Evaluation of a convex relaxation to a quadratic assignment matching approach for relational object views

Schellewald, Christian; Roth, Stefan; Schnörr, Christoph

doi:10.1016/j.imavis.2006.08.005

Cited by 14 publications

(10 citation statements)

References 43 publications

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“…We provide a bound on the performance of this projection step based on eigenvalues of input matrices and the orthogonal relaxation gap. Note that this rounding step is different than previously studied orthogonal projection, which has been shown to have a poor performance in practice [46]. Through analytical performance characterization, simulations on several synthetic graphs, and real-data analysis, we show that our proposed graph alignment methods lead to improved performance compared to some existing graph alignment methods.…”

Section: Introductionmentioning

confidence: 84%

“…Then, they use a greedy approach to reject assignments with low associations. Similarly, [46] uses a spectral relaxation of QAP to compute a probabilistic subgraph matching across images when the size of graphs are the same, while [47] uses a heuristic multi-scale spectral signature of graphs to compute an alignment across them.…”

Section: Review Of Prior Workmentioning

confidence: 99%

“…Spectral inference methods have received significant attention in problems such as graph clustering [41][42][43][44][45] where the underlying mixed integer program is tightly approximated with an optimization whose optimizers can be computed efficiently. However, the use of spectral techniques in the graph alignment problem has been limited [3,4,34,35,46,47], partially owing to difficulty in connecting existing spectral graph alignment methods with relaxations of the underlying QAP. For example, [3] computes an alignment across biological networks using the top eigenvector of a graph which encodes neighborhood similarities.…”

Section: Introductionmentioning

confidence: 99%

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Spectral Alignment of Graphs

Feizi

Quon

Recamonde‐Mendoza

et al. 2020

IEEE Trans. Netw. Sci. Eng.

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Graph alignment refers to the problem of finding a bijective mapping across vertices of two graphs such that, if two nodes are connected in the first graph, their images are connected in the second graph. This problem arises in many fields such as computational biology, social sciences, and computer vision and is often cast as a quadratic assignment problem (QAP). Most standard graph alignment methods consider an optimization that maximizes the number of matches between the two graphs, ignoring the effect of mismatches. We propose a generalized graph alignment formulation that considers both matches and mismatches in a standard QAP formulation. This modification can have a major impact in aligning graphs with different sizes and heterogenous edge densities. Moreover, we propose two methods for solving the generalized graph alignment problem based on spectral decomposition of matrices. We compare the performance of proposed methods with some existing graph alignment algorithms including Natalie2, GHOST, IsoRank, NetAlign, Klau's approach as well as a semidefinite programmingbased method over various synthetic and real graph models. Our proposed method based on simultaneous alignment of multiple eigenvectors leads to consistently good performance in different graph models. In particular, in the alignment of regular graph structures which is one of the most difficult graph alignment cases, our proposed method significantly outperforms other methods. # of matches1 represents a matrix of all ones and T r(.) is the trace operator. Most existing scalable Network integration Physical associations Functional associations TF binding network (ChIP) Conserved motifs network Reg-based network (GENIE3) MI-based network (CLR)

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Section: Introductionmentioning

confidence: 84%

Section: Review Of Prior Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spectral Alignment of Graphs

Feizi

Quon

Recamonde‐Mendoza

et al. 2020

IEEE Trans. Netw. Sci. Eng.

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“…Graph matching is a quadratic assignment problem, known to be NP-hard to solve. Similarly to our regularized OT formulation, several convex approximations have been proposed, including for instance linear programming [2] and SDP programming [36].…”

Section: Regularized and Relaxed Transportmentioning

confidence: 99%

Regularized Discrete Optimal Transport

Ferradans

Papadakis

Rabin

et al. 2013

Lecture Notes in Computer Science

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Abstract. This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two features are crucial for image processing tasks, which necessitate to take into account families of multimodal histograms, with large mass variation across modes. The corresponding relaxed and regularized transportation problem is the solution of a convex optimization problem. Depending on the regularization used, this minimization can be solved using standard linear programming methods or first order proximal splitting schemes. The resulting transportation plan can be used as a color transfer map, which is robust to mass variation across images color palettes. Furthermore, the regularization of the transport plan helps to remove colorization artifacts due to noise amplification. We also extend this framework to the computation of barycenters of distributions. The barycenter is the solution of an optimization problem, which is separately convex with respect to the barycenter and the transportation plans, but not jointly convex. A block coordinate descent scheme converges to a stationary point of the energy. We show that the resulting algorithm can be used for color normalization across several images. The relaxed and regularized barycenter defines a common color palette for those images. Applying color transfer toward this average palette performs a color normalization of the input images.

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“…Many problems, such as the traveling salesman problem and graph partitioning, can be formulated as QAP, which is also N P -hard and difficult to even approximate [10]. Schellewald et al study convex relaxations of QAP for feature matching in [13]. A closely related work of Kumar et al deals with convex relaxations of quadratic optimization problems [9].…”

Section: Convex Relaxationsmentioning

confidence: 99%

Co-clustering of image segments using convex optimization applied to EM neuronal reconstruction

Vitaladevuni

2010

2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition

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This paper addresses the problem of jointly clustering two segmentations of closely correlated images. We focus in particular on the application of reconstructing neuronal structures in over-segmented electron microscopy images. We formulate the problem of co-clustering as a quadratic semi-assignment problem and investigate convex relaxations using semidefinite and linear programming. We further introduce a linear programming method with manageable number of constraints and present an approach for learning the cost function. Our method increases computational efficiency by orders of magnitude while maintaining accuracy, automatically finds the optimal number of clusters, and empirically tends to produce binary assignment solutions. We illustrate our approach in simulations and in experiments with real EM data.

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Evaluation of a convex relaxation to a quadratic assignment matching approach for relational object views

Cited by 14 publications

References 43 publications

Spectral Alignment of Graphs

Spectral Alignment of Graphs

Regularized Discrete Optimal Transport

Co-clustering of image segments using convex optimization applied to EM neuronal reconstruction

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