Abstract: This paper addresses a distributed convex optimization problem with a class of coupled constraints, which arise in a multi-agent system composed of multiple communities modeled by cliques. First, we propose a fully distributed gradient-based algorithm with a novel operator inspired by the convex projection, called the clique-based projection. Next, we scrutinize the convergence properties for both diminishing and fixed step sizes. For diminishing ones, we show the convergence to an optimal solution under the assumptions of the smoothness of an objective function and the compactness of the constraint set. Additionally, when the objective function is strongly monotone, the strict convergence to the unique solution is proved without the assumption of compactness.

Abstract: The unit-modulus least squares (UMLS) problem has a wide spectrum of applications in signal processing, e.g., phase-only beamforming, phase retrieval, radar code design, and sensor network localization. Scalable first-order methods such as projected gradient descent (PGD) have recently been studied as a simple yet efficient approach to solving the UMLS problem. Existing results on the convergence of PGD for UMLS often focus on global convergence to stationary points. As a non-convex problem, only a sublinear convergence rate has been established. However, these results do not explain the fast convergence of PGD frequently observed in practice. This manuscript presents a novel analysis of convergence of PGD for UMLS, justifying the linear convergence behavior of the algorithm near the solution.

For environmental, sustainable economic and political reasons, recycling processes are becoming increasingly important, aiming at a much higher use of secondary raw materials. Currently, for the copper and aluminium industries, no method for the non-destructive online analysis of heterogeneous materials are available. The Prompt Gamma Neutron Activation Analysis (PGNAA) has the potential to overcome this challenge. A difficulty when using PGNAA for online classification arises from the small amount of noisy data, due to short-term measurements. In this case, classical evaluation methods using detailed peak by peak analysis fail. Therefore, we propose to view spectral data as probability distributions. Then, we can classify material using maximum log-likelihood with respect to kernel density estimation and use discrete sampling to optimize hyperparameters. For measurements of pure aluminium alloys we achieve near perfect classification of aluminium alloys under 0.25 second.

In this work, we study the problem of partitioning a set of graphs into different groups such that the graphs in the same group are similar while the graphs in different groups are dissimilar. This problem was rarely studied previously, although there have been a lot of work on node clustering and graph classification. The problem is challenging because it is difficult to measure the similarity or distance between graphs. One feasible approach is using graph kernels to compute a similarity matrix for the graphs and then performing spectral clustering, but the effectiveness of existing graph kernels in measuring the similarity between graphs is very limited. To solve the problem, we propose a novel method called Deep Graph-Level Clustering (DGLC). DGLC utilizes a graph isomorphism network to learn graph-level representations by maximizing the mutual information between the representations of entire graphs and substructures, under the regularization of a clustering module that ensures discriminative representations via pseudo labels. DGLC achieves graph-level representation learning and graph-level clustering in an end-to-end manner. The experimental results on six benchmark datasets of graphs show that our DGLC has state-of-the-art performance in comparison to many baselines.

Graph classification is crucial in network analyses. Networks face potential security threats, such as adversarial attacks. Some defense methods may trade off the algorithm complexity for robustness, such as adversarial training, whereas others may trade off clean example performance, such as smoothingbased defense. Most suffer from high complexity or low transferability. To address this problem, we proposed EGC2, an enhanced graph classification model with easy graph compression. EGC2 captures the relationship between the features of different nodes by constructing feature graphs and improving the aggregation of the node-level representations. To achieve lower-complexity defense applied to graph classification models, EGC2 utilizes a centrality-based edge-importance index to compress the graphs, filtering out trivial structures and adversarial perturbations in the input graphs, thus improving the model's robustness. Experiments on ten benchmark datasets demonstrate that the proposed feature read-out and graph compression mechanisms enhance the robustness of multiple basic models, resulting in a state-of-the-art performance in terms of accuracy and robustness against various adversarial attacks.

In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and edges as proposed in [1, 2]. The augmented graph is then embedded in a Euclidean space associated to its Laplacian and we cluster vertices via a modified K-means algorithm, using a new vector-valued distance in the embedding space. Main novelty of our method, which can be classified as an early fusion method, i.e., a method in which additional information on vertices are fused to the structure information before applying clustering, is the interpretation of attributes as new realizations of graph vertices, which can be dealt with as coordinate vectors in a related Euclidean space. This allows us to extend a scalable generalized spectral clustering procedure which substitutes graph Laplacian eigenvectors with some vectors, named algebraically smooth vectors, obtained by a linear-time complexity Algebraic MultiGrid (AMG) method. We discuss the performance of our proposed clustering method by comparison with recent literature approaches and public available results. Extensive experiments on different types of synthetic datasets and real-world attributed graphs show that our new algorithm, embedding attributes information in the clustering, outperforms structure-only-based methods, when the attributed network has an ambiguous structure. Furthermore, our new method largely outperforms the method which originally proposed the graph augmentation, showing that our embedding strategy and vector-valued distance are very effective in taking advantages from the augmented-graph representation.

