Anytime and Distributed Approaches for Graph Matching

Due to the inherent genericity of graph-based representations, and thanks to the improvement of computer capacities, structural representations have become more and more popular in the field of Pattern Recognition (PR). In a graph-based representation, vertices and their attributes describe objects (or part of them) while edges represent interrelationships between the objects. Representing objects by graphs turns the problem of object comparison into graph matching (GM) where correspondences between vertices and edges of two graphs have to be found.In the domain of GM, over the last decade, Graph Edit Distance (GED) has been given a specific attention due to its flexibility to match many types of graphs. GED has been applied to a wide range of specific applications from molecule recognition to image classification. Researchers have shed light on the approximate methods that can find suboptimal solutions hopefully close to the optimal ones but the gap between optimal and suboptimal solutions has not been deeply studied yet. For that reason, in this thesis, we focus on exact GED algorithms. Unfortunately, exact GED methods have an exponential complexity. Thus, coming up with an exact GED algorithm that can be scaled up to match graphs involved in PR tasks is a great challenge. Two promising ways to cut-off computational time are search space pruning and distributed algorithms. To this end, we first propose a depth-first GED algorithm which requires less memory and search time. An evaluation of all possible solutions is performed without explicitly enumerating all of them. Candidates are discarded using an upper and lower bounds strategy.To find a trade-off between speed and optimality, we describe how to convert the proposed depth-first GED method into an anytime one that is capable of delivering a first solution very quickly. It also can find a list of improved solutions and eventually converges to the optimal solution instead of providing one and only one solution (i.e., the optimal solution). With the delight of more time, anytime methods can also reach the optimal solution. To illustrate the usage of anytime GM algorithms, we convert our depth-first GED algorithm into an anytime one. We analyze the properties of such methods to solve GM problems and consider the performance in terms of accuracy of the provided solution compared to the optimal or the best one found by a state-of-the-art methods.This thesis is also considered as a first attempt to reduce the run time of exact GED methods usingparallel and distributed fashions. Two parallel and distributed GED approaches are put forward; both of them are based on the depth-first GED method. The search space is decomposed into smaller search trees which are solved independently in a parallel or a distributed manner.To benchmark the proposed GED methods, we propose not only assessing GED methods in a classification context but also evaluating them in a graph-level one (i.e., evaluating their distance and matchin accuracy). Due to the exponential complexity of exact GED algorithms and in order to obtain this kind of information about methods, we propose analyzing the behavior of the eight compared methods under time and memory constraints. In addition to the performance evaluations metrics, we propose a graph database repository dedicated to GED. In this repository, we add graph-level information to well-known and publicly used databases. Added information consists of the best found edit distance of each pair of graphs as well as their vertex-to-vertex and edge-to-edge mappings corresponding to the best found distance. This information helps in assessing the feasibility of exact and approximate GED methods. This thesis brings into question the usual evidences saying that it is impossible to use exact errortolerant GM methods in real-world applications when matching large graphs, or even in a classification context. However, we argue and show that a new type of GM, referred to as anytime methods, can be successful in a graph-level context as well as a classification one. Anytime videos, pseudo-codes and the publications related to the thesis are publicly available at: http://www.rfai.li.univ-tours.fr/ PagesPerso/zabuaisheh/home.html. The thesis is also publicly available at: http://www.rfai.li.univ-tours.fr/Documents/Articles_RFAI/PhD2016zeina.pd

A study of lagrangean decompositions and dual ascent solvers for graph matching

We study the quadratic assignment problem, in computer vision also known as graph matching. Two leading solvers for this problem optimize the Lagrange decomposition duals with sub-gradient and dual ascent (also known as message passing) updates. We explore this direction further and propose several additional Lagrangean relaxations of the graph matching problem along with corresponding algorithms, which are all based on a common dual ascent framework. Our extensive empirical evaluation gives several theoretical insights and suggests a new state-of-the-art anytime solver for the considered problem. Our improvement over state-of-the-art is particularly visible on a new dataset with large-scale sparse problem instances containing more than 500 graph nodes each

