Subspace-based techniques and applications - Teixeira, Ana (2011)
This work focuses on the study of linear and non-linear subspace projective techniques with two intents: noise elimination and feature extraction. The conducted study is based on the SSA, and Kernel PCA algorithms. Several approaches to optimize the algorithms are addressed along with a description of those algorithms in a distinct approach from the one made in the literature. All methods presented here follow a consistent algebraic formulation to manipulate the data. The subspace model is formed using the elements from the eigendecomposition of kernel or correlation/covariance matrices computed on multidimensional data sets. The complexity of non-linear subspace techniques is exploited, namely the preimage problem and the kernel matrix dimensionality. Different pre-image algorithms are presented together with alternative proposals to optimize them. In this work some approximations to the kernel matrix based on its low rank approximation are discussed and the Greedy KPCA algorithm is introduced. Throughout this thesis, the algorithms are applied to artificial signals in order to study the influence of the several parameters in their performance. Furthermore, the exploitation of these techniques is extended to artefact removal in univariate biomedical time series, namely, EEG signals.