In this paper, we present Vi-Fi, a multi-modal system that leverages a user’s smartphone WiFi Fine Timing Measurements (FTM) and inertial measurement unit (IMU) sensor data to associate the user detected on a camera footage with their corresponding smartphone identifier (e.g. WiFi MAC address). Our approach uses a recurrent multi-modal deep neural network that exploits FTM and IMU measurements along with distance between user and camera (depth information) to learn affinity matrices. As a baseline method for comparison, we also present a traditional non deep learning approach that uses bipartite graph matching. To facilitate evaluation, we collected a multi-modal dataset that comprises camera videos with depth information (RGB-D), WiFi FTM and IMU measurements for multiple participants at diverse real-world settings. Using association accuracy as the key metric for evaluating the fidelity of 𝑉𝑖𝑠𝑢𝑎𝑙4 𝑉𝑖𝑠𝑢𝑎𝑙5 Figure 1: Motivation: Successfully associating vision-wireless Vi-Fi in associating human users on camera feed with their phone IDs, we show that Vi-Fi achieves between 81% (real-time) to 91% (offline) association accuracy.
Graph matching aims to find correspondences between two graphs. This paper integrates several well-known graph matching algorithms into a framework: the constrained gradient method. The primary difference among these algorithms lies in tuning a step size parameter and constraining operators. By leveraging these insights, we propose an adaptive step size parameter to guarantee the underlying algorithms' convergence, simultaneously enhancing their efficiency and robustness. For the constraining operator, we introduce a scalable softassign for large graph matching problems. Compared to the original softassign, our approach offers increased speed, improved robustness, and reduced risk of overflow. The advanced constraining operator enables a CSGO for large graph matching, which outperforms state-of-the-art methods in experiments. Notably, in attributed graph matching tasks, CSGO achieves an over 10X increase in speed compared to current constrained gradient algorithms.
Unsupervised domain adaptation for point cloud semantic segmentation has attracted great attention due to its effectiveness in learning with unlabeled data. Most of existing methods use global-level feature alignment to transfer the knowledge from the source domain to the target domain, which may cause the semantic ambiguity of the feature space. In this paper, we propose a graph-based framework to explore the local-level feature alignment between the two domains, which can reserve semantic discrimination during adaptation. Specifically, in order to extract local-level features, we first dynamically construct local feature graphs on both domains and build a memory bank with the graphs from the source domain. In particular, we use optimal transport to generate the graph matching pairs. Then, based on the assignment matrix, we can align the feature distributions between the two domains with the graph-based local feature loss. Furthermore, we consider the correlation between the features of different categories and formulate a category-guided contrastive loss to guide the segmentation model to learn discriminative features on the target domain. Extensive experiments on different synthetic-to-real and real-to-real domain adaptation scenarios demonstrate that our method can achieve state-of-the-art performance.
Public art shapes our shared spaces. Public art should speak to community and context, and yet, recent work has demonstrated numerous instances of art in prominent institutions favoring outdated cultural norms and legacy communities. Motivated by this, we develop a novel recommender system to curate public art exhibits with built-in equity objectives and a local value-based allocation of constrained resources. We develop a cost matrix by drawing on Schelling's model of segregation. Using the cost matrix as an input, the scoring function is optimized via a projected gradient descent to obtain a soft assignment matrix. Our optimization program allocates artwork to public spaces in a way that de-prioritizes "in-group" preferences, by satisfying minimum representation and exposure criteria. We draw on existing literature to develop a fairness metric for our algorithmic output, and we assess the effectiveness of our approach and discuss its potential pitfalls from both a curatorial and equity standpoint.
Estimating accurate 3D locations of objects from monocular images is a challenging problem because of lacking depth. Previous work shows that utilizing the object's keypoint projection constraints to estimate multiple depth candidates boosts the detection performance. However, the existing methods can only utilize vertical edges as projection constraints for depth estimation. So these methods only use a small number of projection constraints and produce insufficient depth candidates, leading to inaccurate depth estimation. In this paper, we propose a method that utilizes dense projection constraints from edges of any direction. In this way, we employ much more projection constraints and produce considerable depth candidates. Besides, we present a graph matching weighting module to merge the depth candidates. The proposed method DCD (Densely Constrained Detector) achieves state-of-the-art performance on the KITTI and WOD benchmarks. Code is released at https://github.com/BraveGroup/DCD.
