Feature extraction from covariance by using kernel method for classifying polysomnographys data

Abstract

Using covariance as natural features for Classifying Polysomnographys signal was not new in the literature. In the literature, space of covariance is an abstract space, the Riemannian manifold. It is non-trivial to classify by using well-known classifier because all algorithms were designed for Euclidean space only. In order to overcome, there are two ways to classify with this feature. First way, it is possible apply directly by using based distance classifier such as k-nearest neighborhoods (k-NN) with the geodesic distance between two points in manifold. The second way, indirect method is to transform all covariance data to approximated tangent space of a specific symmetric and positive definite matrix and apply a classification method as usual way. All of these methods, themselves have drawback due to the distortion and the geometry of data. We introduced a method for extracting latent features by combining a kernel method. Thus, we used Kernel Local Fisher Discriminant Analysis (KLFDA) which is possible to take covariance matrices as its inputs. We evaluated our method on Sleep Stages Dataset and archived a better result compared to distance based and indirect method.