Differentiable solvers for the linear assignment problem (LAP) have attracted much research attention in recent years, which are usually embedded into learning frameworks as components. However, previous algorithms, with or without learning strategies, usually suffer from the degradation of the optimality with the increment of the problem size. In this paper, we propose a learnable linear assignment solver based on deep graph networks. Specifically, we first transform the cost matrix to a bipartite graph and convert the assignment task to the problem of selecting reliable edges from the constructed graph. Subsequently, a deep graph network is developed to aggregate and update the features of nodes and edges. Finally, the network predicts a label for each edge that indicates the assignment relationship. The experimental results on a synthetic dataset reveal that our method outperforms state-of-the-art baselines and achieves consistently high accuracy with the increment of the problem size. Furthermore, we also embed the proposed solver, in comparison with state-of-the-art baseline solvers, into a popular multi-object tracking (MOT) framework to train the tracker in an end-to-end manner. The experimental results on MOT benchmarks illustrate that the proposed LAP solver improves the tracker by the largest margin.
The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their parts and sums over all pairs of parts. Assignment kernels, in contrast, are obtained from an optimal bijection between parts, which can provide a more valid notion of similarity. In general however, optimal assignments yield indefinite functions, which complicates their use in kernel methods. We characterize a class of base kernels used to compare parts th…
Accurate and reliable tracking of multiple moving objects in 3D space is an essential component of urban scene understanding. This is a challenging task because it requires the assignment of detections in the current frame to the predicted objects from the previous one. Existing filter-based approaches tend to struggle if this initial assignment is not correct, which can happen easily. We propose a novel optimization-based approach that does not rely on explicit and fixed assignments. Instead, we represent the result of an off-the-shelf 3D object detector as Gaussian mixture model, which is in…
This paper extends the recently introduced assignment flow approach for supervised image labeling to unsupervised scenarios where no labels are given. The resulting self-assignment flow takes a pairwise data affinity matrix as input data and maximizes the correlation with a low-rank matrix that is parametrized by the variables of the assignment flow, which entails an assignment of the data to themselves through the formation of latent labels (feature prototypes). A single user parameter, the neighborhood size for the geometric regularization of assignments, drives the entire process. By smooth…
NICTA（澳大利亚国家信息与通信技术研究院）；Australian National University（澳大利亚国立大学）；Stanford University（斯坦福大学）
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for app…
Graph matching involves combinatorial optimization based on edge-to-edge affinity matrix, which can be generally formulated as Lawler's Quadratic Assignment Problem (QAP). This paper presents a QAP network directly learning with the affinity matrix (equivalently the association graph) whereby the matching problem is translated into a constrained vertex classification task. The association graph is learned by an embedding network for vertex classification, followed by Sinkhorn normalization and a cross-entropy loss for end-to-end learning. We further improve the embedding model on association g…
RDSA: A Robust Deep Graph Clustering Framework via Dual Soft Assignment
Department of Computing, Xi'an Jiaotong-Liverpool University, Suzhou China（西安交通大学利物浦大学计算机学院，中国苏州市）；Department of Computer Science, University of Liverpool, Liverpool United Kingdom（利物浦大学计算机科学系，英国利物浦）
In this work an iterative algorithm based on unsupervised learning is presented, specifically on a Restricted Boltzmann Machine (RBM) to solve a perfect matching problem on a bipartite weighted graph. Iteratively is calculated the weights $w_{ij}$ and the bias parameters $θ= ( a_i, b_j) $ that maximize the energy function and assignment element $i$ to element $j$. An application of real problem is presented to show the potentiality of this algorithm.
TU Dortmund University（多特蒙德工业大学）；Université Littoral Côte d’Opale（法国滨海大学）；University of York（约克大学）
Finding an optimal assignment between two sets of objects is a fundamental problem arising in many applications, including the matching of `bag-of-words' representations in natural language processing and computer vision. Solving the assignment problem typically requires cubic time and its pairwise computation is expensive on large datasets. In this paper, we develop an algorithm which can find an optimal assignment in linear time when the cost function between objects is represented by a tree distance. We employ the method to approximate the edit distance between two graphs by matching their …
College of Computer and Big Data, Fuzhou University（福州大学计算机与大数据学院）；School of Computer Science and Engineering, South China University of Technology（华南理工大学计算机科学与工程学院）；Navigation College, Dalian Maritime University（大连海事大学航海学院）
With the rise of contrastive learning, unsupervised graph representation learning has been booming recently, even surpassing the supervised counterparts in some machine learning tasks. Most of existing contrastive models for graph representation learning either focus on maximizing mutual information between local and global embeddings, or primarily depend on contrasting embeddings at node level. However, they are still not exquisite enough to comprehensively explore the local and global views of network topology. Although the former considers local-global relationship, its coarse global inform…
Despite the success of Graph Neural Networks (GNNs) on various applications, GNNs encounter significant performance degradation when the amount of supervision signals, i.e., number of labeled nodes, is limited, which is expected as GNNs are trained solely based on the supervision obtained from the labeled nodes. On the other hand,recent self-supervised learning paradigm aims to train GNNs by solving pretext tasks that do not require any labeled nodes, and it has shown to even outperform GNNs trained with few labeled nodes. However, a major drawback of self-supervised methods is that they fall …
Stochastic computation graphs (SCGs) provide a formalism to represent structured optimization problems arising in artificial intelligence, including supervised, unsupervised, and reinforcement learning. Previous work has shown that an unbiased estimator of the gradient of the expected loss of SCGs can be derived from a single principle. However, this estimator often has high variance and requires a full model evaluation per data point, making this algorithm costly in large graphs. In this work, we address these problems by generalizing concepts from the reinforcement learning literature. We in…
