HABILITATION A DIRIGER DES RECHERCHESromain.raveaux.free.fr/document/PresentationHDRfinalsans...HABILITATION A DIRIGER DES RECHERCHES Contributions and perspectives on combinatorial

HABILITATION A DIRIGER DES RECHERCHESContributions and perspectives on combinatorial optimization

and machine learning for graph classification and matching

Romain Raveaux

Polytech’Tours - Universite de Tours - LIFAT

26 Juin 2019

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Curriculum vitæ and pedagogical activitiesScientific activities

Research on graph matching and classificationConclusions and perspectives

Content

1 Curriculum vitæ and pedagogical activities

2 Scientific activities

3 Research on graph matching and classification

4 Conclusions and perspectives

Romain Raveaux HABILITATION A DIRIGER DES RECHERCHES

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Educations, diplomas and qualificationsPedagogical activities

Curriculum vitæ and pedagogical activities






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Education

Diplomas:Date Degree Discipline Establishment2004-2006 Master Electrical/computer

engineeringUniversite de Rouen

2004-2006 Master Computer science Universite de Rouen

2006-2010 PhD Computer science Universite de La Rochelle

Master thesis: Symbol recognition in electrical diagram images.Supervised by Sebastien Adam and Pierre Heroux.

PhD thesis: Graph mining and graph classification: Application tocadastral map analysis. Supervised by Jean-Marc Ogier andJean-Christophe Burie.


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Education

Diplomas:Date Degree Discipline Establishment2004-2006 Master Electrical/computer

engineeringUniversite de Rouen

2004-2006 Master Computer science Universite de Rouen2006-2010 PhD Computer science Universite de La Rochelle

Master thesis: Symbol recognition in electrical diagram images.Supervised by Sebastien Adam and Pierre Heroux.PhD thesis: Graph mining and graph classification: Application tocadastral map analysis. Supervised by Jean-Marc Ogier andJean-Christophe Burie.


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Qualifications and positions

1 In 2010, qualified to be assistant professor

CNU sections: 27, 6127: Computer science61: Automatic and signal processing

2 In 2012, assistant professor

Universite de ToursTeaching: Engineering school: Polytech’ToursResearch: Computer science laboratory: LIFAT


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Pedagogical activities

1 Teaching: around 240h (EqTD) per year in average.

Licence level:Networking(L3), Python and data sciences(L2)Master level: Mobile systems(M2), Multimedia systems(M2)2012-2015: Lecturer in the International Master onComputer-Aided Decision Support

2 Pedagogical responsibilities: around 25h (EqTD) per year.

In charge of the fifth year of an engineering specialtyIn charge of student projects (collective and final projects)


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Co-supervisions of studentsAnimations and responsibilitiesProjects and collaborationsDissemination

Scientific activities






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Co-supervisions of PhD students

Date Name Funding Teaching Co-supervised by2012-2016 Zeina Abu-Aisheh Minister Assistant lecturer J.Y Ramel, P. Martineau∗

2015-2018 Mostafa Darwiche Region Assistant lecturer D. Conte, V. T’Kindt∗

2015-2019 Maxime Martineau Project Assistant lecturer D. Conte, G. Venturini

∗: A collaborative work: RFAI and ROOT teamsQuality of the management:

1 In numbers:3.3 Journal papers in average by PhD4.6 Conference, workshop papers in average by PhD

2 Without numbers:After the PhD: they stay with us (postdoc, lecturer)Then, they find jobs (Shape.ai, CIRELT, ...)

PhD supervision: a method

1 Available, relevant feed-backs, schedule

2 PhDs as young researchers, kindness communication


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Co-supervisions of PhD students

Date Name Funding Teaching Co-supervised by2012-2016 Zeina Abu-Aisheh Minister Assistant lecturer J.Y Ramel, P. Martineau∗

2015-2018 Mostafa Darwiche Region Assistant lecturer D. Conte, V. T’Kindt∗

2015-2019 Maxime Martineau Project Assistant lecturer D. Conte, G. Venturini

∗: A collaborative work: RFAI and ROOT teamsQuality of the management:

