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1. Bayesian Topology Learning and noise removal from network data

   https://doi.org/10.1007/s43926-021-00011-w  

   Ramezani Mayiami, Mahmoud; Hajimirsadeghi, Mohammad; Skretting, Karl; Dong, Xiaowen; Blum, Rick S.; Poor, H. Vincent (December 2021, Discover Internet of Things)

   null (Ed.)

   Abstract Learning the topology of a graph from available data is of great interest in many emerging applications. Some examples are social networks, internet of things networks (intelligent IoT and industrial IoT), biological connection networks, sensor networks and traffic network patterns. In this paper, a graph topology inference approach is proposed to learn the underlying graph structure from a given set of noisy multi-variate observations, which are modeled as graph signals generated from a Gaussian Markov Random Field (GMRF) process. A factor analysis model is applied to represent the graph signals in a latent space where the basis is related to the underlying graph structure. An optimal graph filter is also developed to recover the graph signals from noisy observations. In the final step, an optimization problem is proposed to learn the underlying graph topology from the recovered signals. Moreover, a fast algorithm employing the proximal point method has been proposed to solve the problem efficiently. Experimental results employing both synthetic and real data show the effectiveness of the proposed method in recovering the signals and inferring the underlying graph. 

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2. Active Learning for Graphs with Noisy Structures

   Chi, Hongliang; Qi, Cong; Wang, Suhang; Ma, Yao (April 2024, SIAM)

   Graph Neural Networks (GNNs) have seen significant success in tasks such as node classification, largely contingent upon the availability of sufficient labeled nodes. Yet, the excessive cost of labeling large-scale graphs led to a focus on active learning on graphs, which aims for effective data selection to maximize downstream model performance. Notably, most existing methods assume reliable graph topology, while real-world scenarios often present noisy graphs. Given this, designing a successful active learning framework for noisy graphs is highly needed but challenging, as selecting data for labeling and obtaining a clean graph are two tasks naturally interdependent: selecting high-quality data requires clean graph structure while cleaning noisy graph structure requires sufficient labeled data. Considering the complexity mentioned above, we propose an active learning framework, GALClean, which has been specifically designed to adopt an iterative approach for conducting both data selection and graph purification simultaneously with best information learned from the prior iteration. Importantly, we summarize GALClean as an instance of the Expectation-Maximization algorithm, which provides a theoretical understanding of its design and mechanisms. This theory naturally leads to an enhanced version, GALClean+. Extensive experiments have demonstrated the effectiveness and robustness of our proposed method across various types and levels of noisy graphs. 

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3. Topology Inference of Directed Graphs by Gaussian Processes With Sparsity Constraints

   https://doi.org/10.1109/TSP.2024.3381071  

   Cui, Chen; Banelli, Paolo; Djurić, Petar M (January 2024, IEEE Transactions on Signal Processing)

   In machine learning applications, data are often high-dimensional and intricately related. It is often of interest to find the underlying structure and Granger causal relationships among the data and represent these relationships with directed graphs. In this paper, we study multivariate time series, where each series is associated with a node of a graph, and where the objective is to estimate the topology of a sparse graph that reflects how the nodes of the graph affect each other, if at all. We propose a novel fully Bayesian approach that employs a sparsity-encouraging prior on the hyperparameters. The proposed method allows for nonlinear and multiple lag relationships among the time series. The method is based on Gaussian processes, and it treats the entries of the graph adjacency matrix as hyperparameters. It utilizes a modified automatic relevance determination (ARD) kernel and allows for learning the mapping function from selected past data to current data as edges of a graph . We show that the resulting adjacency matrix provides the intrinsic structure of the graph and answers causality-related questions. Numerical tests show that the proposed method has comparable or better performance than state-of-the-art methods. 

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4. Data-Driven Graph Construction of Power Flow Graphs for Electric Power Transmission Networks

   https://doi.org/10.1109/ICMLA61862.2024.00053  

   Poole, Benjamin; Ratnakumar, Rajan; Madurasinghe, Dulip Tharaka; Kümmerle, Christian; Venayagamoorthy, Ganesh Kumar; Lee, Minwoo (December 2024, IEEE)

   A comprehensive understanding of the topology of the electric power transmission network (EPTN) is essential for reliable and robust control of power systems. While existing research primarily relies on domain-specific methods, it lacks data-driven approaches that have proven effective in modeling the topology of complex systems. To address this gap, this paper explores the potential of data-driven methods for more accurate and adaptive solutions to uncover the true underlying topology of EPTNs. First, this paper examines Gaussian Graphical Models (GGM) to create an EPTN network graph (i.e., undirected simple graph). Second, to further refine and validate this estimated network graph, a physics-based, domain specific refinement algorithm is proposed to prune false edges and construct the corresponding electric power flow network graph (i.e., directed multi-graph). The proposed method is tested using a synchrophasor dataset collected from a two-area, four-machine power system simulated on the real-time digital simulator (RTDS) platform. Experimental results show both the network and flow graphs can be reconstructed using various operating conditions and topologies with limited failure cases. 

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5. GraSSNet: Graph Soft Sensing Neural Networks

   https://doi.org/10.1109/BigData52589.2021.9671903  

   Huang, Yu; Zhang, Chao; Yella, Jaswanth; Petrov, Sergei; Qian, Xiaoye; Tang, Yufei; Zhu, Xingquan; Bom, Sthitie (December 2021, Proc. of the 2021 IEEE International Conference on Big Data (Big Data))

   In the era of big data, data-driven based classification has become an essential method in smart manufacturing to guide production and optimize inspection. The industrial data obtained in practice is usually time-series data collected by soft sensors, which are highly nonlinear, nonstationary, imbalanced, and noisy. Most existing soft-sensing machine learning models focus on capturing either intra-series temporal dependencies or pre-defined inter-series correlations, while ignoring the correlation between labels as each instance is associated with multiple labels simultaneously. In this paper, we propose a novel graph based soft-sensing neural network (GraSSNet) for multivariate time-series classification of noisy and highly-imbalanced soft-sensing data. The proposed GraSSNet is able to 1) capture the inter-series and intra-series dependencies jointly in the spectral domain; 2) exploit the label correlations by superimposing label graph that built from statistical co-occurrence information; 3) learn features with attention mechanism from both textual and numerical domain; and 4) leverage unlabeled data and mitigate data imbalance by semi-supervised learning. Comparative studies with other commonly used classifiers are carried out on Seagate soft sensing data, and the experimental results validate the competitive performance of our proposed method. 

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