We present Hindsight Network Credit Assignment (HNCA), a novel learning method for stochastic neural networks, which works by assigning credit to each neuron's stochastic output based on how it influences the output of its immediate children in the network. We prove that HNCA provides unbiased gradient estimates while reducing variance compared to the REINFORCE estimator. We also experimentally demonstrate the advantage of HNCA over REINFORCE in a contextual bandit version of MNIST. The computational complexity of HNCA is similar to that of backpropagation. We believe that HNCA can help stimul…
We present a novel data-driven approach of learning traffic flow patterns of a transportation network given that many instances of origin to destination (OD) travel demand and link flows of the network are available. Instead of estimating traffic flow patterns assuming certain user behavior (e.g., user equilibrium or system optimal), here we explore the idea of learning those flow patterns directly from the data. To implement this idea, we have formulated the traffic-assignment problem as a data-driven learning problem and developed a neural network-based framework known as Graph Convolutional…
Institute of Exact and Applied Sciences (EA7484), University of New Caledonia（精确与应用科学研究所（EA7484），新喀里多尼亚大学）；Big Data Institute, College of Computer Science and Software Engineering（大数据研究所，计算机科学与软件工程学院）；Shenzhen University, China（深圳大学，中国）
INRIA（法国国家信息与自动化研究所）；Ecole Normale Superieure（巴黎高等师范学院）；Courant Institute, New York University（纽约大学柯朗研究所）；Center for Data Science, New York University（纽约大学数据科学中心）
Inverse problems correspond to a certain type of optimization problems formulated over appropriate input distributions. Recently, there has been a growing interest in understanding the computational hardness of these optimization problems, not only in the worst case, but in an average-complexity sense under this same input distribution. In this revised note, we are interested in studying another aspect of hardness, related to the ability to learn how to solve a problem by simply observing a collection of previously solved instances. These 'planted solutions' are used to supervise the training …
We prove that the $α$-expansion algorithm for MAP inference always returns a globally optimal assignment for Markov Random Fields with Potts pairwise potentials, with a catch: the returned assignment is only guaranteed to be optimal for an instance within a small perturbation of the original problem instance. In other words, all local minima with respect to expansion moves are global minima to slightly perturbed versions of the problem. On "real-world" instances, MAP assignments of small perturbations of the problem should be very similar to the MAP assignment(s) of the original problem instan…
Learning traffic flows: Graph Neural Networks for Metamodelling Traffic Assignment
Department of Technology, Management and Economics, Technical University of Denmark, Lyngby, Denmark（技术、管理与经济系，丹麦技术大学）；Department of Civil, Constructional and Environmental Engineering, Sapienza University of Rome, Rome, Italy（土木、建筑与环境工程系，罗马萨皮恩扎大学）；Department of Aeronautics and Astronautics, Stanford University, Stanford, California（航空与航天系，斯坦福大学）
UiT the Arctic University of Norway（挪威北极大学）；NORCE Norwegian Research Centre（NORCE挪威研究中心）
The objective functions used in spectral clustering are usually composed of two terms: i) a term that minimizes the local quadratic variation of the cluster assignments on the graph and; ii) a term that balances the clustering partition and helps avoiding degenerate solutions. This paper shows that a graph neural network, equipped with suitable message passing layers, can generate good cluster assignments by optimizing only a balancing term. Results on attributed graph datasets show the effectiveness of the proposed approach in terms of clustering performance and computation time.
The graph matching problem seeks to find an alignment between the nodes of two graphs that minimizes the number of adjacency disagreements. Solving the graph matching is increasingly important due to it's applications in operations research, computer vision, neuroscience, and more. However, current state-of-the-art algorithms are inefficient in matching very large graphs, though they produce good accuracy. The main computational bottleneck of these algorithms is the linear assignment problem, which must be solved at each iteration. In this paper, we leverage the recent advances in the field of…
Technical University of Munich（慕尼黑工业大学）；CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）
A cursory reading of the literature suggests that we have made a lot of progress in designing effective adversarial defenses for Graph Neural Networks (GNNs). Yet, the standard methodology has a serious flaw - virtually all of the defenses are evaluated against non-adaptive attacks leading to overly optimistic robustness estimates. We perform a thorough robustness analysis of 7 of the most popular defenses spanning the entire spectrum of strategies, i.e., aimed at improving the graph, the architecture, or the training. The results are sobering - most defenses show no or only marginal improveme…
Neural Graduated Assignment for Maximum Common Edge Subgraphs
School of Data Science, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）数据科学学院）；School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）理工学院）
Congruence Decomposition with Neural Block Solvers for Large-Scale PCI Assignment
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Research Institute of Big Data（深圳大数据研究院）；Columbia University（哥伦比亚大学）；Sun Yat-sen University（中山大学）；Tongji University（同济大学）；University of Chinese Academy of Sciences（中国科学院大学）；Huawei Technologies（华为技术有限公司）
Graph Attention-based Reinforcement Learning for Trajectory Design and Resource Assignment in Multi-UAV Assisted Communication
Hainan University（海南大学）；Singapore University of Technology and Design（新加坡科技设计大学）；Shanghai Jiao Tong University（上海交通大学）；University of Naples Federico II（那不勒斯费德里科二世大学）；Nanyang Technological University（南洋理工大学）
Johns Hopkins University（约翰斯·霍普金斯大学）；University of Pittsburgh（匹兹堡大学）
In network inference applications, it is often desirable to detect community structure, namely to cluster vertices into groups, or blocks, according to some measure of similarity. Beyond mere adjacency matrices, many real networks also involve vertex covariates that carry key information about underlying block structure in graphs. To assess the effects of such covariates on block recovery, we present a comparative analysis of two model-based spectral algorithms for clustering vertices in stochastic blockmodel graphs with vertex covariates. The first algorithm uses only the adjacency matrix, an…
