Kernel PCA for feature extraction and de-noising in nonlinear regression

Roman Rosipal, Mark Girolami, Leonard J. Trejo, Andrzej Cichocki

Research output: Contribution to journalArticlepeer-review

157 Citations (Scopus)


In this paper, we propose the application of the Kernel Principal Component Analysis (PCA) technique for feature selection in a high-dimensional feature space, where input variables are mapped by a Gaussian kernel. The extracted features are employed in the regression problems of chaotic Mackey-Glass time-series prediction in a noisy environment and estimating human signal detection performance from brain event-related potentials elicited by task relevant signals. We compared results obtained using either Kernel PCA or linear PCA as data preprocessing steps. On the human signal detection task, we report the superiority of Kernel PCA feature extraction over linear PCA. Similar to linear PCA, we demonstrate de-noising of the original data by the appropriate selection of various nonlinear principal components. The theoretical relation and experimental comparison of Kernel Principal Components Regression, Kernel Ridge Regression and ∈-insensitive Support Vector Regression is also provided.

Original languageEnglish
Pages (from-to)231-243
Number of pages13
JournalNeural Computing and Applications
Issue number3
Publication statusPublished - 2001
Externally publishedYes


  • De-noising
  • Feature extraction
  • Human performance monitoring
  • Kernel functions
  • Nonlinear regression
  • Principal components


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