Network Distance Prediction Based on Decentralized Matrix Factorization

Network Coordinate Systems (NCS) are promising techniques
to predict unknown network distances from a limited number of measurements.
Most NCS algorithms are based on metric space embedding and
suffer from the inability to represent distance asymmetries and Triangle
Inequality Violations (TIVs). To overcome these drawbacks, we formulate
the problem of network distance prediction as guessing the missing
elements of a distance matrix and solve it by matrix factorization. A distinct
feature of our approach, called Decentralized Matrix Factorization
(DMF), is that it is fully decentralized. The factorization of the incomplete
distance matrix is collaboratively and iteratively done at all nodes
with each node retrieving only a small number of distance measurements.
There are no special nodes such as landmarks nor a central node where
the distance measurements are collected and stored. We compare DMF
with two popular NCS algorithms: Vivaldi and IDES. The former is based
on metric space embedding, while the latter is also based on matrix factorization
but uses landmarks. Experimental results show thatDMF achieves
competitive accuracy with the double advantage of having no landmarks
and of being able to represent distance asymmetries and TIVs.