| Abstract: |
Nonstationary time series can be conceptualized as concatenations of quasi-stationary spells. It is of interest to divide experimentally obtained time-series into quasi-stationary segments, as the partitions could indicate a change of state in the underlying complex system. In particular, such a segmentation method would provide a useful tool for EEG data analysis. Traditionally EEG data were studied using the event-related potential (ERP) technique. It is based on selecting fragments of the EEG data surrounding an event (like the subject making a response) for each trial and then averaging these fragments separately for each electrode. This approach involves discarding possibly relevant information in the averaging process, its results depend on the electrode location and some data preprocessing details, and it cannot be adapted to detect a change in the state of the system (such as detection of an error in the case of EEG recording of a subject performing a task) in a single trial. A segmentation-based method taking advantage of the fluctuation properties could provide an improvement in these regards.
In this work, a segmentation algorithm based on the distribution-free Kolmogorov-Smirnov (KS) test proposed by Camargo, Duarte Queirós & Anteneodo (2011) is investigated. The algorithm involves recursively placing partitions such that the KS statistic is maximized (if its value indicates statistical significance and the resulting segments are sufficiently long). The algorithm was tested for both artificial time series and EEG data from 6 subjects performing the Eriksen flanker task – a simple response inhibition task in which each trial involves the subject deciding on pressing one of two buttons based on the stimuli displayed on a screen.
Firstly, the method was applied to several types of artificially generated time series that have been used as a model for the EEG (Gaussian and autoregressive series, and 1/f noise). Segmentation quality was assessed with Normalized Mutual Information and with the number of correctly identified partitions. Although the KS segmentation algorithm accurately segments Gaussian series in a wide range of parameters, oversegmentation was found to occur for autoregressive and 1/f series.
Preliminary results for the EEG data indicate that the segmentation method detects stimulus ERPs as well as the components related to detection and monitoring of errors, such as the well-documented error-related negativity. Stimulus-locked and response-locked ERP components were obtained from preprocessed data in the time range from -200 ms to 1000 ms for each subject and condition (erroneous/correct response) separately. Segmentation was performed for each trial at minimal segment length of 100 ms. Then probability distribution of a partition at a particular time point. The experimental distributions were compared with probability distributions for surrogate ARMA series fitted to the corresponding data to verify that the results are not artifactual Comparing the probability distribution with the ERP waveform suggests that partitions are most likely where the slope of the ERP waveform is the steepest.
Camargo, S., Duarte Queirós, S. M., & Anteneodo, C. (2011). Nonparametric segmentation of nonstationary time series. Physical review. E, Statistical, nonlinear, and soft matter physics, 84(4 Pt 2), 046702. https://doi.org/10.1103/PhysRevE.84.046702. |