Network Coordination Algorithm Based on Distributed Probability Matrix Factorization

Network Coordination Systems (NCS) are powerful mechanisms to efficiently predict the network latency of pairwise hosts in Internet without directly network measurement between them. Each host is embedded into a distance space where the latency between nodes is calculated according to the distant function defined by the space with assigned coordination of hosts. In terms of the properties of distant space, most popular NCS can be classified into two categories. One is based on metric space and the other is based on vector space obtained by matrix factorization. Unfortunately, the metric space such as Euclidean space based NCS is known to severely suffer from the weakness of inaccurate formulation of the Triangle Inequality Violation (TIV) and asymmetric latency frequently observed in Internet. To overcome the limitations of metric space, matrix factorization methodology is therefore proposed to represent the latency matrix with missing data by the product of two low-dimension vector matrices. In contrast to the huge amount of work on metric space type of NCS, there are fewer study of matrix factorization NCS up to now. This leads us to consider a probabilistic matrix factorization (PMF) based network distance prediction framework. In this paper we propose a model of distributed probabilistic matrix factorization (DPMF) which provides a probabilistic view of NCS with introduction of latent random variables to the incoming and outgoing vectors of hosts. Simulation on the real word data set shows that DPMF can achieve competitive prediction accuracy compared with two matrix factorization based NCS algorithms. Although the convergence rate of DPMF is relatively slow, the probabilistic viewpoint of delay matrix allows automatic regularization parameter selection in latent vector iteration process which makes the algorithm much practical for various latency data sets. Therefore, DPMF provides a promising generative process of latency value which potentially extends the usage scope of NCS.