Any-k: Anytime Top-k Tree Pattern Retrieval in Labeled Graphs

Many problems in areas as diverse as recommendation systems, social network analysis, semantic search, and distributed root cause analysis can be modeled as pattern search on labeled graphs (also called "heterogeneous information networks" or HINs). Given a large graph and a query pattern with node and edge label constraints, a fundamental challenge is to nd the top-k matches ac- cording to a ranking function over edge and node weights. For users, it is di cult to select value k . We therefore propose the novel notion of an any-k ranking algorithm: for a given time budget, re- turn as many of the top-ranked results as possible. Then, given additional time, produce the next lower-ranked results quickly as well. It can be stopped anytime, but may have to continues until all results are returned. This paper focuses on acyclic patterns over arbitrary labeled graphs. We are interested in practical algorithms that effectively exploit (1) properties of heterogeneous networks, in particular selective constraints on labels, and (2) that the users often explore only a fraction of the top-ranked results. Our solution, KARPET, carefully integrates aggressive pruning that leverages the acyclic nature of the query, and incremental guided search. It enables us to prove strong non-trivial time and space guarantees, which is generally considered very hard for this type of graph search problem. Through experimental studies we show that KARPET achieves running times in the order of milliseconds for tree patterns on large networks with millions of nodes and edges.Comment: To appear in WWW 201

Coarse-to-Fine Lifted MAP Inference in Computer Vision

There is a vast body of theoretical research on lifted inference in probabilistic graphical models (PGMs). However, few demonstrations exist where lifting is applied in conjunction with top of the line applied algorithms. We pursue the applicability of lifted inference for computer vision (CV), with the insight that a globally optimal (MAP) labeling will likely have the same label for two symmetric pixels. The success of our approach lies in efficiently handling a distinct unary potential on every node (pixel), typical of CV applications. This allows us to lift the large class of algorithms that model a CV problem via PGM inference. We propose a generic template for coarse-to-fine (C2F) inference in CV, which progressively refines an initial coarsely lifted PGM for varying quality-time trade-offs. We demonstrate the performance of C2F inference by developing lifted versions of two near state-of-the-art CV algorithms for stereo vision and interactive image segmentation. We find that, against flat algorithms, the lifted versions have a much superior anytime performance, without any loss in final solution quality.Comment: Published in IJCAI 201

Complexity of coalition structure generation

We revisit the coalition structure generation problem in which the goal is to partition the players into exhaustive and disjoint coalitions so as to maximize the social welfare. One of our key results is a general polynomial-time algorithm to solve the problem for all coalitional games provided that player types are known and the number of player types is bounded by a constant. As a corollary, we obtain a polynomial-time algorithm to compute an optimal partition for weighted voting games with a constant number of weight values and for coalitional skill games with a constant number of skills. We also consider well-studied and well-motivated coalitional games defined compactly on combinatorial domains. For these games, we characterize the complexity of computing an optimal coalition structure by presenting polynomial-time algorithms, approximation algorithms, or NP-hardness and inapproximability lower bounds.Comment: 17 page

Anytime Stereo Image Depth Estimation on Mobile Devices

Many applications of stereo depth estimation in robotics require the generation of accurate disparity maps in real time under significant computational constraints. Current state-of-the-art algorithms force a choice between either generating accurate mappings at a slow pace, or quickly generating inaccurate ones, and additionally these methods typically require far too many parameters to be usable on power- or memory-constrained devices. Motivated by these shortcomings, we propose a novel approach for disparity prediction in the anytime setting. In contrast to prior work, our end-to-end learned approach can trade off computation and accuracy at inference time. Depth estimation is performed in stages, during which the model can be queried at any time to output its current best estimate. Our final model can process 1242$\times$375 resolution images within a range of 10-35 FPS on an NVIDIA Jetson TX2 module with only marginal increases in error -- using two orders of magnitude fewer parameters than the most competitive baseline. The source code is available at https://github.com/mileyan/AnyNet .Comment: Accepted by ICRA201