We introduce Joint Multidimensional Scaling, a novel approach for unsupervised manifold alignment, which maps datasets from two different domains, without any known correspondences between data instances across the datasets, to a common low-dimensional Euclidean space. Our approach integrates Multidimensional Scaling (MDS) and Wasserstein Procrustes analysis into a joint optimization problem to simultaneously generate isometric embeddings of data and learn correspondences between instances from two different datasets, while only requiring intra-dataset pairwise dissimilarities as input. This unique characteristic makes our approach applicable to datasets without access to the input features, such as solving the inexact graph matching problem. We propose an alternating optimization scheme to solve the problem that can fully benefit from the optimization techniques for MDS and Wasserstein Procrustes. We demonstrate the effectiveness of our approach in several applications, including joint visualization of two datasets, unsupervised heterogeneous domain adaptation, graph matching, and protein structure alignment. The implementation of our work is available at https://github.com/BorgwardtLab/JointMDS
Recently, deep graph matching (GM) methods have gained increasing attention. These methods integrate graph nodes¡¯s embedding, node/edges¡¯s affinity learning and final correspondence solver together in an end-to-end manner. For deep graph matching problem, one main issue is how to generate consensus node's embeddings for both source and target graphs that best serve graph matching tasks. In addition, it is also challenging to incorporate the discrete one-to-one matching constraints into the differentiable correspondence solver in deep matching network. To address these issues, we propose a novel Graph Adversarial Matching Network (GAMnet) for graph matching problem. GAMnet integrates graph adversarial embedding and graph matching simultaneously in a unified end-to-end network which aims to adaptively learn distribution consistent and domain invariant embeddings for GM tasks. Also, GAMnet exploits sparse GM optimization as correspondence solver which is differentiable and can also incorporate discrete one-to-one matching constraints approximately in natural in the final matching prediction. Experimental results on three public benchmarks demonstrate the effectiveness and benefits of the proposed GAMnet.
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last decades. Since a common standard benchmark has not been developed, their performance claims are often hard to verify as evaluation on differing problem instances and criteria make the results incomparable. To address these shortcomings, we present a comparative study of graph matching algorithms. We create a uniform benchmark where we collect and categorize a large set of existing and publicly available computer vision graph matching problems in a common format. At the same time we collect and categorize the most popular open-source implementations of graph matching algorithms. Their performance is evaluated in a way that is in line with the best practices for comparing optimization algorithms. The study is designed to be reproducible and extensible to serve as a valuable resource in the future. Our study provides three notable insights: 1.) popular problem instances are exactly solvable in substantially less than 1 second and, therefore, are insufficient for future empirical evaluations; 2.) the most popular baseline methods are highly inferior to the best available methods; 3.) despite the NP-hardness of the problem, instances coming from vision applications are often solvable in a few seconds even for graphs with more than 500 vertices.
This paper is about extremely robust and lightweight localisation using LiDAR point clouds based on instance segmentation and graph matching. We model 3D point clouds as fully-connected graphs of semantically identified components where each vertex corresponds to an object instance and encodes its shape. Optimal vertex association across graphs allows for full 6-Degree-of-Freedom (DoF) pose estimation and place recognition by measuring similarity. This representation is very concise, condensing the size of maps by a factor of 25 against the state-of-the-art, requiring only 3kB to represent a 1.4MB laser scan. We verify the efficacy of our system on the SemanticKITTI dataset, where we achieve a new state-of-the-art in place recognition, with an average of 88.4% recall at 100% precision where the next closest competitor follows with 64.9%. We also show accurate metric pose estimation performance - estimating 6-DoF pose with median errors of 10 cm and 0.33 deg.
Large displacement optical flow is an integral part of many computer vision tasks. Variational optical flow techniques based on a coarse-to-fine scheme interpolate sparse matches and locally optimize an energy model conditioned on colour, gradient and smoothness, making them sensitive to noise in the sparse matches, deformations, and arbitrarily large displacements. This paper addresses this problem and presents HybridFlow, a variational motion estimation framework for large displacements and deformations. A multi-scale hybrid matching approach is performed on the image pairs. Coarse-scale clusters formed by classifying pixels according to their feature descriptors are matched using the clusters' context descriptors. We apply a multi-scale graph matching on the finer-scale superpixels contained within each matched pair of coarse-scale clusters. Small clusters that cannot be further subdivided are matched using localized feature matching. Together, these initial matches form the flow, which is propagated by an edge-preserving interpolation and variational refinement. Our approach does not require training and is robust to substantial displacements and rigid and non-rigid transformations due to motion in the scene, making it ideal for large-scale imagery such as Wide-Area Motion Imagery (WAMI). More notably, HybridFlow works on directed graphs of arbitrary topology representing perceptual groups, which improves motion estimation in the presence of significant deformations. We demonstrate HybridFlow's superior performance to state-of-the-art variational techniques on two benchmark datasets and report comparable results with state-of-the-art deep-learning-based techniques.
