Mining Novel Multivariate Relationships in Time Series Data Using Correlation Networks

In many domains, there is significant interest in capturing novel relationships between time series that represent activities recorded at different nodes of a highly complex system. In this paper, we introduce multipoles, a novel class of linear relationships between more than two time series. A multipole is a set of time series that have strong linear dependence among themselves, with the requirement that each time series makes a significant contribution to the linear dependence. We demonstrate that most interesting multipoles can be identified as cliques of negative correlations in a correlation network. Such cliques are typically rare in a real-world correlation network, which allows us to find almost all multipoles efficiently using a clique-enumeration approach. Using our proposed framework, we demonstrate the utility of multipoles in discovering new physical phenomena in two scientific domains: climate science and neuroscience. In particular, we discovered several multipole relationships that are reproducible in multiple other independent datasets and lead to novel domain insights.Comment: This is the accepted version of article submitted to IEEE Transactions on Knowledge and Data Engineering 201

A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

Enumerating Maximal Bicliques from a Large Graph using MapReduce

We consider the enumeration of maximal bipartite cliques (bicliques) from a large graph, a task central to many practical data mining problems in social network analysis and bioinformatics. We present novel parallel algorithms for the MapReduce platform, and an experimental evaluation using Hadoop MapReduce. Our algorithm is based on clustering the input graph into smaller sized subgraphs, followed by processing different subgraphs in parallel. Our algorithm uses two ideas that enable it to scale to large graphs: (1) the redundancy in work between different subgraph explorations is minimized through a careful pruning of the search space, and (2) the load on different reducers is balanced through the use of an appropriate total order among the vertices. Our evaluation shows that the algorithm scales to large graphs with millions of edges and tens of mil- lions of maximal bicliques. To our knowledge, this is the first work on maximal biclique enumeration for graphs of this scale.Comment: A preliminary version of the paper was accepted at the Proceedings of the 3rd IEEE International Congress on Big Data 201

Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications

Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem of extracting dense subgraphs has remained largely unexplored so far. In this work we study the problem of core decomposition of a multilayer network. The multilayer context is much challenging as no total order exists among multilayer cores; rather, they form a lattice whose size is exponential in the number of layers. In this setting we devise three algorithms which differ in the way they visit the core lattice and in their pruning techniques. We then move a step forward and study the problem of extracting the inner-most (also known as maximal) cores, i.e., the cores that are not dominated by any other core in terms of their core index in all the layers. Inner-most cores are typically orders of magnitude less than all the cores. Motivated by this, we devise an algorithm that effectively exploits the maximality property and extracts inner-most cores directly, without first computing a complete decomposition. Finally, we showcase the multilayer core-decomposition tool in a variety of scenarios and problems. We start by considering the problem of densest-subgraph extraction in multilayer networks. We introduce a definition of multilayer densest subgraph that trades-off between high density and number of layers in which the high density holds, and exploit multilayer core decomposition to approximate this problem with quality guarantees. As further applications, we show how to utilize multilayer core decomposition to speed-up the extraction of frequent cross-graph quasi-cliques and to generalize the community-search problem to the multilayer setting

Mining for Social Serendipity

A common social problem at an event in which people do not personally know all of the other participants is the natural tendency for cliques to form and for discussions to mainly happen between people who already know each other. This limits the possibility for people to make interesting new acquaintances and acts as a retarding force in the creation of new links in the social web. Encouraging users to socialize with people they don't know by revealing to them hidden surprising links could help to improve the diversity of interactions at an event. The goal of this paper is to propose a method for detecting "surprising" relationships between people attending an event. By "surprising" relationship we mean those relationships that are not known a priori, and that imply shared information not directly related with the local context of the event (location, interests, contacts) at which the meeting takes place. To demonstrate and test our concept we used the Flickr community. We focused on a community of users associated with a social event (a computer science conference) and represented in Flickr by means of a photo pool devoted to the event. We use Flickr metadata (tags) to mine for user similarity not related to the context of the event, as represented in the corresponding Flickr group. For example, we look for two group members who have been in the same highly specific place (identified by means of geo-tagged photos), but are not friends of each other and share no other common interests or, social neighborhood