Yongjun Liao

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 that DMF achieves competitive accuracy with the double advantage of having no landmarks and of being able to represent distance asymmetries and TIVs.

DMFSGD: a decentralized matrix factorization algorithm for network distance prediction

The knowledge of end-to-end network distances is essential to many Internet applications. As active probing of all pairwise distances is infeasible in large-scale networks, a natural idea is to measure a few pairs and to predict the other ones without actually measuring them. This paper formulates the prediction problem as matrix completion where the unknown entries in a pairwise distance matrix constructed from a network are to be predicted. By assuming that the distance matrix has low-rank characteristics, the problem is solvable by low-rank approximation based on matrix factorization. The new formulation circumvents the well-known drawbacks of existing approaches based on Euclidean embedding. A new algorithm, so-called Decentralized Matrix Factorization by Stochastic Gradient Descent (DMFSGD), is proposed. By letting network nodes exchange messages with each other, the algorithm is fully decentralized and only requires each node to collect and to process local measurements, with neither explicit matrix constructions nor special nodes such as landmarks and central servers. In addition, we compared comprehensively matrix factorization and Euclidean embedding to demonstrate the suitability of the former on network distance prediction. We further studied the incorporation of a robust loss function and of nonnegativity constraints. Extensive experiments on various publicly available datasets of network delays show not only the scalability and the accuracy of our approach, but also its usability in real Internet applications.

Detecting Triangle Inequality Violations in Internet Coordinate Systems by Supervised Learning

Internet Coordinates Systems (ICS) are used to predict Internet distances with limited measurements. However the precision of an ICS is degraded by the presence of Triangle Inequality Violations (TIVs). Simple methods have been proposed to detect TIVs, based e.g. on the empirical observation that a TIV is more likely when the distance is underestimated by the coordinates. In this paper, we apply supervised machine learning techniques to try and derive more powerful criteria to detect TIVs. We first show that (ensembles of) Decision Trees (DTs) learnt on our datasets are very good models for this problem. Moreover, our approach brings out a discriminative variable (called OREE ), which combines the classical estimation error with the variance of the estimated distance. This variable alone is as good as an ensemble of DTs, and provides a much simpler criterion. If every node of the ICS sorts its neighbours according to OREE , we show that cutting these lists after a given number of neighbours, or when OREE crosses a given threshold value, achieves very good performance to detect TIVs.

A lightweight network proximity service based on neighborhood models

This paper proposes a network proximity service based on the neighborhood models used in recommender systems. Unlike previous approaches, our service infers network proximity without trying to recover the latency between network nodes. By asking each node to probe a number of landmark nodes which can be servers at Google, Yahoo and Facebook, etc., a simple proximity measure is computed and allows the direct ranking and rating of network nodes by their proximity to a target node. The service is thus lightweight and can be easily deployed in e.g. P2P and CDN applications. Simulations on existing datasets and experiments with a deployment over PlanetLab showed that our service achieves an accurate proximity inference that is comparable to state-of-the-art latency prediction approaches, while being much simpler.

Rating network paths for locality-aware overlay construction and routing

This paper investigates the rating of network paths, i.e., acquiring quantized measures of path properties such as round-trip time and available bandwidth. Compared to fine-grained measurements, coarse-grained ratings are appealing in that they are not only informative but also cheap to obtain. Motivated by this insight, we first address the scalable acquisition of path ratings by statistical inference. By observing similarities to recommender systems, we examine the applicability of solutions to a recommender system and show that our inference problem can be solved by a class of matrix factorization techniques. A technical contribution is an active and progressive inference framework that not only improves the accuracy by selectively measuring more informative paths, but also speeds up the convergence for available bandwidth by incorporating its measurement methodology. Then, we investigate the usability of rating-based network measurement and inference in applications. A case study is performed on whether locality awareness can be achieved for overlay networks of Pastry and BitTorrent using inferred ratings. We show that such coarse-grained knowledge can improve the performance of peer selection and that finer granularities do not always lead to larger improvements.