the Extended YaleB, PIE, ORL and USPS databases demonstrate that our graph outperforms several state-of-the-art graphs, especially when the labeled samples are very scarce.