Bipartite Graph Matching Research Articles

Multimodal Data Mining Based on Self Attention Feature Alignment

This study explores the application of multimodal data mining in text and image vector processing, aiming to improve the depth and breadth of data analysis by integrating information from different data types. We use the FairFace dataset combined with the CLIP model encoding layer to obtain text and image vectors, and use the K-Means clustering algorithm to achieve vector dimensionality reduction. Subsequently, we introduced the bipartite graph matching algorithm to achieve maximum matching between text vectors and image vectors, and calculated the contrastive learning loss and similarity loss. The entire process covers steps such as data preparation, feature extraction, vector dimensionality reduction, matching algorithms, and loss assessment, constructing a complete text and image matching task process. Our research contributions include using K-Means clustering algorithm to achieve vector dimensionality reduction, as well as introducing bipartite graph matching algorithm and calculating two types of losses in text and image vector matching, further improving matching quality.

DETR-ORD: An Improved DETR Detector for Oriented Remote Sensing Object Detection with Feature Reconstruction and Dynamic Query

Optical remote sensing images often feature high resolution, dense target distribution, and uneven target sizes, while transformer-based detectors like DETR reduce manually designed components, DETR does not support arbitrary-oriented object detection and suffers from high computational costs and slow convergence when handling large sequences of images. Additionally, bipartite graph matching and the limit on the number of queries result in transformer-based detectors performing poorly in scenarios with multiple objects and small object sizes. We propose an improved DETR detector for Oriented remote sensing object detection with Feature Reconstruction and Dynamic Query, termed DETR-ORD. It introduces rotation into the transformer architecture for oriented object detection, reduces computational cost with a hybrid encoder, and includes an IFR (image feature reconstruction) module to address the loss of positional information due to the flattening operation. It also uses ATSS to select auxiliary dynamic training queries for the decoder. This improved DETR-based detector enhances detection performance in challenging oriented optical remote sensing scenarios with similar backbone network parameters. Our approach achieves superior results on most optical remote sensing datasets, such as DOTA-v1.5 (72.07% mAP) and DIOR-R (66.60% mAP), surpassing the baseline detector.

Meta-collaborative comparison for effective cross-domain few-shot learning

Recent advancements in cross-domain few-shot learning (CD-FSL) primarily focus on learning to compare global representations between query and support images for classification. However, due to the notorious cross-domain semantic gap, the ideal global representations can be totally different across domains, thereby solely learning to compare global representations is not sufficient to achieve effective generalization in challenging cases. To mitigate this problem, we present a Meta-collaborative Comparison Network (MeCo-Net) for CD-FSL, which imitates humans to recognize unfamiliar objects through collaborative comparison on both global and local representations. Following this idea, paralleling with a conventional global comparison branch, we additionally feed random crops of both query and support images into a feature encoder to separately extract their local representations. Subsequently, we associate these local representations across images through bipartite graph matching for local comparison. Thanks to the complementary global and local comparisons, we can obtain a more generalizable classifier for CD-FSL by meta-integrating them for final prediction. Experimental results on eight benchmarks demonstrate that the proposed model generalizes to multiple target domains with state-of-the-art performance without the need for fine-tuning.

Generalizing Time Aggregation to Out-of-Sample Data Using Minimum Bipartite Graph Matching for Power Systems Studies

Generalizing Time Aggregation to Out-of-Sample Data Using Minimum Bipartite Graph Matching for Power Systems Studies

Optimal bipartite graph matching-based goal selection for policy-based hindsight learning

The sparse reward problem stands as a significant challenge in the field of reinforcement learning. Hindsight Experience Replay (HER) addresses this by goal relabeling, allowing the agent to learn from unsuccessful experiences. Some studies combine policy gradient methods with HER, resulting in policy-based hindsight learning algorithms. However, Policy-based hindsight learning involves the use of importance sampling, where the distribution of hindsight goals and the distribution of desired goals contribute to the computation of importance weights. When there is a significant difference between the two distributions, importance weights may become skewed, thereby impacting the evaluation of the policy and leading to suboptimal policies. To address this, we propose modeling the goal selection as an optimization problem for distribution matching. After we augment the original desired goals using Kernel Density Estimation (KDE), we further convert the optimization problem for distribution matching into a bipartite graph matching problem that minimizes the sum of weights. Our optimal bipartite graph matching-based hindsight goal selection method can select hindsight goals that are the most closely aligned with the original goals. Experimental results show that algorithms combined with the optimal bipartite graph matching-based hindsight goal selection outperform the original algorithms. Visualizations also demonstrate the superiority of our method in selecting hindsight goals.

