- Online Learning and Nonlinear Adaptive Filtering -


During the last few years, kernel methods have been very useful to solve nonlinear identification problems. The main drawback of these methods resides in the fact that the number of elements of the kernel development, i.e., the size of the dictionary, increases with the number of input data, making the solution not suitable for online problems especially time series applications, adaptive filtering and online identification.

Our main contributions are described in the following, from newer to older, with some selected publications.

Framework for Online Sparsification Criteria (2015-2016):

We provide a framework that englobes the state-of-the-art online sparsification criteria, such as the distance, linear approximation, coherence, Babel (or cumulative coherence) and entropy. Within this framework, we derive many theoretical results, including bounds on the approximation errors and eigenvalues associated to the dictionary.

P. Honeine

Approximation errors of online sparsification criteria

IEEE Trans. on Signal Processing

63 (17): 4700-4709, Sept. 2015

P. Honeine

Analyzing sparse dictionaries for online learning with kernels

IEEE Trans. on Signal Processing

63 (23), 6343-6353, Dec. 2015

Dictionary online adaptation (2013-2015):

See page Online Dictionary Adaptation (Sparse Learning) for details...

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

Unsupervised Nonlinear Online Learning (2012):

This is the first time that online sparsification, initially derived for nonlinear adaptive filtering, is extended to unsupervised learning.

P. Honeine

Online kernel principal component analysis: a reduced-order model.

IEEE Transactions on Pattern Analysis and Machine Intelligence

34 (9), 1814-1826, Sep. 2012

Online Detection with Adaptive One-class Learning (2011-2014):

See page .... for details...

Adaptive Learning for Wireless Sensor Networks (2008-2011):

See page Collaborative Learning in (Wireless) Sensor Networks for details...

Adaptive Learning with Nonlinear Adaptive Algorithms (2005-2009):

Here, we proposed the coherence criterion for online sparsification, and developed the corresponding algorithms (Kernel Recursive Least Squares, Kernel (Normalized) Least Mean Squares and Kernel Affine Projection)

C. Richard, J. C. M. Bermudez, and P. Honeine
Online prediction of time series data with kernels

IEEE Trans. on Signal Processing
57(3):1058-1067, 2009

P. Honeine, C. Richard, J. C. M. Bermudez, and H. Snoussi
Distributed prediction of time series data with kernels and adaptive filtering techniques in sensor networks

Proc. of 42nd Annual ASILOMAR Conference on Signals, Systems & Computers
Pacific Grove (CA), USA, 26-29 Oct. 2008
(invited paper)

P. Honeine,

Méthodes à noyau pour l'analyse et la décision en environnement non-stationnaire

PhD Thesis, Ecole doctoral UTT Troyes

France, 2007

P. Honeine, C. Richard, and J. C. M. Bermudez
On-line nonlinear sparse approximation of functions

Proc. of IEEE International Symposium on Information Theory (ISIT)
Nice, France, 24-29 June 2007

Research Project (part of my PhD studies)


José Carlos M. Bermudez                                      (FUSC, Brazil)

Cédric Richard                                                  (ICD/LM2S, UTT)


Part-Financed by an ANRT’s CIFRE grant and the ANR grant KernSig


Adaptive filtering, nonlinear system identification, machine learning, sparse representation, online learning

Online Learning and Nonlinear Adaptive Filtering