1 In numbers:3.3 Journal papers in average by PhD4.6 Conference, workshop papers in average by PhD

2 Without numbers:After the PhD: they stay with us (postdoc, lecturer)Then, they find jobs (Shape.ai, CIRELT, ...)

PhD supervision: a method

1 Available, relevant feed-backs, schedule

2 PhDs as young researchers, kindness communication


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Scientific expertise

1 Program Committee: Conferences

International Conference on Document Analysis andRecognition: ICDAR 2019, 2017Graph-Based Representation for pattern recognition: GBR2019Graphics Recognition: GREC 2019, 2015, 2013, 2011International Conference on Hybrid Artificial IntelligenceSystems: HAIS 2010, 2011

2 Reviewer for:

Pattern Recognition Letters (PRL) (1 per year)Pattern Recognition (PR)(1 per year)IEEE Transaction on Image Processing (TIP) (occasionally)International Journal On Document Analysis and Recognition(IJDAR) (occasionally)Expert Systems with Applications (ESWA)(1 per year)


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Scientific animation

Science administration:

Since 2016, member of the board of VALCONUM.VALCONUM is a European public-private structure aiming toaccelerate the technological transfer in the field ofdematerialization and the valorization of digital contents.

Contest organization:

2011, participation to the organization of a contest on symbolrecognition.

Conference organizations:

Participation to the organization of GBR 2019, DAS 2014 andGREC 2009


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Scientific animation

Science administration:

Since 2016, member of the board of VALCONUM.VALCONUM is a European public-private structure aiming toaccelerate the technological transfer in the field ofdematerialization and the valorization of digital contents.

Contest organization:

2011, participation to the organization of a contest on symbolrecognition.

Conference organizations:

Participation to the organization of GBR 2019, DAS 2014 andGREC 2009


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Projects and collaborations

Projects:

Name Date Scope Funding Involvement Statuse-trap2 2019 National 450K 15% Submitted

LOR 2019 National 600K 33% SubmittedVISIT 2019 Regional 150K (LIFAT) 20% Accepted. Running

ADAM-IoT 2019 European 1M – RejectedFibravasc 2018 Regional 100K (LIFAT) 10% Accepted. RunningMalagga 2018 National - - Rejected

ScannerLoire 2018 Regional - - RejectedADT 2016 Regional - - Rejected

Caramba 2016-2019 Regional 200K 33% Accepted. RunningDoD 2014-2015 Industrial 200K 33% Accepted. Done

Collaborations:

Institute Country Topic PublicationGREYC France, Caen Graph edit distance 1 journalLITIS France, Rouen Graph prototype, Graph edit distance 2 journals

Griffith University Australia Image quality 2 journalsCampinas University Brazil Learning graph matching 1 journal


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Publications

International journal IF 5 years 1 SNIP 2 SRJ 3 #articles

Pattern Recognition 4.3 2.47 1.06 2Expert Systems with Applications 3.7 2.4 1.27 2Computer and Operation Research 3.2 2.094 1.9 1Computer Vision and Image Understanding 2.7 1.8 0.71 1Pattern Recognition Letters 2.3 1.58 0.662 6Journal of Visual Communication and Image Representation 2.02 1.36 0.5 1International Journal on Document Analysis and Recogni-tion

1.26 1.4 0.387 1

Signal Image and Video Processing 1.6 NA NA 115

International Conference Rank4 #articles

International Conference on Document Analysis and Recognition (ICDAR) A 2Structural, Syntactic, and Statistical Pattern Recognition (SSPR) A 1International Workshop on Document Analysis Systems (DAS) B 2European Signal Processing Conference (EUSIPCO) B 1International Conference on Pattern Recognition (ICPR) B 3

8

1Impact factor from editor websites (June 2018).

2Source Normalized Impact per Paper from editor websites (June 2018).

3SCImago Journal Rank from editor websites (June 2018).

4CORE 2018 : http://portal.core.edu.au


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Data sets, codes and contest

Data sets are available online

http://www.rfai.li.univ-tours.fr/PublicData/

GDR4GED/home.html

Codes are available online

http://www.rfai.lifat.univ-tours.fr/PublicData/

GraphLib/home.html

https://networkx.github.io/networkx/algorithms/

similarity

Participation to a contest ICPR 2016

https://gdc2016.greyc.fr/


http://www.rfai.li.univ-tours.fr/PublicData/GDR4GED/home.html

http://www.rfai.li.univ-tours.fr/PublicData/GDR4GED/home.html

http://www.rfai.lifat.univ-tours.fr/PublicData/GraphLib/home.html

http://www.rfai.lifat.univ-tours.fr/PublicData/GraphLib/home.html

https://networkx.github.io/networkx/algorithms/similarity

https://networkx.github.io/networkx/algorithms/similarity

https://gdc2016.greyc.fr/

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Overview of research topicsProblems and state of the artMy contributions

Research on graph matching and classification






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Problems and techniques

1 Problems: graph matching and graph classification

2 Techniques: thanks to machine learning and operationsresearch

3 A coherent work: my PhD, PhDs of Zeina Abu-aisheh,Mostafa Darwiche and Maxime Martineau.


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Toward Graph matching: A set of nodes

Each node can be a vector, an image or a word, ...


