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1. Direction-Optimizing Label Propagation Framework for Structure Detection in Graphs: Design, Implementation, and Experimental Analysis

   https://doi.org/10.1145/3564593  

   Liu, Xu T. ; Lumsdaine, Andrew ; Halappanavar, Mahantesh ; Barker, Kevin ; Gebremedhin, Assefaw H. ( October 2022 , ACM Journal of Experimental Algorithmics)

   Label Propagation is not only a well-known machine learning algorithm for classification, but it is also an effective method for discovering communities and connected components in networks. We propose a new Direction-Optimizing Label Propagation Algorithm (DOLPA) framework that enhances the performance of the standard Label Propagation Algorithm (LPA), increases its scalability, and extends its versatility and application scope. As a central feature, the DOLPA framework relies on the use of frontiers and alternates between label push and label pull operations to attain high performance. It is formulated in such a way that the same basic algorithm can be used for finding communities or connected components in graphs by only changing the objective function used. Additionally, DOLPA has parameters for tuning the processing order of vertices in a graph to reduce the number of edges visited and improve the quality of solution obtained. We present the design and implementation of the enhanced algorithm as well as our shared-memory parallelization of it using OpenMP. We also present an extensive experimental evaluation of our implementations using the LFR benchmark and real-world networks drawn from various domains. Compared with an implementation of LPA for community detection available in a widely used network analysis software, we achievemore »at most five times the F-Score while maintaining similar runtime for graphs with overlapping communities. We also compare DOLPA against an implementation of the Louvain method for community detection using the same LFR-graphs and show that DOLPA achieves about three times the F-Score at just 10% of the runtime. For connected component decomposition, our algorithm achieves orders of magnitude speedups over the basic LP-based algorithm on large diameter graphs, up to 13.2 × speedup over the Shiloach-Vishkin algorithm, and up to 1.6 × speedup over Afforest on an Intel Xeon processor using 40 threads.« less
2. Hyperbolic Graph Convolutional Neural Networks

   Chami, I. ; Ying, R. ; Ré, C. ; Leskovec, J. ( December 2019 , Advances in neural information processing systems)

   Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers an exciting alternative, as it enables embeddings with much smaller distortion. However, extending GCNs to hyperbolic geometry presents several unique challenges because it is not clear how to define neural network operations, such as feature transformation and aggregation, in hyperbolic space. Furthermore, since input features are often Euclidean, it is unclear how to transform the features into hyperbolic embeddings with the right amount of curvature. Here we propose Hyperbolic Graph Convolutional Neural Network (HGCN), the first inductive hyperbolic GCN that leverages both the expressiveness of GCNs and hyperbolic geometry to learn inductive node representations for hierarchical and scale-free graphs. We derive GCNs operations in the hyperboloid model of hyperbolic space and map Euclidean input features to embeddings in hyperbolic spaces with different trainable curvature at each layer. Experiments demonstrate that HGCN learns embeddings that preserve hierarchical structure, and leads to improved performance when compared to Euclidean analogs, even with very low dimensional embeddings: compared to state-of-the-art GCNs, HGCN achieves an error reduction of up to 63.1%more »in ROC AUC for link prediction and of up to 47.5% in F1 score for node classification, also improving state-of-the art on the PubMed dataset.« less
3. Optimal Frameworks for Detecting Anomalies in Sensor-Intensive Heterogeneous Networks

   https://doi.org/10.1287/ijoc.2022.1192  

   Moghaddass, Ramin ; Guan, Yongtao ( January 2022 , INFORMS Journal on Computing)

   Many network/graph structures are continuously monitored by various sensors that are placed at a subset of nodes and edges. The multidimensional data collected from these sensors over time create large-scale graph data in which the data points are highly dependent. Monitoring large-scale attributed networks with thousands of nodes and heterogeneous sensor data to detect anomalies and unusual events is a complex and computationally expensive process. This paper introduces a new generic approach inspired by state-space models for network anomaly detection that can utilize the information from the network topology, the node attributes (sensor data), and the anomaly propagation sets in an integrated manner to analyze the entire network all at once. This article presents how heterogeneous network sensor data can be analyzed to locate the sources of anomalies as well as the anomalous regions in a network, which can be impacted by one or multiple anomalies at any time instance. Experimental results demonstrate the superior performance of our proposed framework in detecting anomalies in attributed graphs. Summary of Contribution: With the increasing availability of large-scale network sensors and rapid advances in artificial intelligence methods, fundamentally new analytical tools are needed that can integrate data collected from sensors across the networksmore »for decision making while taking into account the stochastic and topological dependencies between nodes, sensors, and anomalies. This paper develops a framework to intelligently and efficiently analyze complex and highly dependent data collected from disparate sensors across large-scale network/graph structures to detect anomalies and abnormal behavior in real time. Unlike general purpose (often black-box) machine learning models, this paper proposes a unique framework for network/graph structures that incorporates the complexities of networks and interdependencies between network entities and sensors. Because of the multidisciplinary nature of the paper that involves optimization, machine learning, and system monitoring and control, it can help researchers in both operations research and computer science domains to develop new network-specific computing tools and machine learning frameworks to efficiently manage large-scale network data.« less
4. Classifying Component Function in Product Assemblies With Graph Neural Networks