Decentralized optimization is increasingly popular in machine learning for its scalability and efficiency. Intuitively, it should also provide better privacy guarantees, as nodes only observe the messages sent by their neighbors in the network graph. But formalizing and quantifying this gain is challenging: existing results are typically limited to Local Differential Privacy (LDP) guarantees that overlook the advantages of decentralization. In this work, we introduce pairwise network differential privacy, a relaxation of LDP that captures the fact that the privacy leakage from a node $u$ to a node $v$ may depend on their relative position in the graph. We then analyze the combination of local noise injection with (simple or randomized) gossip averaging protocols on fixed and random communication graphs. We also derive a differentially private decentralized optimization algorithm that alternates between local gradient descent steps and gossip averaging. Our results show that our algorithms amplify privacy guarantees as a function of the distance between nodes in the graph, matching the privacy-utility trade-off of the trusted curator, up to factors that explicitly depend on the graph topology. Finally, we illustrate our privacy gains with experiments on synthetic and real-world datasets.
Current Graph Neural Networks (GNN) architectures generally rely on two important components: node features embedding through message passing, and aggregation with a specialized form of pooling. The structural (or topological) information is implicitly taken into account in these two steps. We propose in this work a novel point of view, which places distances to some learnable graph templates at the core of the graph representation. This distance embedding is constructed thanks to an optimal transport distance: the Fused Gromov-Wasserstein (FGW) distance, which encodes simultaneously feature and structure dissimilarities by solving a soft graph-matching problem. We postulate that the vector of FGW distances to a set of template graphs has a strong discriminative power, which is then fed to a non-linear classifier for final predictions. Distance embedding can be seen as a new layer, and can leverage on existing message passing techniques to promote sensible feature representations. Interestingly enough, in our work the optimal set of template graphs is also learnt in an end-to-end fashion by differentiating through this layer. After describing the corresponding learning procedure, we empirically validate our claim on several synthetic and real life graph classification datasets, where our method is competitive or surpasses kernel and GNN state-of-the-art approaches. We complete our experiments by an ablation study and a sensitivity analysis to parameters.
Image matching is a key component of many tasks in computer vision and its main objective is to find correspondences between features extracted from different natural images. When images are represented as graphs, image matching boils down to the problem of graph matching which has been studied intensively in the past. In recent years, graph neural networks have shown great potential in the graph matching task, and have also been applied to image matching. In this paper, we propose a graph neural network for the problem of image matching. The proposed method first generates initial soft correspondences between keypoints using localized node embeddings and then iteratively refines the initial correspondences using a series of graph neural network layers. We evaluate our method on natural image datasets with keypoint annotations and show that, in comparison to a state-of-the-art model, our method speeds up inference times without sacrificing prediction accuracy.
Embedding discrete solvers as differentiable layers has given modern deep learning architectures combinatorial expressivity and discrete reasoning capabilities. The derivative of these solvers is zero or undefined, therefore a meaningful replacement is crucial for effective gradient-based learning. Prior works rely on smoothing the solver with input perturbations, relaxing the solver to continuous problems, or interpolating the loss landscape with techniques that typically require additional solver calls, introduce extra hyper-parameters, or compromise performance. We propose a principled approach to exploit the geometry of the discrete solution space to treat the solver as a negative identity on the backward pass and further provide a theoretical justification. Our experiments demonstrate that such a straightforward hyper-parameter-free approach is able to compete with previous more complex methods on numerous experiments such as backpropagation through discrete samplers, deep graph matching, and image retrieval. Furthermore, we substitute the previously proposed problem-specific and label-dependent margin with a generic regularization procedure that prevents cost collapse and increases robustness.
Graph similarity learning refers to calculating the similarity score between two graphs, which is required in many realistic applications, such as visual tracking, graph classification, and collaborative filtering. As most of the existing graph neural networks yield effective graph representations of a single graph, little effort has been made for jointly learning two graph representations and calculating their similarity score. In addition, existing unsupervised graph similarity learning methods are mainly clustering-based, which ignores the valuable information embodied in graph pairs. To this end, we propose a contrastive graph matching network (CGMN) for self-supervised graph similarity learning in order to calculate the similarity between any two input graph objects. Specifically, we generate two augmented views for each graph in a pair respectively. Then, we employ two strategies, namely cross-view interaction and cross-graph interaction, for effective node representation learning. The former is resorted to strengthen the consistency of node representations in two views. The latter is utilized to identify node differences between different graphs. Finally, we transform node representations into graph-level representations via pooling operations for graph similarity computation. We have evaluated CGMN on eight real-world datasets, and the experiment results show that the proposed new approach is superior to the state-of-the-art methods in graph similarity learning downstream tasks.