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Toward Graph matching: Two sets of nodes


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Toward Graph matching: Set matching


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Toward Graph matching: Two graphs


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Toward Graph matching (f : V1 → V2)

ij kl


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Graph classification

Toxic or not


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Operations Research

A problem has to be solved

1 Operations Research models and solves combinatorialproblems

2 Optimization problems need to be formalized and wellstructured

3 The human or (a priori) knowledge about the problems isintroduced through variables, constraints and objectives

=⇒ link with expert systems


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Machine Learning


But: lack of formal specifications.

A possible solution:

1 Formulate a (statistical) proxy problem that relies on data

2 then use machine learning.

Machine Learning:

1 discover regularities on a given set of data (from“unstructured” or “not formalized” information)

2 generalizes to unseen data

3 solves the original problem without using explicit instructions


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Machine Learning






Machine Learning:





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Machine Learning






Machine Learning:





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Problems and state of the art1 Curriculum vitæ and pedagogical activities


2 Scientific activitiesCo-supervisions of studentsAnimations and responsibilitiesProjects and collaborationsDissemination

3 Research on graph matching and classificationOverview of research topicsProblems and state of the artMy contributions

4 Conclusions and perspectivesConclusionsShort term perspectivesLong term perspectivesRomain Raveaux HABILITATION A DIRIGER DES RECHERCHES

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Graph matching: the problem at glance

Input:

1 Two graphs: G1, G2

2 Similarity functions:sV , sE

sV (i , k)

sV (j , k)

sE (ij , kl)

sV (i , l)

sV (j , l)


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Output:

Node-to-nodematching

Binary variables: YYi,k = 1 if i and kare matched

Yi ,k

Yj ,k

Yi ,l

Yj ,l


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Objective function: similarity of two graphs: Yi ,k = Yj ,l = 1S(G1,G2,Y ) = sV (i , k).Yi ,k + sV (j , l).Yj ,l + sE (ij , kl).Yi ,k .Yj ,l

sV (i , k) ∗ Yi ,k

sE (ij , kl) ∗ Yi ,k ∗ Yj ,l

sV (j , l) ∗ Yj ,l


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Graph matching problem: NP-hard [Gold and Rangarajan, 1996]

Find Y such that:

1 the sum of similarities is maximized.

2 a node of G1 is matched to at most one node of G2

3 a node of G2 is matched to at most one node of G1


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Graph matching: state of the art


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Graph matching: state of the art

Bottom lines from the state of the art:

1 Many fast heuristics can be found in the literature

2 How accurate are these heuristics compared to exactmethods?


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Graph matching: pattern recognition applications

Graph matching can be involved in several pattern recognitionapplications.


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1 Graph comparison

2 Graph similarity search

Compare the query withall the graphsSort by similarities

3 Graph classification:K-Nearest Neighbors(KNN)

Compare the query withall the graphsSort by similaritiesRetain the K most similargraphsThe most frequent classlabel


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1 Graph comparison2 Graph similarity search





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Retain the K most similargraphsThe most frequent classlabel


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Issue: many calls to the graph matching methodRomain Raveaux HABILITATION A DIRIGER DES RECHERCHES

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Graph matching: KNN state of the art

Graph KNN can be sped up thanks to:

1 Fast graph matching methods [K. Riesen, 2015]2 Reducing the number of graphs by graph prototypes [M.

Ferrer, 2011], [R. Raveaux, 2011].1 Keep the most significant graphs


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Graph matching: KNN state of the art

Graph KNN can be sped up thanks to:

1 Fast graph matching methods [K. Riesen, 2015]2 Reducing the number of graphs by graph prototypes [M.

Ferrer, 2011], [R. Raveaux, 2011].1 Keep the most significant graphs

How to reduce the number of comparisons without loss ofinformation?


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We know how to compare graphs thank to graph matching.Graph matching offers an elegant manner to compare graphsdirectly in graph space.

But how to choose the similarity functions between nodes andedges?

