Description

Soft Ordinal Embedding (SOE) is a simple new method for ordinal embedding problem. SOE can deal with a part of ordinal comparisons: dissimilarity(i,j)<dissimilarity(k,l) for certain quadruples of indices (i,j,k,l).

The local point of view suggests ordinal embedding as an interesting alternative to graph drawing algorithms. If vertex i is connected by an edge to vertex j, but not to vertex k, we interpret this constellation as a constraint of the form dissimilarity(i,j)<dissimilarity(i,k). With this interpretation, graph embedding (graph drawing) becomes a special case of ordinal embedding. We call SOE for graph embedding problem Local Ordinal Embedding (LOE). For the connectivity matrix of given unweighted graph, LOE provides a low-dimensional embedding which preserves the original graph structure.

This package provides SOE and LOE.

Details

The functions for SOE on ordinal comparison matrices and LOE on unweighted adjacency matrices are SOE() and LOE(), respectively.

Acknowledgement

The authors wishes to express their thanks to Dr. Michio Yamamoto and Mr. Yuichi Saito for their help in creating this package. This work was partially supported by Grant-in-Aid for JSPS Fellows Number 24-2466.

Author(s)

Yoshikazu Terada and Ulrike von Luxburg

Maintainer: Yoshikazu Terada terada@sigmath.es.osaka-u.ac.jp