DocumentCode :
180210
Title :
Subspace metrics for multivariate dictionaries and application to EEG
Author :
Chevallier, Sylvain ; Barthelemy, Quentin ; Atif, Jamal
fYear :
2014
fDate :
4-9 May 2014
Firstpage :
7178
Lastpage :
7182
Abstract :
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.
Keywords :
brain-computer interfaces; dictionaries; electroencephalography; learning (artificial intelligence); matrix algebra; medical signal processing; pattern clustering; BCI-inefficiency phenomenon; EEG; Grassmannian manifold; Grassmannian spaces; brain-computer interfaces; clustering algorithm; dictionary learning algorithm; machine learning community; matrix manifolds; multivariate overcomplete dictionaries; overcomplete representation; set-metrics; subspace metrics; synthetic datasets; Atomic measurements; Clustering algorithms; Dictionaries; Manifolds; Signal processing; Signal processing algorithms; Dictionary Learning; Frames; Grass-mannian Manifolds; Metrics; Multivariate Dataset;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2014 IEEE International Conference on
Conference_Location :
Florence
Type :
conf
DOI :
10.1109/ICASSP.2014.6854993
Filename :
6854993
Link To Document :
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