title: Orthogonal Procrustes Analysis for Dictionary Learning in Sparse Linear Representation.
abstract: In the sparse representation model, the design of overcomplete dictionaries plays a key role for the effectiveness and applicability in different domains. Recent research has produced several dictionary learning approaches, being proven that dictionaries learnt by data examples significantly outperform structured ones, e.g. wavelet transforms. In this context, learning consists in adapting the dictionary atoms to a set of training signals in order to promote a sparse representation that minimizes the reconstruction error. Finding the best fitting dictionary remains a very difficult task, leaving the question still open. A well-established heuristic method for tackling this problem is an iterative alternating scheme, adopted for instance in the well-known K-SVD algorithm. Essentially, it consists in repeating two stages; the former promotes sparse coding of the training set and the latter adapts the dictionary to reduce the error. In this paper we present R-SVD, a new method that, while maintaining the alternating scheme, adopts the Orthogonal Procrustes analysis to update the dictionary atoms suitably arranged into groups. Comparative experiments on synthetic data prove the effectiveness of R-SVD with respect to well known dictionary learning algorithms such as K-SVD, ILS-DLA and the online method OSDL. Moreover, experiments on natural data such as ECG compression, EEG sparse representation, and image modeling confirm R-SVD's robustness and wide applicability.
authors.affiliation: Department of Computer Science, University of Milan, Via Comelico 39, 20135 Milan, Italy.
authors.forename: Giuliano
authors.initials: G
authors.lastname: Grossi
authors.affiliation: Department of Computer Science, University of Milan, Via Comelico 39, 20135 Milan, Italy.
authors.forename: Raffaella
authors.identifier: http://orcid.org/0000-0002-8534-4413
authors.initials: R
authors.lastname: Lanzarotti
authors.affiliation: Department of Applied Mathematics and Sciences, Khalifa University, Al Saada St., PO Box 127788, Abu Dhabi, United Arab Emirates.
authors.forename: Jianyi
authors.initials: J
authors.lastname: Lin
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D044962:Data Compression; D004014:Dictionaries as Topic; D004562:Electrocardiography / Q000706:statistics & numerical data; D004569:Electroencephalography / Q000706:statistics & numerical data; D006801:Humans; D007091:Image Processing, Computer-Assisted; D000069550:Machine Learning / Q000706:statistics & numerical data*; D010363:Pattern Recognition, Automated; D012815:Signal Processing, Computer-Assisted