Applications of Structural Balance in Signed Social Networks

We present measures, models and link prediction algorithms based on the structural balance in signed social networks. Certain social networks contain, in addition to the usual 'friend' links, 'enemy' links. These networks are called signed social networks. A classical and major concept for signed social networks is that of structural balance, i.e., the tendency of triangles to be 'balanced' towards including an even number of negative edges, such as friend-friend-friend and friend-enemy-enemy triangles. In this article, we introduce several new signed network analysis methods that exploit structural balance for measuring partial balance, for finding communities of people based on balance, for drawing signed social networks, and for solving the problem of link prediction. Notably, the introduced methods are based on the signed graph Laplacian and on the concept of signed resistance distances. We evaluate our methods on a collection of four signed social network datasets.Comment: 37 page

Towards an SDP-based Approach to Spectral Methods: A Nearly-Linear-Time Algorithm for Graph Partitioning and Decomposition

In this paper, we consider the following graph partitioning problem: The input is an undirected graph $G=(V,E),$ a balance parameter $b \in (0,1/2]$ and a target conductance value $\gamma \in (0,1).$ The output is a cut which, if non-empty, is of conductance at most $O(f),$ for some function $f(G, \gamma),$ and which is either balanced or well correlated with all cuts of conductance at most $\gamma.$ Spielman and Teng gave an $\tilde{O}(|E|/\gamma^{2})$-time algorithm for $f= \sqrt{\gamma \log^{3}|V|}$ and used it to decompose graphs into a collection of near-expanders. We present a new spectral algorithm for this problem which runs in time $\tilde{O}(|E|/\gamma)$ for $f=\sqrt{\gamma}.$ Our result yields the first nearly-linear time algorithm for the classic Balanced Separator problem that achieves the asymptotically optimal approximation guarantee for spectral methods. Our method has the advantage of being conceptually simple and relies on a primal-dual semidefinite-programming SDP approach. We first consider a natural SDP relaxation for the Balanced Separator problem. While it is easy to obtain from this SDP a certificate of the fact that the graph has no balanced cut of conductance less than $\gamma,$ somewhat surprisingly, we can obtain a certificate for the stronger correlation condition. This is achieved via a novel separation oracle for our SDP and by appealing to Arora and Kale's framework to bound the running time. Our result contains technical ingredients that may be of independent interest.Comment: To appear in SODA 201

Reflection methods for user-friendly submodular optimization

Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular functions, especially for minimization problems. While general submodular minimization is challenging, we propose a new method that exploits existing decomposability of submodular functions. In contrast to previous approaches, our method is neither approximate, nor impractical, nor does it need any cumbersome parameter tuning. Moreover, it is easy to implement and parallelize. A key component of our method is a formulation of the discrete submodular minimization problem as a continuous best approximation problem that is solved through a sequence of reflections, and its solution can be easily thresholded to obtain an optimal discrete solution. This method solves both the continuous and discrete formulations of the problem, and therefore has applications in learning, inference, and reconstruction. In our experiments, we illustrate the benefits of our method on two image segmentation tasks.Comment: Neural Information Processing Systems (NIPS), \'Etats-Unis (2013

Image Parsing with a Wide Range of Classes and Scene-Level Context

This paper presents a nonparametric scene parsing approach that improves the overall accuracy, as well as the coverage of foreground classes in scene images. We first improve the label likelihood estimates at superpixels by merging likelihood scores from different probabilistic classifiers. This boosts the classification performance and enriches the representation of less-represented classes. Our second contribution consists of incorporating semantic context in the parsing process through global label costs. Our method does not rely on image retrieval sets but rather assigns a global likelihood estimate to each label, which is plugged into the overall energy function. We evaluate our system on two large-scale datasets, SIFTflow and LMSun. We achieve state-of-the-art performance on the SIFTflow dataset and near-record results on LMSun.Comment: Published at CVPR 2015, Computer Vision and Pattern Recognition (CVPR), 2015 IEEE Conference o