DN-DETR: Accelerate DETR Training by Introducing Query DeNoising.

We present in this paper a novel denoising training method to speed up DETR (DEtection TRansformer) training and offer a deepened understanding of the slow convergence issue of DETR-like methods. We show that the slow convergence results from the instability of bipartite graph matching which causes inconsistent optimization goals in early training stages. To address this issue, except for the Hungarian loss, our method additionally feeds GT bounding boxes with noises into the Transformer decoder and trains the model to reconstruct the original boxes, which effectively reduces the bipartite graph matching difficulty and leads to faster convergence. Our method is universal and can be easily plugged into any DETR-like method by adding dozens of lines of code to achieve a remarkable improvement. As a result, our DN-DETR results in a remarkable improvement ( +1.9AP) under the same setting and achieves 46.0 AP and 49.5 AP trained for 12 and 50 epochs with the ResNet-50 backbone. Compared with the baseline under the same setting, DN-DETR achieves comparable performance with 50% training epochs. We also demonstrate the effectiveness of denoising training in CNN-based detectors (Faster R-CNN), segmentation models (Mask2Former, Mask DINO), and more DETR-based models (DETR, Anchor DETR, Deformable DETR).

Anti-Ramsey number for perfect matchings in 3-regular bipartite graphs

The anti-Ramsey number AR(G,H) is the maximum number of colors in an edge-coloring of a graph in the family G without any rainbow copy of H. The anti-Ramsey number for matchings has been studied extensively in several graph families, while the problem for perfect matchings was only solved in complete graphs. The anti-Ramsey number of matchings in the family of regular bipartite graphs of order large enough was determined by Li and Xu. Jin improved their bounds on the order of 3-regular bipartite graphs. In this paper, we consider the problem for perfect matchings in 3-regular bipartite graphs. Let G be the family of 3-regular bipartite graphs with m vertices in each partite set. First, we characterize the structure of extremal graphs for the Turán number of perfect matchings in graphs with maximum degree three. Using this characterization, we show that AR(G,mK2)=3m−3. Moreover, we show that AR(F,mK2)=3m−5, where F is the subfamily of 3-edge-connected graphs in G. In order to prove this result, we characterize the structure of bipartite graphs, which contains no perfect matchings, with maximum degree three and size Turán number minus one.

Bubble tracking method based on Kuhn-Munkres algorithm for boiling two-phase flow study

The study of bubble dynamics is important in various engineering applications as it can provide a fundamental understanding of the bubbly flow behavior. This paper presents a novel method for tracking bubble trajectories and classifying bubble behaviors, including formation, extinction, continuous movement, fragmentation, and coalescence. The method is based on the theory of perfect matching in bipartite graphs. By establishing the perfect matching between bubbles identified at adjacent time instants, judging the continuity of bubble motion, and simply calculating the number of bubbles in the neighbor of matching bubbles at adjacent time instants, the method can deal with the challenging situation where the bubble position and volume significantly change between two adjacent time instants. The method is validated in a simulated vertical pipe boiling flow, showing that the tracking accuracy is 100% and classification accuracies for continuous movement, fragmentation, and coalescence events are estimated to be larger than 90% in a wide range of time steps between two adjacent time instants.

Kartograf: A Geometrically Accurate Atom Mapper for Hybrid-Topology Relative Free Energy Calculations.

