Data mining practitioners are facing challenges from data with network structure. In this paper, we address a specific class of global-state networks which comprises of a set of network instances sharing a similar structure yet having different values at local nodes. Each instance is associated with a global state which indicates the occurrence of an event. The objective is to uncover a small set of discriminative subnetworks that can optimally classify global network values. Unlike most existing studies which explore an exponential subnetwork space, we address this difficult problem by adopting a space transformation approach. Specifically, we present an algorithm that optimizes a constrained dualobjective function to learn a low-dimensional subspace that is capable of discriminating networks labelled by different global states, while reconciling with common network topology sharing across instances. Our algorithm takes an appealing approach from spectral graph learning and we show that the globally optimum solution can be achieved via matrix eigen-decomposition.
In many real-world applications, data is represented in the form of networks with structures and attributes changing over time. The dynamic changes not only happen at nodes/edges, forming local subnetwork processes, but also eventually influence global states of networks. The need to understand what these local network processes are, how they evolve and consequently govern the progression of global network states has become increasingly important. In this paper, we explore these questions and develop a novel algorithm for mining a succinct set of subnetworks that are predictive and evolve along with the progression of global network states. Our algorithm is designed in the framework of logistic regression that fits a model for multi-states of network samples. Its objective function considers both the spatial network topology and temporal smooth transition between adjacent global network states, and we show that its global optimum solution can be achieved via steepest descent. Extensive experimental analysis on both synthetic and real world datasets demonstrates the effectiveness of our algorithm against competing methods, not only in the prediction accuracy but also in terms of domain relevance of the discovered subnetworks.
Network regularization is an effective tool for incorporating structural prior knowledge to learn coherent models over networks, and has yielded provably accurate estimates in applications ranging from spatial economics to neuroimaging studies. Recently, there has been an increasing interest in extending network regularization to the spatio-temporal case to accommodate the evolution of networks. However, in both static and spatiotemporal cases, missing or corrupted edge weights can compromise the ability of network regularization to discover desired solutions. To address these gaps, we propose a novel approach-discrepancy-aware network regularization (DANR)-that is robust to inadequate regularizations and effectively captures model evolution and structural changes over spatio-temporal networks. We develop a distributed and scalable algorithm based on alternating direction method of multipliers (ADMM) to solve the proposed problem with guaranteed convergence to global optimum solutions. Experimental results on both synthetic and real-world networks demonstrate that our approach achieves improved performance on various tasks, and enables interpretation of model changes in evolving networks.
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