Random Walks on Hypergraphs with Edge-Dependent Vertex Weights

Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random walks to develop a spectral theory for hypergraphs with edge-dependent vertex weights: hypergraphs where every vertex $v$ has a weight $\gamma_e(v)$ for each incident hyperedge $e$ that describes the contribution of $v$ to the hyperedge $e$. We derive a random walk-based hypergraph Laplacian, and bound the mixing time of random walks on such hypergraphs. Moreover, we give conditions under which random walks on such hypergraphs are equivalent to random walks on graphs. As a corollary, we show that current machine learning methods that rely on Laplacians derived from random walks on hypergraphs with edge-independent vertex weights do not utilize higher-order relationships in the data. Finally, we demonstrate the advantages of hypergraphs with edge-dependent vertex weights on ranking applications using real-world datasets.Comment: Accepted to ICML 201

Exploiting random walks for robust, scalable, structure-free data aggregation and routing in mobile ad-hoc networks (MANETs)

The focus of this thesis is on the design of scalable data aggregation protocols for Mobile Ad-hoc Networks (MANETs). Data aggregation Protocols that rely on network structures such as trees or backbones are not well suited for MANETs because the underlying topology of MANETs is constantly changing. On the other hand, unstructured techniques such as flooding and gossiping have a high messaging overhead and take a long time to finish. Therefore, in this thesis, we explore the use of random walks as a structure-free alternative for data aggregation in MANETs.;The basic idea is to introduce one or more tokens that successively visit each node in a MANET by executing a random walk and compute the aggregate state. While random walks are simple, robust and overhead-free, plain random walks tend to be slow in visiting all nodes because the token can get stuck in regions of already visited nodes. Therefore, we first introduce self-repelling random walks (SRRW) in which at each step, the token chooses a neighbor that has been visited the least number of times. While SRRW significantly speeds up random walks in the initial stages, towards the end a slowdown is observed when a significant fraction of nodes are already visited. To address this shortcoming, we then develop two complementary strategies that speed up data aggregation.;First, we introduce gradient biased random walks (a pull-based strategy) where short temporary multi-hop gradients are used to pull the tokens toward unvisited node. We prove that gradient biased random walks achieve a cover time of O(N) and message overhead of O(NlogN) where N is the number of nodes in the network. Next, we introduce a push-based strategy in which self-repelling random walks are complemented by a single step push phase before the random walk phase, in which each node broadcasts its information to its neighbors. We show that this small push goes a long way in speeding up data aggregation. Push based random walks finish data aggregation in O(N) message and time. Finally, we describe hierarchical extension of the push-based protocol which can produce multi-resolution aggregates at each node using only O(NlogN) messages.;All our results are validated using simulations in ns-3 in networks ranging from 100 to 4000 nodes under different network densities, node speed and mobility models

Networking - A Statistical Physics Perspective

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.Comment: (Review article) 71 pages, 14 figure

Cognitive satellite communications and representation learning for streaming and complex graphs.

This dissertation includes two topics. The first topic studies a promising dynamic spectrum access algorithm (DSA) that improves the throughput of satellite communication (SATCOM) under the uncertainty. The other topic investigates distributed representation learning for streaming and complex networks. DSA allows a secondary user to access the spectrum that are not occupied by primary users. However, uncertainty in SATCOM causes more spectrum sensing errors. In this dissertation, the uncertainty has been addressed by formulating a DSA decision-making process as a Partially Observable Markov Decision Process (POMDP) model to optimally determine which channels to sense and access. Large-scale networks have attracted many attentions to discover the hidden information from big data. Particularly, representation learning embeds the network into a lower vector space while maximally preserving the similarity among nodes. I propose a real-time distributed graph embedding algorithm (RTDGE) which is capable of distributively embedding the streaming graph by combining a novel edge partition approach and an incremental negative sample approach. Furthermore, a platform is prototyped based on Kafka and Storm. Real-time Twitter network data can be retrieved, partitioned and processed for state-of-art tasks. For knowledge graphs, existing works cannot capture the complex connection patterns and never consider the impacts from complicated relations, due to the unquantifiable relationships. A novel embedding algorithm is proposed to hierarchically measure the structural similarity and the impacts from relations by constructing a multi-layer graph. Then, an advanced representation learning model is designed based on an entity\u27s context generated by random walks on the multi-layer content graph