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107. Benchopt: Reproducible, efficient and collaborative optimization benchmarks

Author

Thomas Moreau, Mathurin Massias, Alexandre Gramfort, Pierre Ablin, Pierre-Antoine Bannier, Benjamin Charlier, Mathieu Dagréou, Tom Dupré La Tour, Ghislain Durif, Dantas, Cassio F., Quentin Klopfenstein, Johan Larsson, En Lai, Tanguy Lefort, Benoit Malézieux, Badr Moufad, Nguyen, Binh T., Alain Rakotomamonjy, Zaccharie Ramzi, Joseph Salmon, Samuel Vaiter, Modèles et inférence pour les données de Neuroimagerie (MIND), IFR49 - Neurospin - CEA, Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Réseaux dynamiques : approche structurelle et temporelle (DANTE), Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut Rhône-Alpin des systèmes complexes (IXXI), École normale supérieure de Lyon (ENS de Lyon)-Université Lumière - Lyon 2 (UL2)-Université Jean Moulin - Lyon 3 (UJML), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Lumière - Lyon 2 (UL2)-Université Jean Moulin - Lyon 3 (UJML), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Inria Lyon, Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL), Centre National de la Recherche Scientifique (CNRS), Owkin France, Institut Montpelliérain Alexander Grothendieck (IMAG), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), University of California [Berkeley] (UC Berkeley), University of California (UC), Territoires, Environnement, Télédétection et Information Spatiale (UMR TETIS), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-AgroParisTech-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), University of Luxembourg [Luxembourg], Lund University [Lund], Laboratoire Traitement et Communication de l'Information (LTCI), Institut Mines-Télécom [Paris] (IMT)-Télécom Paris, Criteo AI Lab, Criteo [Paris], École normale supérieure - Paris (ENS-PSL), Département de Mathématiques et Applications - ENS Paris (DMA), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR-20-CHIA-0001,CAMELOT,Apprentissage automatique et optimisation coopératifs.(2020), ANR-20-CHIA-0016,BrAIN,Intelligence Artificielle et Neurosciences(2020), ANR-20-THIA-0013,UDOPIA,Programme Doctoral en Intelligence Artificielle de l'Université Paris-Saclay(2020), and ANR-17-CONV-0003,Institut DATAIA (I2-DRIVE),Data Science, Artificial Intelligence and Society(2017)

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Optimization and Control (math.OC), FOS: Mathematics, Machine Learning (stat.ML), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control, Machine Learning (cs.LG)
Abstract

Numerical validation is at the core of machine learning research as it allows to assess the actual impact of new methods, and to confirm the agreement between theory and practice. Yet, the rapid development of the field poses several challenges: researchers are confronted with a profusion of methods to compare, limited transparency and consensus on best practices, as well as tedious re-implementation work. As a result, validation is often very partial, which can lead to wrong conclusions that slow down the progress of research. We propose Benchopt, a collaborative framework to automate, reproduce and publish optimization benchmarks in machine learning across programming languages and hardware architectures. Benchopt simplifies benchmarking for the community by providing an off-the-shelf tool for running, sharing and extending experiments. To demonstrate its broad usability, we showcase benchmarks on three standard learning tasks: $\ell_2$-regularized logistic regression, Lasso, and ResNet18 training for image classification. These benchmarks highlight key practical findings that give a more nuanced view of the state-of-the-art for these problems, showing that for practical evaluation, the devil is in the details. We hope that Benchopt will foster collaborative work in the community hence improving the reproducibility of research findings., Comment: Accepted in proceedings of NeurIPS 22; Benchopt library documentation is available at https://benchopt.github.io/

Published
2022
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127. Online multimodal dictionary learning

Author

Maxime Berar, Alain Rakotomamonjy, Abraham Traoré, Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU), Equipe Apprentissage (DocApp - LITIS), and Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie)

Subjects
0209 industrial biotechnology, Sequence, Basis (linear algebra), Computer science, Cognitive Neuroscience, MathematicsofComputing_NUMERICALANALYSIS, online dictionary learning, 02 engineering and technology, Computational resource, tensor, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Computer Science Applications, Set (abstract data type), 020901 industrial engineering & automation, Artificial Intelligence, recursive computations, block coordinate descent, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Tensor, Gradient descent, Coordinate descent, Algorithm, gradient descent, Block (data storage)
Abstract

International audience; We propose a new online approach for multimodal dictionary learning. The method developed in this work addresses the great challenges posed by the computational resource constraints in dynamic environment when dealing with large scale tensor sequences. Given a sequence of tensors, i.e. a set composed of equal-size tensors, the approach proposed in this paper allows to infer a basis of latent factors that generate these tensors by sequentially processing a small number of data samples instead of using the whole sequence at once. Our technique is based on block coordinate descent, gradient descent and recursive computations of the gradient. A theoretical result is provided and numerical experiments on both real and synthetic data sets are performed.

