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Singular Value Decomposition (SVD) is a popular approach in various networkapplications, such as link prediction and network parameter characterization.Incremental SVD approaches are proposed to process newly changed nodes andedges in dynamic networks. However, incremental SVD approaches suffer fromserious error accumulation inevitably due to approximation on incrementalupdates. SVD restart is an effective approach to reset the aggregated error,but when to restart SVD for dynamic networks is not addressed in literature. Inthis paper, we propose TIMERS, Theoretically Instructed Maximum-Error-boundedRestart of SVD, a novel approach which optimally sets the restart time in orderto reduce error accumulation in time. Specifically, we monitor the marginbetween reconstruction loss of incremental updates and the minimum loss in SVDmodel. To reduce the complexity of monitoring, we theoretically develop a lowerbound of SVD minimum loss for dynamic networks and use the bound to replace theminimum loss in monitoring. By setting a maximum tolerated error as athreshold, we can trigger SVD restart automatically when the margin exceedsthis threshold.We prove that the time complexity of our method is linear withrespect to the number of local dynamic changes, and our method is generalacross different types of dynamic networks. We conduct extensive experiments onseveral synthetic and real dynamic networks. The experimental resultsdemonstrate that our proposed method significantly outperforms the existingmethods by reducing 27% to 42% in terms of the maximum error for dynamicnetwork reconstruction when fixing the number of restarts. Our method reducesthe number of restarts by 25% to 50% when fixing the maximum error tolerated.

TIMERS: Error-Bounded SVD Restart on Dynamic Networks