Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. In recent years, data are usually collected from diverse sources or have multiple heterogeneous representations. However, how to do multidimensional scaling on multiple input distance matrices is still unsolved to our best knowledge. In this paper, we first define this new task formally. Then, we propose a new algorithm called Multi-View Multidimensional Scaling (MVMDS) by considering each input distance matrix as one view. The proposed algorithm can learn the weights of views (i.e., distance matrices) automatically by exploring the consensus information and complementary nature of views. Experimental results on synthetic as well as real datasets demonstrate the effectiveness of MVMDS. We hope that our work encourages a wider consideration in many domains where MDS is needed.

Diffusion process has advanced visual retrieval greatly owing to its capacity in capturing the geometry structure of the underlying manifold. Recent studies (Donoser and Bischof 2013) have experimentally demonstrated that diffusion process on the tensor product graph yields better retrieval performances than that on the original affinity graph. However, the principle behind this kind of diffusion process remains unclear, i.e., what kind of manifold structure is captured and how it is reflected. In this paper, we propose a new variant o diffusion process, which also operates on a tensor product graph. It is defined in three equivalent formulations (regularization framework, iterative framework and limit framework, respectively). Based on our study, three insightful conclusions are drawn which theoretically explain how this kind of diffusion process can better reveal the intrinsic relationship between objects. Besides, extensive experimental results on various retrieval tasks testify the validity of the proposed method.