Multidimensional Scaling on Multiple Input Distance Matrices
This addresses a previously unsolved task for domains requiring MDS, though it appears incremental as it extends classic MDS to multiple views.
The paper tackles the problem of performing multidimensional scaling on multiple input distance matrices, which arises from diverse data sources, by proposing a new algorithm called Multi-View Multidimensional Scaling (MVMDS) that automatically learns view weights, with experimental results demonstrating its effectiveness.
Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have multiple heterogeneous representations. 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. Our algorithm is able to 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.