Published
2019
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132. Theoretical Guarantees for Bridging Metric Measure Embedding and Optimal Transport

Author

Alain Rakotomamonjy, Mokhtar Z. Alaya, Maxime Berar, Gilles Gasso, Laboratoire de Mathématiques Appliquées de Compiègne (LMAC), Université de Technologie de Compiègne (UTC), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Alaya, Mokhtar Z., Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), and Normandie Université (NU)

Subjects
[INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], FOS: Computer and information sciences, Computer Science - Machine Learning, Matching (graph theory), Cognitive Neuroscience, Machine Learning (stat.ML), 02 engineering and technology, 01 natural sciences, Measure (mathematics), Machine Learning (cs.LG), [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Mathematics, Discrete mathematics, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Euclidean space, 010102 general mathematics, 020207 software engineering, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Computer Science Applications, Metric space, Distribution (mathematics), Metric (mathematics), Embedding, Pairwise comparison
Abstract

We propose a novel approach for comparing distributions whose supports do not necessarily lie on the same metric space. Unlike Gromov-Wasserstein (GW) distance which compares pairwise distances of elements from each distribution, we consider a method allowing to embed the metric measure spaces in a common Euclidean space and compute an optimal transport (OT) on the embedded distributions. This leads to what we call a sub-embedding robust Wasserstein (SERW) distance. Under some conditions, SERW is a distance that considers an OT distance of the (low-distorted) embedded distributions using a common metric. In addition to this novel proposal that generalizes several recent OT works, our contributions stand on several theoretical analyses: (i) we characterize the embedding spaces to define SERW distance for distribution alignment; (ii) we prove that SERW mimics almost the same properties of GW distance, and we give a cost relation between GW and SERW. The paper also provides some numerical illustrations of how SERW behaves on matching problems.

Published
2020

133. Editorial: A Successful Year and Looking Forward to 2017 and Beyond

Author

Jose A. Lozano, Jacek Mańdziuk, Jun Fu, Johan A. K. Suykens, Meng Wang, Dhireesha Kudithipudi, Fakhri Karray, Hong Qiao, Alain Rakotomamonjy, Haibo He, Robert S. Haas, Teresa B. Ludermir, Daniel W. C. Ho, Barbara Hammer, Shiliang Sun, Stefano Melacci, and Antonio Paiva

Subjects
0209 industrial biotechnology, Impact factor, Artificial neural network, Operations research, Computer Networks and Communications, Computer science, 02 engineering and technology, Computer Science Applications, Engineering management, 020901 industrial engineering & automation, Artificial Intelligence, Citation, GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries), Software
Abstract

This issue marks the first anniversary issue since I was honored to serve as the Editor-in-Chief (EiC) of the IEEE Transactions on Neural Networks and Learning Systems (TNNLS). I am happy to report that we had a very successful year and here are a few highlights that I would like to share with the community. • The latest impact factor of TNNLS is 4.854 according to the Journal Citation Reports. This marks a record high impact factor for our journal and places TNNLS as the number one scholarly publication in Computer Science (Hardware & Architecture), number three in Computer Science (Theory & Methods), and number ten in Electrical and Electronic Engineering journals.

Published
2017
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134. Statistical Learning for BCIs

Author

Rémi Flamary, Michèle Sebag, and Alain Rakotomamonjy

Subjects
Statistical learning, business.industry, Computer science, Hyperparameter optimization, Sensor selection, Artificial intelligence, Machine learning, computer.software_genre, business, computer, Brain–computer interface
Published
2016
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135. A Review of Classification Algorithms for EEG-based Brain-Computer Interfaces: A 10-year Update

Author

Florian Yger, Laurent Bougrain, Alain Rakotomamonjy, Andrzej Cichocki, Fabien Lotte, Maureen Clerc, Marco Congedo, Popular interaction with 3d content (Potioc), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), RIKEN Center for Brain Science [Wako] (RIKEN CBS), RIKEN - Institute of Physical and Chemical Research [Japon] (RIKEN), Analysis and modeling of neural systems by a system neuroscience approach (NEUROSYS), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Complex Systems, Artificial Intelligence & Robotics (LORIA - AIS), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Skolkovo Institute of Science and Technology [Moscow] (Skoltech), Nicolaus Copernicus University [Toruń], Computational Imaging of the Central Nervous System (ATHENA), Inria Sophia Antipolis - Méditerranée (CRISAM), GIPSA - Vision and Brain Signal Processing (GIPSA-VIBS), Département Images et Signal (GIPSA-DIS), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Equipe Apprentissage (DocApp - LITIS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Université Le Havre Normandie (ULH), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA), Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision (LAMSADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Inria Bordeaux - Sud-Ouest, Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), and Normandie Université (NU)

Subjects
Signal processing, Time Factors, Computer science, Feature extraction, Biomedical Engineering, 02 engineering and technology, Adaptive classifiers, Tensors, Machine learning, computer.software_genre, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], 03 medical and health sciences, Cellular and Molecular Neuroscience, 0302 clinical medicine, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], 0202 electrical engineering, electronic engineering, information engineering, Animals, Humans, EEG, Riemannian geometry, BCI, Brain–computer interface, Spatial filtering, business.industry, Deep learning, Brain, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Signal Processing, Computer-Assisted, Electroencephalography, Linear discriminant analysis, Classification, Random forest, Transfer learning, Statistical classification, ComputingMethodologies_PATTERNRECOGNITION, Brain-Computer Interfaces, 020201 artificial intelligence & image processing, Artificial intelligence, business, Transfer of learning, computer, Classifier (UML), [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Algorithms, 030217 neurology & neurosurgery
Abstract

