Abstract
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 non-linear principal components. The theoretical relation and experimental comparison of Kernel Principal Components Regression, Kernel Ridge Regression and $\epsilon$-insensitive Support Vector Regression is also provided.
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