Jobs on high-performance computing (HPC) clusters can suffer significant performance degradation due to inter-job network interference. Topology-aware job allocation problem (TJAP) is such a problem that decides how to dedicate nodes to specific applications to mitigate inter-job network interference. In this paper, we study the window-based TJAP on a fat-tree network aiming at minimizing the cost of communication hop, a defined inter-job interference metric. The window-based approach for scheduling repeats periodically taking the jobs in the queue and solving an assignment problem that maps jobs to the available nodes. Two special allocation strategies are considered, i.e., static continuity assignment strategy (SCAS) and dynamic continuity assignment strategy (DCAS). For the SCAS, a 0-1 integer programming is developed. For the DCAS, an approach called neural simulated algorithm (NSA), which is an extension to simulated algorithm (SA) that learns a repair operator and employs them in a guided heuristic search, is proposed. The efficacy of NSA is demonstrated with a computational study against SA and SCIP. The results of numerical experiments indicate that both the model and algorithm proposed in this paper are effective.

How to interpret a data mining model has received much attention recently, because people may distrust a black-box predictive model if they do not understand how the model works. Hence, it will be trustworthy if a model can provide transparent illustrations on how to make the decision. Although many rule-based interpretable classification algorithms have been proposed, all these existing solutions cannot directly construct an interpretable model to provide personalized prediction for each individual test sample. In this paper, we make a first step towards formally introducing personalized interpretable classification as a new data mining problem to the literature. In addition to the problem formulation on this new issue, we present a greedy algorithm called PIC (Personalized Interpretable Classifier) to identify a personalized rule for each individual test sample. To demonstrate the necessity, feasibility and advantages of such a personalized interpretable classification method, we conduct a series of empirical studies on real data sets. The experimental results show that: (1) The new problem formulation enables us to find interesting rules for test samples that may be missed by existing non-personalized classifiers. (2) Our algorithm can achieve the same-level predictive accuracy as those state-of-the-art (SOTA) interpretable classifiers. (3) On a real data set for predicting breast cancer metastasis, such a personalized interpretable classifier can outperform SOTA methods in terms of both accuracy and interpretability.

Time lag between variables is a key characteristics of dynamical systems in different fields and identifying such time lag is an important problem in complex systems with many applications. Transfer Entropy (TE) was proposed as a tool for time lag identification recently. Unfortunately, estimating TE has been a notoriously difficult problem. Copula Entropy (CE) is a measure of statistical independence and it was proved that TE can be represented with only CE. Therefore, a non-parametric estimator of TE based on CE was proposed according to such representation recently. In this paper we propose to use the CE-based estimator of TE to identify time lag in dynamical systems. Both simulated and real data are used to verify the effectiveness of the proposed method in the experiments. Experimental results show that the proposed method can identify the time lags in the four simulated systems. The real data experiment with the data on power consumption of the Tetouan city also demonstrates that our method can identify the pattern of time lags through the estimated TE from the weather factors to the power consumption of the city.

Recent years have witnessed a swelling rise of hateful and abusive content over online social networks. While detection and moderation of hate speech have been the early go-to countermeasures, the solution requires a deeper exploration of the dynamics of hate generation and propagation. We analyze more than 32 million posts from over 6.8 million users across three popular online social networks to investigate the interrelations between hateful behavior, information dissemination, and polarised organization mediated by echo chambers. We find that hatemongers play a more crucial role in governing the spread of information compared to singled-out hateful content. This observation holds for both the growth of information cascades as well as the conglomeration of hateful actors. Dissection of the core-wise distribution of these networks points towards the fact that hateful users acquire a more well-connected position in the social network and often flock together to build up information cascades. We observe that this cohesion is far from mere organized behavior; instead, in these networks, hatemongers dominate the echo chambers -- groups of users actively align themselves to specific ideological positions. The observed dominance of hateful users to inflate information cascades is primarily via user interactions amplified within these echo chambers. We conclude our study with a cautionary note that popularity-based recommendation of content is susceptible to be exploited by hatemongers given their potential to escalate content popularity via echo-chambered interactions.