Kernel nonnegative matrix factorization for spectral EEG feature extraction

Hyekyoung Lee, Andrzej Cichocki, Seungjin Choi

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


Nonnegative matrix factorization (NMF) seeks a decomposition of a nonnegative matrix X≥0 into a product of two nonnegative factor matrices U≥0 and V≥0, such that a discrepancy between X and UV⊤ is minimized. Assuming U = XW in the decomposition (for W≥0), kernel NMF (KNMF) is easily derived in the framework of least squares optimization. In this paper we make use of KNMF to extract discriminative spectral features from the time-frequency representation of electroencephalogram (EEG) data, which is an important task in EEG classification. Especially when KNMF with linear kernel is used, spectral features are easily computed by a matrix multiplication, while in the standard NMF multiplicative update should be performed repeatedly with the other factor matrix fixed, or the pseudo-inverse of a matrix is required. Moreover in KNMF with linear kernel, one can easily perform feature selection or data selection, because of its sparsity nature. Experiments on two EEG datasets in brain computer interface (BCI) competition indicate the useful behavior of our proposed methods.

Original languageEnglish
Pages (from-to)3182-3190
Number of pages9
Issue number13-15
Publication statusPublished - Aug 2009
Externally publishedYes


  • EEG classification
  • Feature extraction
  • Kernel methods
  • Multiplicative updates
  • Nonnegative matrix factorization


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