International audience; Objective: Most current Electroencephalography (EEG)-based Brain-Computer Interfaces (BCIs) are based on machine learning algorithms. There is a large diversity of classifier types that are used in this field, as described in our 2007 review paper. Now, approximately 10 years after this review publication, many new algorithms have been developed and tested to classify EEG signals in BCIs. The time is therefore ripe for an updated review of EEG classification algorithms for BCIs. Approach: We surveyed the BCI and machine learning literature from 2007 to 2017 to identify the new classification approaches that have been investigated to design BCIs. We synthesize these studies in order to present such algorithms, to report how they were used for BCIs, what were the outcomes, and to identify their pros and cons. Main results: We found that the recently designed classification algorithms for EEG-based BCIs can be divided into four main categories: adaptive classifiers, matrix and tensor classifiers, transfer learning and deep learning, plus a few other miscellaneous classifiers. Among these, adaptive classifiers were demonstrated to be generally superior to static ones, even with unsupervised adaptation. Transfer learning can also prove useful although the benefits of transfer learning remain unpredictable. Riemannian geometry-based methods have reached state-of-the-art performances on multiple BCI problems and deserve to be explored more thoroughly, along with tensor-based methods. Shrinkage linear discriminant analysis and random forests also appear particularly useful for small training samples settings. On the other hand, deep learning methods have not yet shown convincing improvement over state-of-the-art BCI methods. Significance: This paper provides a comprehensive overview of the modern classification algorithms used in EEG-based BCIs, presents the principles of these Review of Classification Algorithms for EEG-based BCI 2 methods and guidelines on when and how to use them. It also identifies a number of challenges to further advance EEG classification in BCI.

Published
2018
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136. Filter bank learning for signal classification

Author

Alain Rakotomamonjy, Maxime Sangnier, Jerome Gauthier, Laboratoire Sciences des Données et de la Décision (LS2D), Département Métrologie Instrumentation & Information (DM2I), Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Laboratoire d'Informatique, du Traitement de l'Information et des Systèmes (LITIS), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA), This work was partially supported by the Direction Générale de l'Armement (French Ministry of Defense) and by the French ANR (09-EMER-001 and 12-BS03-003)., Laboratoire d'analyse des données et d'intelligence des systèmes (LADIS), Laboratoire d'Intégration des Systèmes et des Technologies (LIST), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Laboratoire d'Intégration des Systèmes et des Technologies (LIST), Equipe Apprentissage (DocApp - LITIS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), and Normandie Université (NU)

Subjects
Optimization, Design, Support vector machine, Computer science, SVM, Pooling, Feature extraction, 02 engineering and technology, Overfitting, computer.software_genre, Machine learning, Filter bank, Scattering, Discriminative feature-extraction, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], 0202 electrical engineering, electronic engineering, information engineering, Kernel adaptive filter, Electrical and Electronic Engineering, Representation (mathematics), [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG], [STAT.AP]Statistics [stat]/Applications [stat.AP], Multiple kernel learning, business.industry, Kernel learning, 020206 networking & telecommunications, Signal classification, artificial intelligence, SUPPORT VECTOR MACHINES, Recognition, machine learning, classification, Control and Systems Engineering, Signal Processing, 020201 artificial intelligence & image processing, Computer Vision and Pattern Recognition, Artificial intelligence, Data mining, business, computer, Software
Abstract

This paper addresses the problem of feature extraction for signal classification. It proposes to build features by designing a data-driven filter bank and by pooling the time-frequency representation to provide time-invariant features. For this purpose, our work tackles the problem of jointly learning the filters of a filter bank with a support vector machine. It is shown that, in a restrictive case (but consistent to prevent overfitting), the problem boils down to a multiple kernel learning instance with infinitely many kernels. To solve such a problem, we build upon existing methods and propose an active constraint algorithm able to handle a non-convex combination of an infinite number of kernels. Numerical experiments on both a brain-computer interface dataset and a scene classification problem prove empirically the appeal of our method. Graphical abstractDisplay Omitted HighlightsWe propose a method of feature extraction, using a large-margin framework.We extend generalized multiple kernel learning to infinitely many kernels.We take a fresh look at learning convolutional features for signal classification.

Published
2015
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137. Concave losses for robust dictionary learning

Author

Alain Rakotomamonjy, Rafael Will M. de Araujo, Roberto Hirata, Equipe Apprentissage (DocApp - LITIS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Normandie Université (NU), Universidade de São Paulo (USP), Rakotomamonjy, Alain, Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Université Le Havre Normandie (ULH), and Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)

Subjects
FOS: Computer and information sciences, 0209 industrial biotechnology, Iterative method, Computer science, Computation, [SCCO.COMP]Cognitive science/Computer science, Initialization, Machine Learning (stat.ML), 02 engineering and technology, outlier detection, Machine learning, computer.software_genre, Machine Learning (cs.LG), 020901 industrial engineering & automation, Quadratic equation, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [SCCO.COMP] Cognitive science/Computer science, Robustness (computer science), Statistics - Machine Learning, 0202 electrical engineering, electronic engineering, information engineering, concave loss function, ComputingMilieux_MISCELLANEOUS, Concave function, business.industry, Computer Science - Learning, Robust dictionary learning, Outlier, 020201 artificial intelligence & image processing, Anomaly detection, Artificial intelligence, business, computer
Abstract

