MASTER: across Multiple social networks, integrate Attribute and STructure Embedding for Reconciliation

Recently, reconciling social networks receives significant attention. Most of the existing studies have limitations in the following three aspects: multiplicity, comprehensiveness and robustness. To address these three limitations, we rethink this problem and propose the MASTER framework, i.e., across Multiple social networks, integrate Attribute and STructure Embedding for Reconciliation. In this framework, we first design a novel Constrained Dual Embedding model by simultaneously embedding and reconciling multiple social networks to formulate our problem into a unified optimization. To address this optimization, we then design an effective algorithm called NS-Alternating. We also prove that this algorithm converges to KKT points. Through extensive experiments on real-world datasets, we demonstrate that MASTER outperforms the state-of-the-art approaches.

On the Convergence Analysis of the Alternating Direction Method of Multipliers with Three Blocks

We consider a class of linearly constrained separable convex programming problems whose objective functions are the sum of three convex functions without coupled variables. For those problems, Han and Yuan (2012) have shown that the sequence generated by the alternating direction method of multipliers (ADMM) with three blocks converges globally to their KKT points under some technical conditions. In this paper, a new proof of this result is found under new conditions which are much weaker than Han and Yuan’s assumptions. Moreover, in order to accelerate the ADMM with three blocks, we also propose a relaxed ADMM involving an additional computation of optimal step size and establish its global convergence under mild conditions.

Homotopy Interior-Point Method for a General Multiobjective Programming Problem

We present a combined homotopy interior-point method for a general multiobjective programming problem. For solving the KKT points of the multiobjective programming problem, the homotopy equation is constructed. We prove the existence and convergence of a smooth homotopy path from almost any initial interior point to a solution of the KKT system under some basic assumptions.