Node/Edge similarity functions are crucial

Similarity functions link the graph matching problem to the finalapplication.

BUT:

1 How to compare graphs according to a specific objective?

2 How to reach a goal that is defined by data?

3 Where machine learning can be introduced?


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BUT:





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BUT:





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Learning graph matching: the problem at glance


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Learning graph matching: the state of the art

[Cho et al., 2013]

[Nowak et al., 2017] [Cortes et al., 2016]


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Deadlocks

1 How to design fast and accurate graph matching methods?

2 How to reduce the number of graph comparisons?

3 How to learn graph matching for classification?


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My contributions1 Curriculum vitæ and pedagogical activities


2 Scientific activitiesCo-supervisions of studentsAnimations and responsibilitiesProjects and collaborationsDissemination

3 Research on graph matching and classificationOverview of research topicsProblems and state of the artMy contributions

4 Conclusions and perspectivesConclusionsShort term perspectivesLong term perspectivesRomain Raveaux HABILITATION A DIRIGER DES RECHERCHES

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Deadlock 1: How to design fast and accurate graphmatching methods?


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Branch and bound for graph matching

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Search space is a tree

A tree node is a partialmatching

Depth-first search withbacktracking[Abu-Aisheh et al., 2015]


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Anytime branch and bound [Abu-Aisheh et al., 2016]:

finds quickly a solution: Depth-first search[Abu-Aisheh et al., 2015]

keeps on searching for improving solutions

can be easily interrupted at each tree node

can be interrupted anytime to provide the best solution foundso far.

Anytime algorithm: suitable when the time given to graphmatching methods is uncertain. Good for pattern recognitionapplications


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Anytime branch and bound [Abu-Aisheh et al., 2016]:

finds quickly a solution: Depth-first search[Abu-Aisheh et al., 2015]

keeps on searching for improving solutions

can be easily interrupted at each tree node

can be interrupted anytime to provide the best solution foundso far.

Anytime algorithm: suitable when the time given to graphmatching methods is uncertain. Good for pattern recognitionapplications


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2015

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Anytime branch and bound[Abu-Aisheh et al., 2016]

Quick first solution:Depth-first search[Abu-Aisheh et al., 2015]

Parallel branch and bound[Abu-Aisheh et al., 2018].Work-stealing strategy tobalance the load.


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Mathematical programming for graph matching

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ILP for graph matching (F1,F2, F3):[Lerouge et al., 2017]

Linearization of thequadratic problem

Edge matching variables (Z)

sV (i , k) ∗ Yi ,k

sE (ij , kl) ∗ Yi ,k ∗ Yj ,l

sV (j , l) ∗ Yj ,l


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2010

2011

2013

2015

2017

2018

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ILP for graph matching (F1,F2, F3):[Lerouge et al., 2017]

Linearization of thequadratic problem

Edge matching variables (Z)

sV (i , k) ∗ Yi ,k

sE (ij , kl) ∗ Zij ,kl

sV (j , l) ∗ Yj ,l


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New constraints should be addedto ensure that if 2 edges arematched (Zij ,kl = 1) then relatednodes are matched too.Topological constraints:

Zij ,kl ≤ Yi ,k ∀(ij , kl) ∈ E1 × E2

Zij ,kl ≤ Yj ,l ∀(ij , kl) ∈ E1 × E2

sV (i , k) ∗ Yi ,k

sE (ij , kl) ∗ Zij ,kl

sV (j , l) ∗ Yj ,l


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1 Local Branching Heuristic: LocBra [Darwiche et al., 2018]2 The goal is to intelligently explore the solution space

By taking advantage of an ILP and a mathematical solver(Cplex)

3 It is an iterative process starting from an initial solution (x0)

4 x is a vector of binary variables grouping Y and Z


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Local search: Search for an improving solution inside a smallregion of the solution space.

Neighborhood: no more than k variables should be changedbetween the new solution and x0.This neighborhood definition is a new constraint in the ILP


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No improved solutions found → Diversification operator for GM:

Goal: Helps skipping a local optimum.

To change the region, change important variables

Important variables=a high impacts on the objective functionvalue.


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No improved solutions found → Diversification operator for GM:

Goal: Helps skipping a local optimum.To change the region, change important variables

Important variables=a high impacts on the objective functionvalue.


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Deadlock 2: How to reduce the number of graphcomparisons?