International audience; Traditional dictionary learning methods are based on quadratic convex loss function and thus are sensitive to outliers. In this paper, we propose a generic framework for robust dictionary learning based on concave losses. We provide results on composition of concave functions, notably regarding super-gradient computations, that are key for developing generic dictionary learning algorithms applicable to smooth and non-smooth losses. In order to improve identification of outliers, we introduce an initialization heuristic based on undercomplete dictionary learning. Experimental results using synthetic and real data demonstrate that our method is able to better detect outliers, is capable of generating better dictionaries, outperforming state-of-the-art methods such as K-SVD and LC-KSVD.

Published
2017

138. ℓp-norm multiple kernel learning with low-rank kernels

Author

Sukalpa Chanda and Alain Rakotomamonjy

Subjects
Mathematical optimization, Multiple kernel learning, Cognitive Neuroscience, Computer Science Applications, Artificial Intelligence, Variable kernel density estimation, Polynomial kernel, String kernel, Kernel embedding of distributions, Kernel (statistics), Radial basis function kernel, Tree kernel, Algorithm, Mathematics
Abstract

Kernel-based learning algorithms are well-known to poorly scale to large-scale applications. For such large tasks, a common solution is to use low-rank kernel approximation. Several algorithms and theoretical analyses have already been proposed in the literature, for low-rank Support Vector Machine or low-rank Kernel Ridge Regression but not for multiple kernel learning. The proposed method bridges this gap by addressing the problem of scaling @?"p-norm multiple kernel for large learning tasks using low-rank kernel approximations. Our contributions stand on proposing a novel optimization problem, which takes advantage of the low-rank kernel approximations and on introducing a proximal gradient algorithm for solving that optimization problem. We also provide partial theoretical results on the impact of the low-rank approximations over the kernel combination weights. Experimental evidences show that the proposed approach scales better than the SMO-MKL algorithm for tasks involving about several hundred thousands of examples. Experimental comparisons with interior point methods also prove the efficiency of the algorithm we propose.

Published
2014
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139. Greedy methods, randomization approaches and multi-arm bandit algorithms for efficient sparsity-constrained optimization

Author

Liva Ralaivola, Alain Rakotomamonjy, Sokol Koço, Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA), éQuipe AppRentissage et MultimediA [Marseille] (QARMA), Laboratoire d'informatique Fondamentale de Marseille (LIF), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), ANR-12-BS02-0004,GRETA,GREediness: Theory and Algorithms(2012), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Equipe Apprentissage (DocApp - LITIS), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Université Le Havre Normandie (ULH), éQuipe d'AppRentissage de MArseille (QARMA), Laboratoire d'Informatique et Systèmes (LIS), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU), and Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)

Subjects
FOS: Computer and information sciences, Computer Networks and Communications, Computer science, [SCCO.COMP]Cognitive science/Computer science, 02 engineering and technology, Machine Learning (cs.LG), Set (abstract data type), Frank–Wolfe algorithm, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, Orthogonal Matching Pursuit, Selection (genetic algorithm), Best arm identification, Index Terms—Sparsity, Constrained optimization, Frank- Wolfe algorithm, 020206 networking & telecommunications, Matching pursuit, Computer Science Applications, Computer Science - Learning, Identification (information), Frank-Wolfe algorithm, Key (cryptography), 020201 artificial intelligence & image processing, Algorithm design, Greedy methods, Algorithm, Sparsity, Software
Abstract

International audience; Several sparsity-constrained algorithms such as Orthogonal Matching Pursuit or the Frank-Wolfe algorithm with sparsity constraints work by iteratively selecting a novel atom to add to the current non-zero set of variables. This selection step is usually performed by computing the gradient and then by looking for the gradient component with maximal absolute entry. This step can be computationally expensive especially for large-scale and high-dimensional data. In this work, we aim at accelerating these sparsity-constrained optimization algorithms by exploiting the key observation that, for these algorithms to work, one only needs the coordinate of the gradient's top entry. Hence, we introduce algorithms based on greedy methods and randomization approaches that aim at cheaply estimating the gradient and its top entry. Another of our contribution is to cast the problem of finding the best gradient entry as a best arm identification in a multi-armed bandit problem. Owing to this novel insight, we are able to provide a bandit-based algorithm that directly estimates the top entry in a very efficient way. Theoretical observations stating that the resulting inexact Frank-Wolfe or Orthogonal Matching Pursuit algorithms act, with high probability, similarly to their exact versions are also given. We have carried out several experiments showing that the greedy deterministic and the bandit approaches we propose can achieve an acceleration of an order of magnitude while being as efficient as the exact gradient when used in algorithms such as OMP, Frank-Wolfe or CoSaMP.