Relative binding free energy (RBFE) calculations have emerged as a powerful tool that supports ligand optimization in drug discovery. Despite many successes, the use of RBFEs can often be limited by automation problems, in particular, the setup of such calculations. Atom mapping algorithms are an essential component in setting up automatic large-scale hybrid-topology RBFE calculation campaigns. Traditional algorithms typically employ a 2D subgraph isomorphism solver (SIS) in order to estimate the maximum common substructure. SIS-based approaches can be limited by time-intensive operations and issues with capturing geometry-linked chemical properties, potentially leading to suboptimal solutions. To overcome these limitations, we have developed Kartograf, a geometric-graph-based algorithm that uses primarily the 3D coordinates of atoms to find a mapping between two ligands. In free energy approaches, the ligand conformations are usually derived from docking or other previous modeling approaches, giving the coordinates a certain importance. By considering the spatial relationships between atoms related to the molecule coordinates, our algorithm bypasses the computationally complex subgraph matching of SIS-based approaches and reduces the problem to a much simpler bipartite graph matching problem. Moreover, Kartograf effectively circumvents typical mapping issues induced by molecule symmetry and stereoisomerism, making it a more robust approach for atom mapping from a geometric perspective. To validate our method, we calculated mappings with our novel approach using a diverse set of small molecules and used the mappings in relative hydration and binding free energy calculations. The comparison with two SIS-based algorithms showed that Kartograf offers a fast alternative approach. The code for Kartograf is freely available on GitHub (https://github.com/OpenFreeEnergy/kartograf). While developed for the OpenFE ecosystem, Kartograf can also be utilized as a standalone Python package.

Context-aided unicity matching for person re-identification

Most existing person re-identification methods compute the matching relations between person images based on the similarity ranking. It lacks the global viewpoint and context consideration, inevitably leading to ambiguous matching results and sub-optimal performance. Based on a natural assumption that images belonging to the same identity should not match with images belonging to different identities across views, called the unicity of person matching on the identity level, we propose an end-to-end person unicity matching architecture to learn and refine the person matching relations. We first employ the image samples’ context in feature space to generate the initial soft matchings using graph neural networks, and then utilize the samples’ global context to refine the soft matchings and reach the matching unicity by bipartite graph matching. Considering real-world applications, we further develop a fast algorithm without losing performance. Experimental results on five public benchmarks show the superiority of the proposed method.

EDTBERT: Event Detection and Tracking in Twitter using Graph Clustering and Pre-trained Language Model

The identification of events from social media platforms such as Twitter (now known as X) is a hot research problem. It has applications in diverse domains such as journalism, marketing, public safety, crisis management and disaster response. The process includes the identification, monitoring, and analysis of events or incidents while they are being discussed or reported on Twitter. When it comes to identifying events from tweets (i.e. feeds from Twitter), many of the currently available event detection methods mainly rely on keyword burstiness features or structural changes in the network. However, due to the intricate characteristics of tweets and the ever-changing nature of events, they frequently fail to recognise noteworthy occurrences before they become trending. Moreover, these methods face difficulties when it comes to capturing the evolving characteristics of events with limited or insufficient contextual information. In this paper, we propose a window-based tweet-processing method called EDTBERT for detecting events and tracking the evolution of events over time. Our proposed method utilizes the structural and semantic affinities that exist among words in tweets. The method starts by generating graph of tweets, where tweets are represented as nodes, and edges are the similarities between tweets. The method utilizes overlapping hashtags and named entities to capture the structural relationship between tweets. Additionally, a pre-trained sentence transformer model, specifically BERT, is employed to collect contextual knowledge and find semantically similar tweets. Next, the graph clustering technique is employed to identify optimized event clusters. Subsequently, our method generates chain of event clusters for each event to track the evolving variation of the event over time by utilising the ”Maximum-Weight Bipartite Graph Matching” (MWBGM) algorithm. The effectiveness of our approach is assessed using standard Tweet Datasets. Our evaluation demonstrates that our approach outperforms the baseline approaches.

Solving dynamic vehicle routing problem with time windows by ant colony system with bipartite graph matching

Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) is an extension of the traditional VRPTW by considering dynamic customer characteristics. In this problem, new customers with specific time windows are received dynamically as time progresses and must be incorporated into the evolving schedule. The goal of DVRPTW is to use the minimum number of vehicles to fulfill all the customer demands with the minimum total traveling time. Little work has been done for solving this dynamic variant. In this paper, an evolutionary algorithm using Ant Colony System and Kuhn-Munkres bipartite graph matching, named ACS-KM, is proposed. It can tackle the dynamic issues during the evolutionary process. Experiments show that the proposed algorithm is very effective and has fast convergence. It achieves the best results on 40 out of 48 benchmark instances. For the DVRPTW instances with different levels of dynamicity, the algorithm can always produce better solutions than the previous works.

