Correlation-based embedding of pairwise score data

Neighbor-preserving embedding of relational data in low-dimensional Euclidean spaces is studied. Contrary to variants of stochastic neighbor embedding that minimize divergence measures between estimated neighborhood probability distributions, the proposed approach fits configurations in the output space by maximizing correlation with potentially asymmetric or missing relationships in the input space. In addition to the linear Pearson correlation measure, the use of soft formulations of Spearman and Kendall rank correlation is investigated for optimizing embeddings like 2D point cloud configurations. We illustrate how this scale-invariant correlation-based framework of multidimensional scaling (cbMDS) helps going beyond distance-preserving scaling approaches and how the embedding results are characteristically different from recent neighborhood embedding techniques.