Published
2016
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140. Wasserstein Discriminant Analysis

Author

Alain Rakotomamonjy, Rémi Flamary, Marco Cuturi, Nicolas Courty, Joseph Louis LAGRANGE (LAGRANGE), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Observatoire de la Côte d'Azur (OCA), Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Kyoto University [Kyoto], Environment observation with complex imagery (OBELIX), Université de Bretagne Sud (UBS)-SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE (IRISA-D5), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Equipe Apprentissage (DocApp - LITIS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Normandie Université (NU), Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Université de Rennes (UNIV-RENNES)-CentraleSupélec-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec, Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Université Le Havre Normandie (ULH), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Kyoto University, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, Iterative proportional fitting, Scale (ratio), Automatic differentiation, Computer science, Machine Learning (stat.ML), 010103 numerical & computational mathematics, 02 engineering and technology, Linear discriminant analysis, 01 natural sciences, Machine Learning (cs.LG), Linear map, Distribution (mathematics), [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Statistics - Machine Learning, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, 0101 mathematics, Algorithm, Software, MNIST database, Subspace topology
Abstract

Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Lin- ear Discriminant Analysis (LDA), WDA selects the projection matrix that maxi- mizes the ratio of two quantities: the dispersion of projected points coming from different classes, divided by the dispersion of projected points coming from the same class. To quantify dispersion, WDA uses regularized Wasserstein distances, rather than cross-variance measures which have been usually considered, notably in LDA. Thanks to the the underlying principles of optimal transport, WDA is able to capture both global (at distribution scale) and local (at samples scale) interac- tions between classes. Regularized Wasserstein distances can be computed using the Sinkhorn matrix scaling algorithm; We show that the optimization of WDA can be tackled using automatic differentiation of Sinkhorn iterations. Numerical experiments show promising results both in terms of prediction and visualization on toy examples and real life datasets such as MNIST and on deep features ob- tained from a subset of the Caltech dataset.

Published
2016
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141. Importance sampling strategy for non-convex randomized block-coordinate descent

Author

Alain Rakotomamonjy, Gilles Gasso, Rémi Flamary, Joseph Louis LAGRANGE (LAGRANGE), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Observatoire de la Côte d'Azur (OCA), Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Equipe Apprentissage (DocApp - LITIS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Normandie Université (NU)

Subjects
FOS: Computer and information sciences, Optimization problem, Computer science, Sampling (statistics), Approximation algorithm, Machine Learning (cs.LG), Computer Science - Learning, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Optimization and Control (math.OC), FOS: Mathematics, Probability distribution, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Coordinate descent, Algorithm, Mathematics - Optimization and Control, Importance sampling, Block (data storage), Curse of dimensionality
Abstract

International audience; As the number of samples and dimensionality of optimization problems related to statistics an machine learning explode, block coordinate descent algorithms have gained popularity since they reduce the original problem to several smaller ones. Coordinates to be optimized are usually selected randomly according to a given probability distribution. We introduce an importance sampling strategy that helps randomized coordinate descent algorithms to focus on blocks that are still far from convergence. The framework applies to problems composed of the sum of two possibly non-convex terms, one being separable and non-smooth. We have compared our algorithm to a full gradient proximal approach as well as to a randomized block coordinate algorithm that considers uniform sampling and cyclic block coordinate descent. Experimental evidences show the clear benefit of using an importance sampling strategy.

Published
2016
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142. Recovering Sparse Signals With a Certain Family of Nonconvex Penalties and DC Programming

Author

Stéphane Canu, Gilles Gasso, and Alain Rakotomamonjy

Subjects
Mathematical optimization, Optimization problem, Iterative method, MathematicsofComputing_NUMERICALANALYSIS, Feature selection, Sparse approximation, Statistics::Machine Learning, Basis pursuit denoising, Lasso (statistics), Signal Processing, Electrical and Electronic Engineering, Convex function, Mathematics, Sparse matrix
Abstract

This paper considers the problem of recovering a sparse signal representation according to a signal dictionary. This problem could be formalized as a penalized least-squares problem in which sparsity is usually induced by a lscr1-norm penalty on the coefficients. Such an approach known as the Lasso or Basis Pursuit Denoising has been shown to perform reasonably well in some situations. However, it was also proved that nonconvex penalties like the pseudo lscrq-norm with q < 1 or smoothly clipped absolute deviation (SCAD) penalty are able to recover sparsity in a more efficient way than the Lasso. Several algorithms have been proposed for solving the resulting nonconvex least-squares problem. This paper proposes a generic algorithm to address such a sparsity recovery problem for some class of nonconvex penalties. Our main contribution is that the proposed methodology is based on an iterative algorithm which solves at each iteration a convex weighted Lasso problem. It relies on the family of nonconvex penalties which can be decomposed as a difference of convex functions (DC). This allows us to apply DC programming which is a generic and principled way for solving nonsmooth and nonconvex optimization problem. We also show that several algorithms in the literature dealing with nonconvex penalties are particular instances of our algorithm. Experimental results demonstrate the effectiveness of the proposed generic framework compared to existing algorithms, including iterative reweighted least-squares methods.