Intelligent team formation and player selection: a data-driven approach for football coaches

This article presents a data-driven approach called Intelligent Team Formation and Player Selection (ITFPS), aimed at assisting football coaches in making informed decisions about team formation and player selection. The proposed approach utilizes deep neural networks to evaluate the suitability of each player for different positions on the field. The problem is then formulated as finding the maximum weighted matching in a complete bipartite graph, with the objective of achieving the best possible alignment between team members and the positions designated by the coach. The Hungarian algorithm is employed to facilitate this matching process. Furthermore, the approach allows coaches to select a system of distinct representatives for each position, based on the specific qualities expected from players in a given match. The effectiveness of the approach is demonstrated through tests conducted on four teams from the 2021–2022 English Premier League. The results indicate that ITFPS produces decisions comparable to those made by successful coaches. By optimizing team formations and enabling the utilization of rotating formations, this approach not only enhances team performance but also empowers coaches to make strategic decisions while fully leveraging the potential of their players. ITFPS serves as an intelligent assistant for coaches, complementing their strategic perspectives.

CATS: Conditional Adversarial Trajectory Synthesis for privacy-preserving trajectory data publication using deep learning approaches

The prevalence of ubiquitous location-aware devices and mobile Internet enables us to collect massive individual-level trajectory dataset from users. Such trajectory big data bring new opportunities to human mobility research but also raise public concerns with regard to location privacy. In this work, we present the Conditional Adversarial Trajectory Synthesis (CATS), a deep-learning-based GeoAI methodological framework for privacy-preserving trajectory data generation and publication. CATS applies K-anonymity to the underlying spatiotemporal distributions of human movements, which provides a distributional-level strong privacy guarantee. By leveraging conditional adversarial training on K-anonymized human mobility matrices, trajectory global context learning using the attention-based mechanism, and recurrent bipartite graph matching of adjacent trajectory points, CATS is able to reconstruct trajectory topology from conditionally sampled locations and generate high-quality individual-level synthetic trajectory data, which can serve as supplements or alternatives to raw data for privacy-preserving trajectory data publication. The experiment results on over 90k GPS trajectories show that our method has a better performance in privacy preservation, spatiotemporal characteristic preservation, and downstream utility compared with baseline methods, which brings new insights into privacy-preserving human mobility research using generative AI techniques and explores data ethics issues in GIScience.

Graph-based automatic detection and classification of lesion changes in pairs of CT studies for oncology follow-up.

Radiological follow-up of oncology patients requires the quantitative analysis of lesion changes in longitudinal imaging studies, which is time-consuming, requires expertise, and is subject to variability. This paper presents a comprehensive graph-based method for the automatic detection and classification of lesion changes in current and prior CT scans. The inputs are the current and prior CT scans and their organ and lesion segmentations. Classification of lesion changes is formalized as bipartite graph matching where lesion pairings are computed by adaptive overlap-based lesion matching. Six types of lesion changes are computed by connected components analysis. The method was evaluated on 208 pairs of lung and liver CT scans from 57 patients with 4600 lesions, 1713 lesion matchings and 2887 lesion changes. Ground-truth lesion segmentations, lesion matchings and lesion changes were created by an expert radiologist. Our method yields a lesion matching rate accuracy of 99.7% (394/395) and 95.0% (1252/1318) for the lung and liver datasets. Precision and recall are > 0.99 and 0.94 and 0.95 (respectively) for the detection of lesion changes. The analysis of lesion changes helped the radiologist detect 48 missed lesions and 8 spurious lesions in the input ground-truth lesion datasets. The classification of lesion classification provides the clinician with a readily accessible and intuitive identification and classification of the lesion changes and their patterns in support of clinical decision making. Comprehensive automatic computer-aided lesion matching and analysis of lesion changes may improve quantitative follow-up and evaluation of disease status, assessment of treatment efficacy and response to therapy.

On the Set of Stable Matchings in a Bipartite Graph

The topic of stable matchings (marriages) in bipartite graphs gained popularity beginning from the appearance of the classical Gale and Shapley work. In this paper, a detailed review of selected and other related statements in this field that describe structured, polyhedral, and algorithmic properties of such objects and their sets accompanied by short proofs is given.