   https://doi.org/10.1115/1.4052720  

   Ferrero, Vincenzo ; DuPont, Bryony ; Hassani, Kaveh ; Grandi, Daniele ( February 2022 , Journal of Mechanical Design)

   Abstract Function is defined as the ensemble of tasks that enable the product to complete the designed purpose. Functional tools, such as functional modeling, offer decision guidance in the early phase of product design, where explicit design decisions are yet to be made. Function-based design data is often sparse and grounded in individual interpretation. As such, function-based design tools can benefit from automatic function classification to increase data fidelity and provide function representation models that enable function-based intelligent design agents. Function-based design data is commonly stored in manually generated design repositories. These design repositories are a collection of expert knowledge and interpretations of function in product design bounded by function-flow and component taxonomies. In this work, we represent a structured taxonomy-based design repository as assembly-flow graphs, then leverage a graph neural network (GNN) model to perform automatic function classification. We support automated function classification by learning from repository data to establish the ground truth of component function assignment. Experimental results show that our GNN model achieves a micro-average F1-score of 0.617 for tier 1 (broad), 0.624 for tier 2, and 0.415 for tier 3 (specific) functions. Given the imbalance of data features and the subjectivity in the definition of productmore »function, the results are encouraging. Our efforts in this paper can be a starting point for more sophisticated applications in knowledge-based CAD systems and Design-for-X consideration in function-based design.« less
5. Local Access to Huge Random Objects Through Partial Sampling

   Biswas, Amartya Shankha ; Rubinfeld, Ronitt ; Yodpinyanee, Anak ( January 2020 , 11th Innovations in Theoretical Computer Science Conference, ITCS 2020)

   Consider an algorithm performing a computation on a huge random object (for example a random graph or a "long" random walk). Is it necessary to generate the entire object prior to the computation, or is it possible to provide query access to the object and sample it incrementally "on-the-fly" (as requested by the algorithm)? Such an implementation should emulate the random object by answering queries in a manner consistent with an instance of the random object sampled from the true distribution (or close to it). This paradigm is useful when the algorithm is sub-linear and thus, sampling the entire object up front would ruin its efficiency. Our first set of results focus on undirected graphs with independent edge probabilities, i.e. each edge is chosen as an independent Bernoulli random variable. We provide a general implementation for this model under certain assumptions. Then, we use this to obtain the first efficient local implementations for the Erdös-Rényi G(n,p) model for all values of p, and the Stochastic Block model. As in previous local-access implementations for random graphs, we support Vertex-Pair and Next-Neighbor queries. In addition, we introduce a new Random-Neighbor query. Next, we give the first local-access implementation for All-Neighbors queries inmore »the (sparse and directed) Kleinberg’s Small-World model. Our implementations require no pre-processing time, and answer each query using O(poly(log n)) time, random bits, and additional space. Next, we show how to implement random Catalan objects, specifically focusing on Dyck paths (balanced random walks on the integer line that are always non-negative). Here, we support Height queries to find the location of the walk, and First-Return queries to find the time when the walk returns to a specified location. This in turn can be used to implement Next-Neighbor queries on random rooted ordered trees, and Matching-Bracket queries on random well bracketed expressions (the Dyck language). Finally, we introduce two features to define a new model that: (1) allows multiple independent (and even simultaneous) instantiations of the same implementation, to be consistent with each other without the need for communication, (2) allows us to generate a richer class of random objects that do not have a succinct description. Specifically, we study uniformly random valid q-colorings of an input graph G with maximum degree Δ. This is in contrast to prior work in the area, where the relevant random objects are defined as a distribution with O(1) parameters (for example, n and p in the G(n,p) model). The distribution over valid colorings is instead specified via a "huge" input (the underlying graph G), that is far too large to be read by a sub-linear time algorithm. Instead, our implementation accesses G through local neighborhood probes, and is able to answer queries to the color of any given vertex in sub-linear time for q ≥ 9Δ, in a manner that is consistent with a specific random valid coloring of G. Furthermore, the implementation is memory-less, and can maintain consistency with non-communicating copies of itself.« less