Published
2009
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143. Early frame-based detection of acoustic scenes

Author

Jerome Gauthier, Alain Rakotomamonjy, Maxime Sangnier, Laboratoire Sciences des Données et de la Décision (LS2D), Département Métrologie Instrumentation & Information (DM2I), Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Equipe Apprentissage (DocApp - LITIS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Université Le Havre Normandie (ULH), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA), This work was partially funded by the Direction Générale de l’Armement, French Ministry of Defense., Institut Mines-Télécom [Paris] (IMT)-Télécom Paris, Laboratoire d'analyse des données et d'intelligence des systèmes (LADIS), Laboratoire d'Intégration des Systèmes et des Technologies (LIST), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Laboratoire d'Intégration des Systèmes et des Technologies (LIST), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), and Normandie Université (NU)

Subjects
Soundscape, Similarity (geometry), audio signal processing, Computer science, Reliability (computer networking), decision function, scene analysis, 02 engineering and technology, 010501 environmental sciences, Space (commercial competition), Machine learning, computer.software_genre, 01 natural sciences, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], acoustic scenes, temporal sequences, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Complete information, 0202 electrical engineering, electronic engineering, information engineering, Decision-making, signal processing, 0105 earth and related environmental sciences, Signal processing, landmarking space, continuous audio stream, business.industry, acoustic signal processing, scene occurrence, Detectors, Early detection, Acoustics, frame-based detection, Reliability, artificial intelligence, event detection, machine learning, classification, [INFO.INFO-IR]Computer Science [cs]/Information Retrieval [cs.IR], Scalability, [INFO.INFO-SD]Computer Science [cs]/Sound [cs.SD], 020201 artificial intelligence & image processing, Artificial intelligence, business, computer
Abstract

International audience; Let us consider a specific acoustic scene appearing in a continuous audio stream recorded while making a trip a in city. In this work, we aim at detecting at the earliest opportunity the several occurrences of this scene. The objective in early detection is then to build a decision function that is able to go off as soon as possible from the onset of a scene occurrence. This implies making a decision with an incomplete information. This paper proposes a novel framework in this area that i) can guarantee the decision made with a partial observation to be the same as the one with the full observation; ii) incorporates in a non-confusing manner the lack of knowledge about the minimal amount of information needed to make a decision. The proposed detector is based on mapping the temporal sequences to a landmarking space thanks to appropriately designed similarity functions. As a by-product, the built framework benefits from a scalable learning problem. A preliminary experimental study provides compelling results on a soundscape dataset.

Published
2015
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144. More efficient sparsity-inducing algorithms using inexact gradient

Author

Liva Ralaivola, Sokol Koço, Alain Rakotomamonjy, Equipe Apprentissage (DocApp - LITIS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Université Le Havre Normandie (ULH), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA), Laboratoire d'informatique Fondamentale de Marseille - UMR 6166 (LIF), and Université de la Méditerranée - Aix-Marseille 2-Université de Provence - Aix-Marseille 1-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mathematical optimization, Signal processing, Linear programming, Matching pursuit algorithms, [SCCO.COMP]Cognitive science/Computer science, 020206 networking & telecommunications, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Matching pursuit, Set (abstract data type), 010201 computation theory & mathematics, 0202 electrical engineering, electronic engineering, information engineering, Signal processing algorithms, Algorithm, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

In this paper, we tackle the problem of adapting a set of classic sparsity-inducing methods to cases when the gradient of the objective function is either difficult or very expensive to compute. Our contributions are two-fold: first, we propose methodologies for computing fair estimations of inexact gradients, second we propose novel stopping criteria for computing these gradients. For each contribution we provide theoretical backgrounds and justifications. In the experimental part, we study the impact of the proposed methods for two well-known algorithms, Frank-Wolfe and Orthogonal Matching Pursuit. Results on toy datasets show that inexact gradients can be as useful as exact ones provided the appropriate stopping criterion is used.

Published
2015
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145. DC Proximal Newton for Nonconvex Optimization Problems

Author

Alain Rakotomamonjy, Rémi Flamary, and Gilles Gasso

Subjects
Mathematical optimization, Line search, Optimization problem, Computer Networks and Communications, MathematicsofComputing_NUMERICALANALYSIS, Approximation algorithm, 020206 networking & telecommunications, 02 engineering and technology, Function (mathematics), Stationary point, Computer Science Applications, Artificial Intelligence, Iterated function, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Algorithm design, Descent direction, Software, Mathematics
Abstract

We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are nonconvex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal Newton algorithm that is able to deal with such a situation. The algorithm consists in obtaining a descent direction from an approximation of the loss function and then in performing a line search to ensure a sufficient descent. A theoretical analysis is provided showing that the iterates of the proposed algorithm admit as limit points stationary points of the DC objective function. Numerical experiments show that our approach is more efficient than the current state of the art for a problem with a convex loss function and a nonconvex regularizer. We have also illustrated the benefit of our algorithm in high-dimensional transductive learning problem where both the loss function and regularizers are nonconvex.

Published
2015

146. Prévisions de concentrations d'ozone. Comparaison de différentes méthodes statistiques de type « boîte noire »

Author

Patrick Vannoorenberghe, Alain Rakotomamonjy, Stéphane Canu, and Komi Gasso

Subjects
Artificial neural network, Statistical learning, Decision tree, Industrial and Manufacturing Engineering, Regression, Computer Science Applications, Support vector machine, Geography, Control and Systems Engineering, Black box, Statistics, Electrical and Electronic Engineering, Maxima, Air quality index, Cartography
Abstract

The paper investigates the application of black box modelling to the prediction of the daily maxima of ground-ozone level. The main interest of these modelling approaches is their genericity as they are solely based on the available data provided by the Associations of air quality monitoring and they can be transposed from a geographical area to another one. The paper realises a comparative study of four statistical learning approaches, the decisions trees (, the neural networks, the least-angle regression and the support vector regression, to the ozone level prediction. Before concluding, the obtained results and their comments are presented.

