skip to main content

Title: DESTINE: Dense Subgraph Detection on Multi-Layered Networks
Dense subgraph detection is a fundamental building block for a va- riety of applications. Most of the existing methods aim to discover dense subgraphs within either a single network or a multi-view network while ignoring the informative node dependencies across multiple layers of networks in a complex system. To date, it largely remains a daunting task to detect dense subgraphs on multi-layered networks. In this paper, we formulate the problem of dense sub- graph detection on multi-layered networks based on cross-layer consistency principle. We further propose a novel algorithm Des- tine based on projected gradient descent with the following ad- vantages. First, armed with the cross-layer dependencies, Destine is able to detect significantly more accurate and meaningful dense subgraphs at each layer. Second, it scales linearly w.r.t. the num- ber of links in the multi-layered network. Extensive experiments demonstrate the efficacy of the proposed Destine algorithm in various cases.
; ; ; ; ;
Award ID(s):
1939725 1947135
Publication Date:
Journal Name:
Destine: Dense Subgraph Detection on Multi-Layered Networks
Page Range or eLocation-ID:
3558 to 3562
Sponsoring Org:
National Science Foundation
More Like this
  1. Network embedding has gained more attentions in recent years. It has been shown that the learned low-dimensional node vector representations could advance a myriad of graph mining tasks such as node classification, community detection, and link prediction. A vast majority of the existing efforts are overwhelmingly devoted to single-layered networks or homogeneous networks with a single type of nodes and node interactions. However, in many real-world applications, a variety of networks could be abstracted and presented in a multilayered fashion. Typical multi-layered networks include critical infrastructure systems, collaboration platforms, social recommender systems, to name a few. Despite the widespread use of multi-layered networks, it remains a daunting task to learn vector representations of different types of nodes due to the bewildering combination of both within-layer connections and cross-layer network dependencies. In this paper, we study a novel problem of multi-layered network embedding. In particular, we propose a principled framework – MANE to model both within-layer connections and cross-layer network dependencies simultaneously in a unified optimization framework for embedding representation learning. Experiments on real-world multi-layered networks corroborate the effectiveness of the proposed framework.
  2. Multi-layered inter-dependent networks have emerged in a wealth of high-impact application domains. Cross-layer dependency inference, which aims to predict the dependencies between nodes across different layers, plays a pivotal role in such multi-layered network systems. Most, if not all, of existing methods exclusively follow a coupling principle of design and can be categorized into the following two groups, including (1) heterogeneous network embedding based methods (data coupling), and (2) collaborative filtering based methods (module coupling). Despite the favorable achievement, methods of both types are faced with two intricate challenges, including (1) the sparsity challenge where very limited observations of cross-layer dependencies are available, resulting in a deteriorated prediction of missing dependencies, and (2) the dynamic challenge given that the multi-layered network system is constantly evolving over time. In this paper, we first demonstrate that the inability of existing methods to resolve the sparsity challenge roots in the coupling principle from the perspectives of both data coupling and module coupling. Armed with such theoretical analysis, we pursue a new principle where the key idea is to decouple the within-layer connectivity from the observed cross-layer dependencies. Specifically, to tackle the sparsity challenge for static networks, we propose FITO-S, which incorporates a positionmore »embedding matrix generated by random walk with restart and the embedding space transformation function. More essentially, the decoupling principle ameliorates the dynamic challenge, which naturally leads to FITO-D, being capable of tracking the inference results in the dynamic setting through incrementally updating the position embedding matrix and fine-tuning the space transformation function. Extensive evaluations on real-world datasets demonstrate the superiority of the proposed framework FITO for cross-layer dependency inference.« less
  3. We present a new verification algorithm to efficiently and incrementally verify arbitrarily layered network data planes that are implemented using packet encapsulation. Inspired by work on model checking of pushdown systems for recursive programs, we develop a verification algorithm for networks with packets consisting of stacks of headers. Our algorithm is based on a new technique that lazily “repairs” a decomposed stack of header sets on demand to account for cross-layer dependencies. We demonstrate how to integrate our approach with existing fast incremental data plane verifiers and have implemented our ideas in a tool called KATRA. Evaluating KATRA against an alternative approach based on equipping existing incremental verifiers to emulate finite header stacks, we show that KATRA is between 5x-32x faster for packets with just 2 headers (layers), and that its performance advantage grows with both network size and layering.
  4. Network embedding has become the cornerstone of a variety of mining tasks, such as classification, link prediction, clustering, anomaly detection and many more, thanks to its superior ability to encode the intrinsic network characteristics in a compact low-dimensional space. Most of the existing methods focus on a single network and/or a single resolution, which generate embeddings of different network objects (node/subgraph/network) from different networks separately. A fundamental limitation with such methods is that the intrinsic relationship across different networks (e.g., two networks share same or similar subgraphs) and that across different resolutions (e.g., the node-subgraph membership) are ignored, resulting in disparate embeddings. Consequentially, it leads to sub-optimal performance or even becomes inapplicable for some downstream mining tasks (e.g., role classification, network alignment. etc.). In this paper, we propose a unified framework MrMine to learn the representations of objects from multiple networks at three complementary resolutions (i.e., network, subgraph and node) simultaneously. The key idea is to construct the cross-resolution cross-network context for each object. The proposed method bears two distinctive features. First, it enables and/or boosts various multi-network downstream mining tasks by having embeddings at different resolutions from different networks in the same embedding space. Second, Our method is efficientmore »and scalable, with a O(nlog(n)) time complexity for the base algorithm and a linear time complexity w.r.t. the number of nodes and edges of input networks for the accelerated version. Extensive experiments on real-world data show that our methods (1) are able to enable and enhance a variety of multi-network mining tasks, and (2) scale up to million-node networks.« less
  5. Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference outcomes. Different from deep or high-dimensional parametric models, the lack of interpretability in graphical models is due to the cyclic and long-range dependencies and the byzantine inference procedures. Prior works did not tackle cycles and make the inferences interpretable. We formulate the explaination of probabilistic inferences as a constrained cross-entropy minimization problem to find simple subgraphs that faithfully approximate the inferences. We prove that the optimization is NP-hard, while the objective is not monotonic and submodular to guarantee efficient greedy approximation. We propose a beam search algorithm to find trees to enhance the explanation interpretability and diversity. To allow efficient search on large and dense graphs without hurting faithfulness, we further propose parallelization and a pruning strategy. We demonstrate superior performance on four networks from distinct applications, comparing favorably to other explanation methods, including LIME.