Dynamical Component Analysis (DYCA) and Its Application on Epileptic EEG

Abstract

Dynamical Component Analysis (DyCA) is a recentlyproposed method to detect projection vectors to reduce the dimensionality of multi-variate deterministic datasets. It is based on the solution of a generalized eigenvalue problem and therefore straight forward to implement. DyCA is introduced and applied to EEG data of epileptic seizures. The obtained eigenvectors are used to project the signal and the corresponding trajectories in phase space are compared with PCA and ICA-projections. The eigenvalues of DyCA are utilized for seizure detection and the obtained results in terms of specificity, false discovery rate and miss rate are compared to other seizure detection algorithms.

Unsupervised Discovery of Temporal Structure in Noisy Data with Dynamical Components Analysis

“…Finally, DCA is related to the Past-Future Information Bottleneck [37] (see Appendix F). We have been made aware of two existing methods which share the name Dynamical Component(s) Analysis [38][39][40]. Thematically, they share the goal of uncovering low-dimensional dynamics from time series data.…”

“…Thirion and Faugeras [38] perform a two-stage, temporal then kernelized spatial analysis. Seifert et al [39] and Korn et al [40] assume the observed dynamics are formed by lowdimensional latent variables with linear and nonlinear dynamics. To fit a linear approximation of the latent variables, they derive a generalized eigenvalue problem which is sensitive to same-time and one-time step correlations, i.e., the data and the approximation of its first derivative.…”

Subspace Detection and Blind Source Separation of Multivariate Signals by Dynamical Component Analysis (DyCA)

“…This approach has similarities to the method of PIPs (principal interacting patterns) and POPs (principal oscillating patterns) introduced by Hasselmann [5] and further developed by Kwasniok [6], [7]. Compared to [2], [3] we present the proposed method more in-depth and detailed and present a broad spectrum of possible applications.…”

“…In this paper we present a dimensionality reduction method -dynamical component analysis (DyCA) -introduced in the preliminaries works of Seifert et al [2] and Korn et al [3]. The proposed method is governed by the assumption that a multivariate measurement of a dynamical system can be split into a deterministic part, which can be described by a system of differential equations, and independent noise components.…”

“…The proposed method is governed by the assumption that a multivariate measurement of a dynamical system can be split into a deterministic part, which can be described by a system of differential equations, and independent noise components. This is for example the case for EEG data of epileptic seizures, which can approximately be described by a system of ordinary differential equations consisting of two linear and one non-linear equations, as shown in [3], [4]. This approach has similarities to the method of PIPs (principal interacting patterns) and POPs (principal oscillating patterns) introduced by Hasselmann [5] and further developed by Kwasniok [6], [7].…”