Published
2005
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147. Non-parametric regression with wavelet kernels

Author

Xavier Mary, Alain Rakotomamonjy, and Stéphane Canu

Subjects
Mathematical optimization, Representer theorem, MathematicsofComputing_NUMERICALANALYSIS, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Management Science and Operations Research, General Business, Management and Accounting, Kernel principal component analysis, Nonparametric regression, Wavelet, Kernel embedding of distributions, Variable kernel density estimation, Modeling and Simulation, Kernel (statistics), Kernel regression, Algorithm, Mathematics
Abstract

This paper introduces a method to construct a reproducing wavelet kernel Hilbert spaces for non-parametric regression estimation when the sampling points are not equally spaced. Another objective is to make high-dimensional wavelet estimation problems tractable. It then provides a theoretical foundation to build reproducing kernel from operators and a practical technique to obtain reproducing kernel Hilbert spaces spanned by a set of wavelets. A multiscale approximation technique that aims at taking advantage of the multiresolution structure of wavelets is also described. Examples on toy regression and a real-world problem illustrate the effectiveness of these wavelet kernels. Copyright © 2005 John Wiley & Sons, Ltd.

Published
2005
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148. Optimal transport for Domain adaptation

Author

Alain Rakotomamonjy, Devis Tuia, Nicolas Courty, Rémi Flamary, Environment observation with complex imagery (OBELIX), Université de Bretagne Sud (UBS)-SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE (IRISA-D5), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Université de Rennes (UNIV-RENNES)-CentraleSupélec-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-CentraleSupélec, Observatoire de la Côte d'Azur (OCA), Centre National de la Recherche Scientifique (CNRS), Joseph Louis LAGRANGE (LAGRANGE), Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Laboratoire des Systèmes d'Information Géographique [Lausanne] (LASIG), Ecole Polytechnique Fédérale de Lausanne (EPFL), COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), University of Zürich [Zürich] (UZH), Equipe Apprentissage (DocApp - LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Université Le Havre Normandie (ULH), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Universität Zürich [Zürich] (UZH), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Universität Zürich [Zürich] = University of Zurich (UZH), University of Zurich, and SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE (IRISA-D5)

Subjects
FOS: Computer and information sciences, 1707 Computer Vision and Pattern Recognition, Unsupervised domain adaptation, Computer science, Index Terms—Unsupervised Domain Adaptation, Feature extraction, 0211 other engineering and technologies, [SCCO.COMP]Cognitive science/Computer science, 1702 Artificial Intelligence, 02 engineering and technology, transfer learning, Machine learning, computer.software_genre, External Data Representation, Machine Learning (cs.LG), visual adaptation, 2604 Applied Mathematics, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, 910 Geography & travel, Invariant (mathematics), ComputingMilieux_MISCELLANEOUS, 021101 geological & geomatics engineering, business.industry, Applied Mathematics, Deep learning, Pattern recognition, 1712 Software, Computer Science - Learning, 10122 Institute of Geography, classification, optimal transport, Computational Theory and Mathematics, Data analysis, Probability distribution, 020201 artificial intelligence & image processing, Computer Vision and Pattern Recognition, Artificial intelligence, Transfer of learning, business, computer, Classifier (UML), Software, 1703 Computational Theory and Mathematics
Abstract

International audience; Domain adaptation is one of the most chal- lenging tasks of modern data analytics. If the adapta- tion is done correctly, models built on a specific data representation become more robust when confronted to data depicting the same classes, but described by another observation system. Among the many strategies proposed, finding domain-invariant representations has shown excel- lent properties, in particular since it allows to train a unique classifier effective in all domains. In this paper, we propose a regularized unsupervised optimal transportation model to perform the alignment of the representations in the source and target domains. We learn a transportation plan matching both PDFs, which constrains labeled samples of the same class in the source domain to remain close during transport. This way, we exploit at the same time the labeled samples in the source and the distributions observed in both domains. Experiments on toy and challenging real visual adaptation examples show the interest of the method, that consistently outperforms state of the art approaches. In addition, numerical experiments show that our approach leads to better performances on domain invariant deep learning features and can be easily adapted to the semi- supervised case where few labeled samples are available in the target domain.

