Feature Extraction for Change-Point Detection using Stationary Subspace Analysis

Detecting changes in high-dimensional time series is difficult because it involves the comparison of probability densities that need to be estimated from finite samples. In this paper, we present the first feature extraction method tailored to change point detection, which is based on an extended version of Stationary Subspace Analysis. We reduce the dimensionality of the data to the most non-stationary directions, which are most informative for detecting state changes in the time series. In extensive simulations on synthetic data we show that the accuracy of three change point detection algorithms is significantly increased by a prior feature extraction step. These findings are confirmed in an application to industrial fault monitoring.Comment: 24 pages, 20 figures, journal preprin

Can we identify non-stationary dynamics of trial-to-trial variability?"

Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings

The Magnetic Topology of the Weak-Lined T Tauri Star V410 - A Simultaneous Temperature and Magnetic Field Inversion

We present a detailed temperature and magnetic investigation of the T Tauri star V410 Tau by means of a simultaneous Doppler- and Zeeman-Doppler Imaging. Moreover we introduce a new line profile reconstruction method based on a singular value decomposition (SVD) to extract the weak polarized line profiles. One of the key features of the line profile reconstruction is that the SVD line profiles are amenable to radiative transfer modeling within our Zeeman-Doppler Imaging code iMap. The code also utilizes a new iterative regularization scheme which is independent of any additional surface constraints. To provide more stability a vital part of our inversion strategy is the inversion of both Stokes I and Stokes V profiles to simultaneously reconstruct the temperature and magnetic field surface distribution of V410 Tau. A new image-shear analysis is also implemented to allow the search for image and line profile distortions induced by a differential rotation of the star. The magnetic field structure we obtain for V410 Tau shows a good spatial correlation with the surface temperature and is dominated by a strong field within the cool polar spot. The Zeeman-Doppler maps exhibit a large-scale organization of both polarities around the polar cap in the form of a twisted bipolar structure. The magnetic field reaches a value of almost 2 kG within the polar region but smaller fields are also present down to lower latitudes. The pronounced non-axisymmetric field structure and the non-detection of a differential rotation for V410 Tau supports the idea of an underlying $\alpha^2$-type dynamo, which is predicted for weak-lined T Tauri stars.Comment: Accepted for A&A, 18 pages, 10 figure