Non-metric Label Propagation

by Yin Zhang and Zhi-hua Zhou

This paper follows the idea of the non-metric similarity matrix analysis. By decomposing the Gram matrix into two separate graphs (one for positive eigenvalues and the other for the negative), they build two separate Markov chains, which compromise a mixture of Markov model for label propagation (just an explicit solution of linear equations). Their paper contains many experiments as usual, which I think might be the deficit of my own research work.

The idea is not that fancy but the application in label propagation might be novel, the research style of Zhou's :-p That requires keen olfaction.

Feature Discovery in Non-metric Pairwise Data

by Julian Laub Klaus-Robert Muller

This is a paper about how to analysis pairwise "distance" or similarity matrices. Since no all similarity matrices can be transformed into a Gram matrix (as we do in MDS), it is interesting to take a deeper insight into the details.

Basically, we may imagine there are two metrics, one for similarity and another for dissimilarity (penalizing the similarity in human perception). By applying a spetral transformation, we may use metric methods if the spectra can be fixed (no negative).

The problem is how we may utilize the negative part of the spectra.