# Fast Approximate Quadratic Programming for Large (Brain) Graph Matching

@article{Vogelstein2011FastAQ, title={Fast Approximate Quadratic Programming for Large (Brain) Graph Matching}, author={Joshua T. Vogelstein and John M. Conroy and Vince Lyzinski and Louis J. Podrazik and Steven G. Kratzer and Eric T. Harley and Donniell E. Fishkind and R. Jacob Vogelstein and Carey E. Priebe}, journal={arXiv: Optimization and Control}, year={2011} }

Quadratic assignment problems (QAPs) arise in a wide variety of domains, ranging from operations research to graph theory to computer vision to neuroscience. In the age of big data, graph valued data is becoming more prominent, and with it, a desire to run algorithms on ever larger graphs. Because QAP is NP-hard, exact algorithms are intractable. Approximate algorithms necessarily employ an accuracy/efficiency trade-off. We developed a fast approximate quadratic assignment algorithm (FAQ). FAQ… Expand

#### 23 Citations

Robust Seriation and Applications to Cancer Genomics

- Computer Science, Mathematics
- 2018

The robust seriation problem is introduced and it is shown that it is equivalent to a modified 2-SUM problem for a class of similarity matrices modeling those observed in DNA assembly, and several relaxations are explored. Expand

Relaxations of the Seriation problem and applications to de novo genome assembly. (Relaxations du problème de sériation et applications à l'assemblage de génome de novo)

- Computer Science
- 2018

The spectral method can be seamlessly integrated in an OLC framework, yielding competitive results compared to standard methods on real data, and the Robust Seriation framework is introduced, formalizing the task of seriation on corrupted data. Expand

Seeded graph matching for correlated Erd\H{o}s-R\'enyi graphs

- Mathematics
- 2013

Graph matching is an important problem in machine learning and pattern recognition. Herein, we present theoretical and practical results on the consistency of graph matching for estimating a latent… Expand

Diversity in Neural Architecture Search

- Computer Science
- 2020 International Joint Conference on Neural Networks (IJCNN)
- 2020

Diverse M-best architectures are defined that are both of high quality and sufficiently different from each other based on a novel graph-based architecture distance and applied in the progressive neural architecture search (PNAS) algorithm, showing that the diverse M-Best is indeed beneficial for finding better architectures. Expand

Spectral Alignment of Graphs

- Computer Science, Mathematics
- IEEE Transactions on Network Science and Engineering
- 2020

A generalized graph alignment formulation that considers both matches and mismatches in a standard QAP formulation is proposed that significantly outperforms other methods in the alignment of regular graph structures, which is one of the most difficult graph alignment cases. Expand

Testing correlation of unlabeled random graphs

- Mathematics
- 2020

We study the problem of detecting the edge correlation between two random graphs with $n$ unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two… Expand

(Nearly) Efficient Algorithms for the Graph Matching Problem on Correlated Random Graphs

- Computer Science, Mathematics
- NeurIPS
- 2019

A quasipolynomial time algorithm that given a pair of $\gamma$-correlated $G(n,p)$ graphs, recovers the "ground truth" permutation $\pi\in S_n$ that matches the vertices of $G_0$ to the Vertices of G_n in the way that minimizes the number of mismatched edges. Expand

Seeded graph matching

- Computer Science, Mathematics
- Pattern Recognit.
- 2019

The state-of-the-art approximategraph matching algorithm "FAQ" of Vogelstein et al. (2015) is modified to make it a fast approximate seeded graph matching algorithm, adapt its applicability to include graphs with differently sized vertex sets, and extend the algorithm so as to provide, for each individual vertex, a nomination list of likely matches. Expand

A graph-based model to discover preference structure from choice data

- Computer Science
- CogSci
- 2018

A novel nonparametric approach to formally capture the concept of preference structure using preference graphs, thereafter clustering decision-makers based on graph embedding methods is proposed. Expand

Statistical graph models of temporal brain networks

- Philosophy
- 2018

La discipline encore naissante des reseaux complexes est vecteur d'un changement de paradigme dans la neuroscience. Les connectomes estimes a partir de mesures de neuroimagerie comme… Expand

#### References

SHOWING 1-10 OF 56 REFERENCES

Thirty Years Of Graph Matching In Pattern Recognition

- Mathematics, Computer Science
- Int. J. Pattern Recognit. Artif. Intell.
- 2004

This paper will try to characterize the role that graphs play within the Pattern Recognition field, and presents two taxonomies that include almost all the graph matching algorithms proposed from the late seventies and describes the different classes of algorithms. Expand

A new bound for the quadratic assignment problem based on convex quadratic programming

- Mathematics, Computer Science
- Math. Program.
- 2001

The construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for QAP, and appears to be competitive with existing bounds in the trade-off between bound quality and computational effort. Expand

From Diffusion MRI to Brain Connectomics

- Psychology
- 2013

Diffusion MRI (dMRI) is a unique modality of MRI which allows one to indirectly examine the microstructure and integrity of the cerebral white matter in vivo and non-invasively. Its success lies in… Expand

An Extended Path Following Algorithm for Graph-Matching Problem

- Mathematics, Computer Science
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- 2012

The path following algorithm is extended to the matching problems on directed graph models by proposing a concave relaxation for the problem, based on the concave and convex relaxations, and the Frank-Wolfe algorithm is utilized to minimize them. Expand

Connectomic Intermediate Phenotypes for Psychiatric Disorders

- Psychology, Medicine
- Front. Psychiatry
- 2012

Research using connectomic techniques to understand how genetic variation influences the connectivity and topology of human brain networks is reviewed, indicating that imaging connectomics provides a powerful framework for understanding how genetic risk for psychiatric disease is expressed through altered structure and function of the human connectome. Expand

Exploring the Psychosis Functional Connectome: Aberrant Intrinsic Networks in Schizophrenia and Bipolar Disorder

- Psychology, Medicine
- Front. Psychiatry
- 2012

A comprehensive analysis of INs reveals a key role for the default mode in both schizophrenia and bipolar disorder. Expand

Network centrality in the human functional connectome.

- Psychology, Medicine
- Cerebral cortex
- 2012

Using resting state functional magnetic resonance imaging data from 1003 healthy adults, a broad array of network centrality measures are investigated to provide novel insights into connectivity within the whole-brain functional network (i.e., the functional connectome). Expand

Schizophrenia, neuroimaging and connectomics

- Medicine, Psychology
- NeuroImage
- 2012

The published findings suggest that schizophrenia is associated with a widespread and possibly context-independent functional connectivity deficit, upon which are superimposed more circumscribed, context-dependent alterations associated with transient states of hyper- and/or hypo-connectivity. Expand

Schizophrenia, neuroimaging and connectomics. NeuroImage

- Schizophrenia, neuroimaging and connectomics. NeuroImage
- 2012

The dissimilarity space: Bridging structural and statistical pattern recognition

- Mathematics, Computer Science
- Pattern Recognit. Lett.
- 2012

A historical review and discusses the properties of the dissimilarity space approaches illustrated by a set of examples on real world datasets. Expand