There is a growing interest in designing Graph Neural Networks (GNNs) for seeded graph matching, which aims to match two unlabeled graphs using only topological information and a small set of seed nodes. However, most previous GNNs for this task use a semi-supervised approach, which requires a large number of seeds and cannot learn knowledge that is transferable to unseen graphs. In contrast, this paper proposes a new supervised approach that can learn from a training set how to match unseen graphs with only a few seeds. Our SeedGNN architecture incorporates several novel designs, inspired by theoretical studies of seeded graph matching: 1) it can learn to compute and use witness-like information from different hops, in a way that can be generalized to graphs of different sizes; 2) it can use easily-matched node-pairs as new seeds to improve the matching in subsequent layers. We evaluate SeedGNN on synthetic and real-world graphs and demonstrate significant performance improvements over both non-learning and learning algorithms in the existing literature. Furthermore, our experiments confirm that the knowledge learned by SeedGNN from training graphs can be generalized to test graphs of different sizes and categories.
Given a collection of vertex-aligned networks and an additional label-shuffled network, we propose procedures for leveraging the signal in the vertex-aligned collection to recover the labels of the shuffled network. We consider matching the shuffled network to averages of the networks in the vertex-aligned collection at different levels of granularity. We demonstrate both in theory and practice that if the graphs come from different network classes, then clustering the networks into classes followed by matching the new graph to cluster-averages can yield higher fidelity matching performance than matching to the global average graph. Moreover, by minimizing the graph matching objective function with respect to each cluster average, this approach simultaneously classifies and recovers the vertex labels for the shuffled graph. These theoretical developments are further reinforced via an illuminating real data experiment matching human connectomes.
One of the strongest signals for automated matching of knowledge graphs and ontologies are textual concept descriptions. With the rise of transformer-based language models, text comparison based on meaning (rather than lexical features) is available to researchers. However, performing pairwise comparisons of all textual descriptions of concepts in two knowledge graphs is expensive and scales quadratically (or even worse if concepts have more than one description). To overcome this problem, we follow a two-step approach: we first generate matching candidates using a pre-trained sentence transformer (so called bi-encoder). In a second step, we use fine-tuned transformer cross-encoders to generate the best candidates. We evaluate our approach on multiple datasets and show that it is feasible and produces competitive results.
In this paper, we present a novel neural graph matching approach applied to document comparison. Document comparison is a common task in the legal and financial industries. In some cases, the most important differences may be the addition or omission of words, sentences, clauses, or paragraphs. However, it is a challenging task without recording or tracing whole edited process. Under many temporal uncertainties, we explore the potentiality of our approach to proximate the accurate comparison to make sure which element blocks have a relation of edition with others. In beginning, we apply a document layout analysis that combining traditional and modern technics to segment layout in blocks of various types appropriately. Then we transform this issue to a problem of layout graph matching with textual awareness. About graph matching, it is a long-studied problem with a broad range of applications. However, different from previous works focusing on visual images or structural layout, we also bring textual features into our model for adapting this domain. Specifically, based on the electronic document, we introduce an encoder to deal with the visual presentation decoding from PDF. Additionally, because the modifications can cause the inconsistency of document layout analysis between modified documents and the blocks can be merged and split, Sinkhorn divergence is adopted in our graph neural approach, which tries to overcome both these issues with many-to-many block matching. We demonstrate this on two categories of layouts, as follows., legal agreement and scientific articles, collected from our real-case datasets.
In the \emph{graph matching} problem we observe two graphs $G,H$ and the goal is to find an assignment (or matching) between their vertices such that some measure of edge agreement is maximized. We assume in this work that the observed pair $G,H$ has been drawn from the Correlated Gaussian Wigner (CGW) model -- a popular model for correlated weighted graphs -- where the entries of the adjacency matrices of $G$ and $H$ are independent Gaussians and each edge of $G$ is correlated with one edge of $H$ (determined by the unknown matching) with the edge correlation described by a parameter $\sigma\in [0,1)$. In this paper, we analyse the performance of the \emph{projected power method} (PPM) as a \emph{seeded} graph matching algorithm where we are given an initial partially correct matching (called the seed) as side information. We prove that if the seed is close enough to the ground-truth matching, then with high probability, PPM iteratively improves the seed and recovers the ground-truth matching (either partially or exactly) in $\mathcal{O}(\log n)$ iterations. Our results prove that PPM works even in regimes of constant $\sigma$, thus extending the analysis in (Mao et al. 2023) for the sparse Correlated Erdos-Renyi(CER) model to the (dense) CGW model. As a byproduct of our analysis, we see that the PPM framework generalizes some of the state-of-art algorithms for seeded graph matching. We support and complement our theoretical findings with numerical experiments on synthetic data.