In Search of Non-Gaussian Components of a High-Dimensional Distribution

Finding non-Gaussian components of high-dimensional data is an important preprocessing step for effcient information processing. This article proposes a new linear method to identify the ``non-Gaussian subspace´´ within a very general semi-parametric framework. Our proposed method, called NGCA (Non-Gaussian Component Analysis), is essentially based on a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector which belongs to the low dimensional non-Gaussian target subspace up to an estimation error. By applying this operator to a family of different nonlinear functions, one obtains a family of different vectors lying in a vicinity of the target space. As a final step, the target space itself is estimated by applying PCA to this family of vectors. We show that this procedure is consistent in the sense that the estimaton error tends to zero at a parametric rate, uniformly over the family, Numerical examples demonstrate the usefulness of our method.non-Gaussian components, dimension reduction

Independent component analysis and source analysis of auditory evoked potentials for assessment of cochlear implant users

Source analysis of the Auditory Evoked Potential (AEP) has been used before to evaluate the maturation of the auditory system in both adult and children; in the same way, this technique could be applied to ongoing EEG recordings, in response to acoustic specific frequency stimuli, from children with cochlear implants (CI). This is done in oder to objectively assess the performance of this electronic device and the maturation of the child?s hearing. However, these recordings are contaminated by an artifact produced by the normal operation of the CI; this artifact in particular makes the detection and analysis of AEPs much harder and generates errors in the source analysis process. The artifact can be spatially filtered using Independent Component Analysis (ICA); in this research, three different ICA algorithms were compared in order to establish the more suited algorithm to remove the CI artifact. Additionally, we show that pre-processing the EEG recording, using a temporal ICA algorithm, facilitates not only the identification of the AEP peaks but also the source analysis procedure. From results obtained in this research and limited dataset of CI vs normal recordings, it is possible to conclude that the AEPs source locations change from the inferior temporal areas in the first 2 years after implantation to the superior temporal area after three years using the CIs, close to the locations obtained in normal hearing children. It is intended that the results of this research are used as an objective technique for a general evaluation of the performance of children with CIs