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Fused graph matching and KNN problems for classification

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Problem: Solve the KNN problemfor graphs

Issue: Many graph comparisonsand the process is slow

Answer: Merge GM and KNN in asingle problem[Abu-Aisheh et al., 2017]

Why: Global reasoning instead ofconsidering each comparisonindependently


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(GM+KNN):

The search space is organized as a tree

First floor: a tree node is a graph comparison

Each graph comparison is an instance of graph matching

It can be solved by a Branch and Bound method


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Use case: We are looking for the nearest neighbor1 Compare Gq with G1: S(Gq,G1) = 4

2 Start to compare Gq with G2 and use S(Gq,G1) = 4 as alower bound to cut branches.

3 From the first floor, we estimate that S(Gq,G2) ≤ 24 G1 is a better neighbor, no need to explore fully the sub-tree

(Gq,G2)5 Avoid (full) comparisons of very dissimilar graphs

C is function that evaluates a tree node (over estimate)Romain Raveaux HABILITATION A DIRIGER DES RECHERCHES

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Use case: We are looking for the nearest neighbor1 Compare Gq with G1: S(Gq,G1) = 42 Start to compare Gq with G2 and use S(Gq,G1) = 4 as a

lower bound to cut branches.

3 From the first floor, we estimate that S(Gq,G2) ≤ 24 G1 is a better neighbor, no need to explore fully the sub-tree



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lower bound to cut branches.3 From the first floor, we estimate that S(Gq,G2) ≤ 2

4 G1 is a better neighbor, no need to explore fully the sub-tree(Gq,G2)

5 Avoid (full) comparisons of very dissimilar graphs


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lower bound to cut branches.3 From the first floor, we estimate that S(Gq,G2) ≤ 24 G1 is a better neighbor, no need to explore fully the sub-tree

(Gq,G2)

5 Avoid (full) comparisons of very dissimilar graphs


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lower bound to cut branches.3 From the first floor, we estimate that S(Gq,G2) ≤ 24 G1 is a better neighbor, no need to explore fully the sub-tree



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Deadlock 3: How to learn graph matching?


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Learn graph matching for classification

2010

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Parametrized graphmatching[Raveaux et al., 2017]

Learning graph matching forclassification[Martineau et al., 2018]

sV (i , k)

sE (ij , kl)

sV (j , l)Romain Raveaux HABILITATION A DIRIGER DES RECHERCHES

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2013

2015

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Parametrized graphmatching[Raveaux et al., 2017]

Learning graph matching forclassification[Martineau et al., 2018]

sV (i , k).βk

sE (ij , kl).βkl

sV (j , l).βlRomain Raveaux HABILITATION A DIRIGER DES RECHERCHES

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Parameters β are learned by gradient descent.Weakly supervised learning of (discriminative) graph matching


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ConclusionsShort term perspectivesLong term perspectives

Conclusions and perspectives






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Take a step back on graph matchingFrom the operations research side

NP-hard problem

No single method can effectively address all instances.

Computer vision and pattern recognition:

low computational time usually dominates the optimalityguarantees.

Complementary of the methods

There is a need to combine heuristics

Select an heuristic according to the instance at hand


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Take a step back on graph matchingFrom the machine learning viewpoint

Similarity functions are crucial

Learning node/edge embedding, learning similarity functions

To reach a specific objective (the user need).

Good similarity functions

allow to easily differentiate between vertices/edges

can make the problem easier to solve.

Node embedding integrating topological information

can help to recast the quadratic problem to linear assignmentproblem


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Take a step back on graph matchingGraph matching for graph classification

Question: What is the meaning of graph matching for graphclassification?

GM imposes node assignment constraints

GM brings constraints to the learning problem:

Do constraints act like a regularization term to bettergeneralize on unseen data?

Are constraints useful to reduce the number of training data?


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These open questions are important to legitimate graph matchingfor graph classification.


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Graph matching what do we need?

From the operations research side:

1 Fast, scalable and accurate heuristics are always welcome forcomputer vision and pattern recognition communities.

From the machine learning viewpoint:

1 Low complexity (near linear time)

2 Graph matching methods suited to execution on GPU

3 Learning problems are often solved by gradient descent sodifferentiable methods are wanted → link with robustoptimization?

