@article {Pap2013,
	title = {Design of Analysis Modules},
	number = {D4.1},
	year = {2013},
	month = {11/2013},
	institution = {mPlane Consortium},
	type = {Public Deliverable},
	address = {Torino},
	keywords = {algorithms, analysis},
	isbn = {D4.1},
	issn = {D4.1},
	author = {Dimitri Papadimitriou and Zied Ben-Houidi and Samir Ghamri-Doudane and D Rossi and M. Milanesio and P. Casas and Alessandro D{\textquoteright}Alconzo and Edion Tego and Francesco Matera and Maurizio Dusi and Tivadar Szemethy and L. M{\'a}th{\'e} and Alessandro Finamore and Stefano Traverso and Ilias Leontiadis and Yan Grunenberger and L. Baltrunas and Benoit Donnet and Guy Leduc and Y. Liao}
}
@article {Lia2013,
	title = {DMFSGD: A decentralized matrix factorization algorithm for network distance prediction},
	journal = {IEEE/ACM Transactions on Networking},
	volume = {21},
	year = {2013},
	month = {10/2013},
	chapter = {1511},
	abstract = {<p>The knowledge of end-to-end network distances is\&nbsp;essential to many Internet applications. As active probing of all\&nbsp;pairwise distances is infeasible in large-scale networks, a natural\&nbsp;idea is to measure a few pairs and to predict the other ones\&nbsp;without actually measuring them. This paper formulates the\&nbsp;prediction problem as matrix completion where the unknown\&nbsp;entries in a pairwise distance matrix constructed from a network\&nbsp;are to be predicted. By assuming that the distance matrix has\&nbsp;a low-rank characteristics, the problem is solvable by lowrank\&nbsp;approximation based on matrix factorization. The new\&nbsp;formulation circumvents the well-known drawbacks of existing\&nbsp;approaches based on Euclidean embedding.</p><p>A new algorithm, so-called Decentralized Matrix Factorization\&nbsp;by Stochastic Gradient Descent (DMFSGD), is proposed. By\&nbsp;letting network nodes exchange messages with each other, the\&nbsp;algorithm is fully decentralized and only requires each node\&nbsp;to collect and to process local measurements, with neither\&nbsp;explicit matrix constructions nor special nodes such as landmarks\&nbsp;and central servers. In addition, we compared comprehensively\&nbsp;matrix factorization and Euclidean embedding to demonstrate\&nbsp;the suitability of the former on network distance prediction. We\&nbsp;further studied the incorporation of a robust loss function and\&nbsp;of non-negativity constraints. Extensive experiments on various\&nbsp;publicly-available datasets of network delays show not only the\&nbsp;scalability and the accuracy of our approach, but also its usability\&nbsp;in real Internet applications.</p>},
	keywords = {matrix completion, matrix factorization, network distance prediction, stochastic gradient descent},
	author = {Yongjun Liao and Wei Du and Pierre Geurts and Guy Leduc}
}
