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Séminaire Images Optimisation et Probabilités

Responsable : Camille Male

  • Le 30 mars 2023 à 11:00
  • Salle de Conférences
    Simon Vary
    Extensions of principal component analysis: limited data, sparse corruptions, and efficient computation
    Principal component analysis (PCA) is a fundamental tool used for the analysis of datasets with widespread applications across machine learning, engineering, and imaging. The first part of the talk is dedicated to solving Robust PCA from subsampled measurements, which is the inverse problem posed over the set that is the additive combination of the low-rank and the sparse set. Here we develop guarantees using the restricted isometry property that show that rank-r plus sparsity-s matrices can be recovered by computationally tractable methods from p=O(r(m+n-r)+s)log(mn/s) linear measurements. The second part of the talk is focused on finding an efficient way to perform large-scale optimization constrained to the set of orthogonal matrices used in PCA and for training of neural networks. We propose the landing method, which does not enforce the orthogonality exactly in every iteration, instead, it controls the distance to the constraint using computationally inexpensive matrix-vector products and enforces the exact orthogonality only in the limit. We show the practical efficiency of the proposed methods on video separation, direct exoplanet detection, online PCA, and for robust training of neural networks.
  • Le 13 avril 2023 à 11:00
  • Salle de Conférences
    Nicolas Nadisic
    Beyond separability in nonnegative matrix factorization
    Nonnegative matrix factorization (NMF) is a commonly used low-rank model for identifying latent features in nonnegative data. It became a standard tool in applications such as blind source separation, recommender systems, topic modeling, or hyperspectral unmixing. Essentially, NMF consists in finding a few meaningful features such that the data points can be approximated as linear combinations of those features. NMF is generally a difficult problem to solve, since it is both NP-hard and ill-posed (meaning there is no unique solution). However, under the separability assumption, it becomes tractable and well-posed. The separability assumption states that for every feature there is at least one pure data point, that is a data point composed solely of that feature. This is known as the 'pure-pixel' assumption in hyperspectral unmixing.In this presentation I will first provide an overview of separable NMF, that is the family of NMF models and algorithms leveraging the separability assumption. I will then detail recent contributions, notably (i) an extension of this model with sparsity constraints that brings interesting identifiability results; and (ii) new algorithms using the fact that, when the separability assumption holds, then there are often more than one pure data point. I will illustrate the models and methods presented with applications in hyperspectral unmixing.
  • Le 27 avril 2023 à 11:00
  • Salle de Conférences
    Guillaume Lauga (ENS Lyon)
    À préciser.
    À préciser.
  • Le 11 mai 2023 à 11:00
  • Salle de Conférences
    Florentin Coeurdoux (Toulouse INP)
    À préciser.
    À préciser.
  • Le 28 septembre 2023 à 11:00
  • Salle de Conférences
    Julio Backhoff
    À préciser
    À préciser

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