4 Avoid the storage of similarity matrices (|V1|.|V2| × |V1|.|V2|)


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Short term perspectives

Future master students (low hanging fruits)

1 (KNN + GM) solved by the local branching heuristic

2 Parametrized GM as an input layer of a MLP

3 ILP for the MCS problem

Future PhD students

1 Learning graph matching: hierarchical feature learning (GraphNeural Network) + a combinatorial layer (graph matchingmethod)

2 Learning graph matching: learn to branch in a branch andbound (reinforcement learning)

3 Structured classification: graph matching as a loss function


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Long term perspectives

To be curious:1 Cross fertilization: OR, ML: LOR project2 Inspired by other problems:

From computer vision: CRF MAP-inferenceFrom OR: TSP, scheduling problems

Fundamental:

On the relation between graph matching and OptimalTransport (OT) (Gromov-Wasserstein distance).

Applications:1 Graph matching for multiple object tracking in videos, table

comparisons in documents, ...2 Graph matching for unsupervised domain adaptation3 Benchmarks

Still a lot of interesting work to do ...


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Long term perspectives

To be curious:1 Cross fertilization: OR, ML: LOR project2 Inspired by other problems:

From computer vision: CRF MAP-inferenceFrom OR: TSP, scheduling problems

Fundamental:

On the relation between graph matching and OptimalTransport (OT) (Gromov-Wasserstein distance).

Applications:1 Graph matching for multiple object tracking in videos, table

comparisons in documents, ...2 Graph matching for unsupervised domain adaptation3 Benchmarks

Still a lot of interesting work to do ...Romain Raveaux HABILITATION A DIRIGER DES RECHERCHES

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Thank you

Any questions?


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Abu-Aisheh, Z., Raveaux, R., and Ramel, J. (2016).Anytime graph matching.Pattern Recognition Letters, 84:215–224.

Abu-Aisheh, Z., Raveaux, R., and Ramel, J. (2017).Fast nearest neighbors search in graph space based on abranch-and-bound strategy.In [Foggia et al., 2017], pages 197–207.

Abu-Aisheh, Z., Raveaux, R., Ramel, J., and Martineau, P.(2015).An exact graph edit distance algorithm for solving patternrecognition problems.In Marsico, M. D., Figueiredo, M. A. T., and Fred, A. L. N.,editors, ICPRAM 2015 - Proceedings of the InternationalConference on Pattern Recognition Applications and Methods,


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Volume 1, Lisbon, Portugal, 10-12 January, 2015., pages271–278. SciTePress.

Abu-Aisheh, Z., Raveaux, R., Ramel, J., and Martineau, P.(2018).A parallel graph edit distance algorithm.Expert Syst. Appl., 94:41–57.

Cho, M., Alahari, K., and Ponce, J. (2013).Learning graphs to match.In IEEE International Conference on Computer Vision, ICCV2013, pages 25–32.

Cortes, X., Serratosa, F., and Serratosa, F. (2016).Learning graph matching substitution weights based on theground truth node correspondence.IJPRAI, 30(2).


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Darwiche, M., Conte, D., Raveaux, R., and T’Kindt, V.(2018).A local branching heuristic for solving a graph edit distanceproblem.Computers and Operations Research.

Foggia, P., Liu, C., and Vento, M., editors (2017).Graph-Based Representations in Pattern Recognition - 11thIAPR-TC-15 International Workshop, GbRPR 2017, Anacapri,Italy, May 16-18, 2017, Proceedings, volume 10310 of LectureNotes in Computer Science.

Gold, S. and Rangarajan, A. (1996).A graduated assignment algorithm for graph matching.IEEE Transactions on Pattern Analysis and MachineIntelligence, 18(4):377–388.


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Lerouge, J., Abu-Aisheh, Z., Raveaux, R., Heroux, P., andAdam, S. (2017).New binary linear programming formulation to compute thegraph edit distance.Pattern Recognition, 72:254–265.

Martineau, M., Raveaux, R., Conte, D., and Venturini, G.(2018).Learning error-correcting graph matching with a multiclassneural network.Pattern Recognition Letters.

Nowak, A., Villar, S., Bandeira, A. S., and Bruna, J. (2017).A note on learning algorithms for quadratic assignment withgraph neural networks.CoRR, abs/1706.07450.


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Raveaux, R., Martineau, M., Conte, D., and Venturini, G.(2017).Learning graph matching with a graph-based perceptron in aclassification context.In [Foggia et al., 2017], pages 49–58.


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HABILITATION A DIRIGER DES RECHERCHESromain.raveaux.free.fr/document/PresentationHDRfinalsans...HABILITATION A DIRIGER DES RECHERCHES Contributions and perspectives on combinatorial