- Online Dictionary Adaptation (Sparse Learning) -


Nonlinear adaptive filtering has been extensively studied in the literature, using for example Volterra filters or Neural Networks. Recently, kernel methods have been offering an interesting alternative since they provide a simple extension of linear algorithms to the nonlinear case. The main drawback of online system identification with kernel methods is that the filter complexity increases with time, a limitation resulting from the representer theorem which states that all past input vectors (i.e., training samples) are required. To overcome this drawback, a particular subset of these input vectors (called dictionary) must be selected to ensure complexity control and good performance. See  page Online Learning and Nonlinear Adaptive Filtering for more details.

Prior to our work, all authors considered that, after being introduced into the dictionary, elements stay unchanged even if, due to nonstationarity, they become useless to predict the system output. Our work presents an adaptation scheme of dictionary elements, which are considered in our framework as adjustable model parameters. To this end, we derive several algorithms, such as a gradient-based method under collinearity constraints. By adapting the dictionary elements, we ensure a better tracking performance, as confirmed by experiments where complexity reduction and a decrease of the instantaneous quadratic error are observed.

Selected Publications

C. Saidé, R. Lengellé, P. Honeine, C. Richard, and R. Achkar

Nonlinear Adaptive Filtering using Kernel-based Algorithms with Dictionary Adaptation

International Journal of Adaptive Control and Signal Processing

29 (11), 1391-1410, Nov. 2015

C. Saidé, R. Lengellé, P. Honeine, and R. Achkar

Online kernel adaptive algorithms with dictionary adaptation for MIMO models

IEEE Signal Processing Letters

20 (5), 535-538, May 2013

C. Saidé, R. Lengellé, P. Honeine, C. Richard, and R. Achkar

Dictionary Adaptation for Online Prediction of Time Series Data with Kernels

Proc. IEEE workshop on Statistical Signal Processing (SSP)

Ann Arbor, Michigan, USA, pp. 604-607, 5-8 Aug. 2012


C. Saidé, P. Honeine, R. Lengellé, C. Richard, and R. Achkar

Adaptation en ligne d'un dictionnaire pour les méthodes à noyaux

Actes du 24-ème Colloque GRETSI sur

le Traitement du Signal et des Images

Brest, France, Sept. 2013


Chafic Saïdé

(PhD student)

Régis Lengellé

(Université de technologie de Troyes)

Roger Achkar 

(American University of Science & Technology, Lebanon)

Cédric Richard

(Université de Nice)


Adaptive filtering, nonlinear system identification, machine learning, sparse representation, adaptive dictionary learning

Related Works

see Online Learning and Nonlinear Adaptive Filtering

Online Dictionary Adaptation (Sparse Learning)