Related papers: Graph Matching via convex relaxation to the simple…
Matching one set of objects to another is a ubiquitous task in machine learning and computer vision that often reduces to some form of the quadratic assignment problem (QAP). The QAP is known to be notoriously hard, both in theory and in…
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes…
We consider the problem of identifying the densest k-node subgraph in a given graph. We write this problem as an instance of rank-constrained cardinality minimization and then relax using the nuclear and 11 norms. Although the original…
Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…
This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather…
We present an accelerated relax-and-round algorithm for concave coverage problems, which generalize the classic maximum coverage problem. Building on the relax-and-round framework of Barman et al. [STACS 2021], we propose two significant…
We consider the class of conditional graph patterns (\emph{CGPs}) that allow user to query data graphs with complex patterns that contain negation and predicates. To overcome the prohibitive cost of subgraph isomorphism, we consider…
We consider the general problem of finding the minimum weight $\bm$-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP)…
This paper studies the problem of matching two complete graphs with edge weights correlated through latent geometries, extending a recent line of research on random graph matching with independent edge weights to geometric models.…
We consider the incomplete multi-graph matching problem, which is a generalization of the NP-hard quadratic assignment problem for matching multiple finite sets. Multi-graph matching plays a central role in computer vision, e.g., for…
The importance of aggregated count data, which is calculated from the data of multiple individuals, continues to increase. Collective Graphical Model (CGM) is a probabilistic approach to the analysis of aggregated data. One of the most…
In this paper, we tackle the problem of measuring similarity among graphs that represent real objects with noisy data. To account for noise, we relax the definition of similarity using the maximum weighted co-$k$-plex relaxation method,…
Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…
We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…
Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…
Graph matching finds the correspondence of nodes across two correlated graphs and lies at the core of many applications. When graph side information is not available, the node correspondence is estimated on the sole basis of network…
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…
This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…
In this paper we propose the Graduated NonConvexity and Graduated Concavity Procedure (GNCGCP) as a general optimization framework to approximately solve the combinatorial optimization problems on the set of partial permutation matrices.…
Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the…