cbMDS Correlation Based Multi Dimensional Scaling 1.2

marc strickert — Sat, 27 Jul 2013 14:35:36 -0000

The aim is to embed a given data relationship matrix into a low-dimensional Euclidean space such that the point distances / distance ranks correlate best with the original input relationships. Input relationships may be given as (sparse) (asymmetric) distance, dissimilarity, or (negative!) score matrices. Input-output relations are modeled as low-conditioned. (Weighted) Pearson and soft Spearman rank correlation, and unweighted soft Kendall correlation are supported correlation measures for input/output object neighborhood relationships.

Correlation-based multidimensional scaling is implemented for reconstructing pairwise dissimilarity or score relationships in a Euclidean space. Pearson correlation between pairs of objects in source and target space are directly maximized by gradient methods. Alternatively, optimization of Spearman rank correlation and Kendall correlation is achieved by a numerically soft formulation. Scale and shift invariance properties of correlation help circumventing typical norm concentration problems.

Contrary to non-metric MDS based on isotonic regression and high-throughput MDS (HiT-MDS) maximizing Pearson correlation, the implementation is not matrix-conditioned (global) but row-conditioned (local) which allows for embedding asymmetric of relational score matrices. That is, instance-specific similarity profiles are reconstructed rather than global rank or distance relationships.

mloss.org cbMDS Correlation Based Multi Dimensional Scaling

cbMDS Correlation Based Multi Dimensional Scaling 1.2