Published
2014
Full Text
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149. SVM with feature selection and smooth prediction in images: Application to CAD of prostate cancer

Author

Alain Rakotomamonjy, Rémi Flamary, Emilie Niaf, Carole Lartizien, Olivier Rouvière, Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé ( CREATIS ), Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Université de Lyon-Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Hospices Civils de Lyon ( HCL ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Centre National de la Recherche Scientifique ( CNRS ), Application des ultrasons à la thérapie ( LabTAU ), Centre Léon Bérard [Lyon]-Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Université de Lyon-Institut National de la Santé et de la Recherche Médicale ( INSERM ), A*Star-Nus, Clinical Imaging Research Centre, Joseph Louis LAGRANGE ( LAGRANGE ), Université Nice Sophia Antipolis ( UNS ), Université Côte d'Azur ( UCA ) -Université Côte d'Azur ( UCA ) -Observatoire de la Côte d'Azur, Université Côte d'Azur ( UCA ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes ( LITIS ), Université Le Havre Normandie ( ULH ), Normandie Université ( NU ) -Normandie Université ( NU ) -Université de Rouen Normandie ( UNIROUEN ), Normandie Université ( NU ) -Institut national des sciences appliquées Rouen Normandie ( INSA Rouen Normandie ), Normandie Université ( NU ), 2 - Images et Modèles, Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Hospices Civils de Lyon ( HCL ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Claude Bernard Lyon 1 ( UCBL ), Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé (CREATIS), Université Jean Monnet [Saint-Étienne] (UJM)-Hospices Civils de Lyon (HCL)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM), Application des ultrasons à la thérapie (LabTAU), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre Léon Bérard [Lyon]-Institut National de la Santé et de la Recherche Médicale (INSERM), Joseph Louis LAGRANGE (LAGRANGE), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU), Images et Modèles, and Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Jean Monnet [Saint-Étienne] (UJM)-Hospices Civils de Lyon (HCL)-Institut National des Sciences Appliquées de Lyon (INSA Lyon)

Subjects
Optimization problem, Computer science, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Feature selection, [ SPI.SIGNAL ] Engineering Sciences [physics]/Signal and Image processing, computer.software_genre, Machine learning, Malignancy, Regularization (mathematics), Prostate cancer, Voxel, medicine, [ SDV.IB.IMA ] Life Sciences [q-bio]/Bioengineering/Imaging, medicine.diagnostic_test, Structured support vector machine, business.industry, Magnetic resonance imaging, Pattern recognition, medicine.disease, Linear discriminant analysis, Support vector machine, ComputingMethodologies_PATTERNRECOGNITION, Norm (mathematics), Artificial intelligence, business, computer, Classifier (UML), [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract

International audience; We propose a new computer-aided detection scheme for prostate cancer screening on multiparametric magnetic resonance (mp-MR) images. Based on an annotated training database of mp-MR images from thirty patients, we train a novel support vector machine (SVM)-inspired classifier which simultaneously learns an optimal linear discriminant and a subset of predictor variables (or features) that are most relevant to the classification task, while promoting spatial smoothness of the malignancy prediction maps. The approach uses a ℓ1-norm in the regularization term of the optimization problem that rewards sparsity. Spatial smoothness is promoted via an additional cost term that encodes the spatial neighborhood of the voxels, to avoid noisy prediction maps. Experimental comparisons of the proposed ℓ1-Smooth SVM scheme to the regular ℓ2-SVM scheme demonstrate a clear visual and numerical gain on our clinical dataset.

Published
2014
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150. Learning Constrained Task Similarities in Graph-Regularized Multi-Task Learning

Author

Gilles Gasso, Multi-Task Learning Rémi Flamary, and Alain Rakotomamonjy

Subjects
Theoretical computer science, Similarity (geometry), Computational complexity theory, Generalization, Multi-task learning, Context (language use), Logical matrix, Adjacency matrix, Bilevel optimization, Mathematics
Abstract

Remi Flamary Laboratoire Lagrange, Observatoire de la Cote d’Azur, Universite de Nice Sophia-AntipolisAlain Rakotomamonjy LITIS, Universite de RouenGilles Gasso LITIS, INSA de Rouen5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.2 Similarity Based Multi-Task Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065.2.1 Multi-Task Learning Framework . . . . . . . . . . . . . . . . . . . . . . . . 106 5.2.2 Similarity-Based Regularization . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.2.3 Solving the Multi-Task Learning Problem . . . . . . . . . . . . . . 1085.3 Non-Convex Proximal Algorithm for Learning Similarities . . . . . 110 5.3.1 Bilevel Optimization Framework . . . . . . . . . . . . . . . . . . . . . . . . 110 5.3.2 Gradient Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.3.3 Constraints on P and λt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.3.4 Computational Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1145.4 Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.4.1 Toy Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.4.2 Real-World Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.4.2.1 Experimental Set-Up . . . . . . . . . . . . . . . . . . . . . . . 119 5.4.2.2 School Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.4.2.3 Brain Computer Interface Dataset . . . . . . . . 121 5.4.2.4 OCR Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127VectorThis chapter addresses the problem of learning constrained task relatedness in a graph-regularized multi-task learning framework. In such a context, the weighted adjacency matrix of a graph encodes the knowledge on task similarities and each entry of this matrix can be interpreted as a hyperparameter of the learning problem. This task relation matrix is learned via a bilevel optimization procedure where the outer level optimizes a proxy of the generalization errors over all tasks with respect to the similarity matrix and the inner level estimates the parameters of the tasks knowing this similarity matrix. Constraints on task similarities are also taken into account in this optimization framework and they allow the task similarity matrix to be more interpretable, for instance, by imposing a sparse similarity matrix. Since the global problem is non-convex, we propose a non-convex proximal algorithm that provably converges to a stationary point of the problem. Empirical evidence illustrates the approach is competitive compared to existing methods that also learn task relation and exhibits an enhanced interpretability of the learned task similarity matrix.

Published
2014
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