2013/02/26 by Sylvain Chevallier, Quentin Barthélemy, Jamal Atif · 3 citations
Computer Science · Mathematics · #Artificial intelligence #Autoencoder #Blind Source Separation Techniques #Brain–computer interface #Cluster analysis #Computer science #Deep learning #Electroencephalography #Face and Expression Recognition #Grassmannian #Machine learning #Mathematics #Multivariate statistics #Pattern recognition (psychology) #Perspective (graphical) #Rough Sets and Fuzzy Logic #Set (abstract data type) #Subspace topology #acm:28C15 #acm:42C15 #acm:53A20 #acm:53A45 #cs.LG #msc:28C15 #msc:42C15 #msc:53A20 #msc:53A45 #stat.ML
paper · pdf · doi:10.1109/icassp.2014.6854993
arxiv created 2013/02/26 · openalex publication_date 2014/05/01 · arxiv updated 2021/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Overcomplete representations and dictionary learning algorithms are attracting a growing interest in the machine learning community. This paper addresses the emerging problem of comparing multivariate overcomplete dictionaries. Despite a recurrent need to rely on a distance for learning or assessing multivariate overcomplete dictionaries, no metrics in their underlying spaces have yet been proposed. Henceforth we propose to study overcomplete representations from the perspective of matrix manifolds. We consider distances between multivariate dictionaries as distances between their spans which reveal to be elements of a Grassmannian manifold. We introduce set-metrics defined on Grassmannian spaces and study their properties both theoretically and numerically. Thanks to the introduced metrics, experimental convergences of dictionary learning algorithms are assessed on synthetic datasets. Set-metrics are embedded in a clustering algorithm for a qualitative analysis of real EEG signals for Brain-Computer Interfaces (BCI). The obtained clusters of subjects are associated with subject performances. This is a major methodological advance to understand the BCI-inefficiency phenomenon and to predict the ability of a user to interact with a BCI.