A Socially-Aware Dependent Tasks Offloading Strategy in Mobile Edge Computing

With the advent of 5G, Mobile Edge Computing (MEC), a promising computing paradigm sits closer to users than cloud computing, is being broadly used in various Internet of Things (IoT) applications, and achieve high-quality user experience. Task offloading, as a critical research issue in MEC, is playing an important role in optimizing computational resources and management. However, many tasks are executed dependent on the computational results of other tasks. Moreover, in the case of offloading tasks with other devices, it is often required to consider the success rate of offloading, since not all users are willing to lend their mobile devices to others for task execution. To address this challenge, by taking social relationships between users into account, this paper intends to combine computational resources of local devices and edge clouds and provide more flexible offloading and execution solutions, for achieving the efficient offloading of dependent tasks with the joint consideration of network latency and energy consumption. This paper develops a dependent task offloading strategy based on Bipartite Graph Matching. Extensive simulations are conducted for validating the effectiveness of our proposed strategy. Experimental results demonstrate that our proposed strategy can significantly minimize the overhead compared with other baseline strategies. In particular, the overhead is reduced 8.2%, compared with the strategy which consider the Device-to-Device (D2D) offloading only.

Energy-Efficient Task Offloading for Three-Tier Wireless-Powered Mobile-Edge Computing

Mobile edge computing (MEC) is envisioned to address the computation demands of Internet of Things (IoT) devices. However, it is crucial for the MEC to operate in coordination with the cloud tier to achieve a highly scalable IoT system. In addition, IoT devices require regular maintenance to either recharge or replace their batteries which may not always be feasible. Wireless energy transfer (WET) can provide IoT devices with a stable source of energy. Nonetheless, proper scheduling of energy harvesting and efficient allocation of computing resources are the key to the sustainable operation of these devices. In this paper, we introduce a three-tier wireless powered mobile edge computing (WPMEC) consisting of cloud, MEC servers, and IoT devices. We first formulate a combinatorial optimization problem that aims to minimize the wireless energy transmission. To tackle the complexity of the problem, we use bipartite graph matching and propose a harvest-then-offload mechanism for IoT devices. We also exploit parallel processing to increase the performance of the proposed algorithm. Through numerical experiments, we evaluate the performance of our proposed mechanism. Our results show that the proposed mechanism significantly reduces the required energy for the operation of IoT devices comparing to different offloading policies. We further show that WiEnTM results in up to 34% less wireless energy transmission in comparison to an existing work in the literature.

An analysis of one-to-one matching algorithms for entity resolution

AbstractEntity resolution (ER) is the task of finding records that refer to the same real-world entities. A common scenario, which we refer to as Clean-Clean ER, is to resolve records across two clean sources (i.e., they are duplicate-free and contain one record per entity). Matching algorithms for Clean-Clean ER yield bipartite graphs, which are further processed by clustering algorithms to produce the end result. In this paper, we perform an extensive empirical evaluation of eight bipartite graph matching algorithms that take as input a bipartite similarity graph and provide as output a set of matched records. We consider a wide range of matching algorithms, including algorithms that have not previously been applied to ER, or have been evaluated only in other ER settings. We assess the relative performance of these algorithms with respect to accuracy and time efficiency over ten established real-world data sets, from which we generated over 700 different similarity graphs. Our results provide insights into the relative performance of these algorithms and guidelines for choosing the best one, depending on the data at hand.

Sequential importance sampling for estimating expectations over the space of perfect matchings

This paper makes three contributions to estimating the number of perfect matching in bipartite graphs. First, we prove that the popular sequential importance sampling algorithm works in polynomial time for dense bipartite graphs. More carefully, our algorithm gives a (1±ϵ)-approximation for the number of perfect matchings of a λ-dense bipartite graph, using O(n1−2λλϵ−2) samples. With size n on each side and for 1 2>λ>0, a λ-dense bipartite graph has all degrees greater than (λ+1 2)n. Second, practical applications of the algorithm requires many calls to matching algorithms. A novel preprocessing step is provided which makes significant improvements. Third, three applications are provided. The first is for counting Latin squares, the second is a practical way of computing the greedy algorithm for a card guessing game with feedback and the third is for stochastic block models. In all three examples, sequential importance sampling allows treating practical problems of reasonably large sizes.