A Fast Framework for Abrupt Change Detection Based on Binary Search Trees and Kolmogorov Statistic

Change-Point (CP) detection has attracted considerable attention in the fields of data mining and statistics; it is very meaningful to discuss how to quickly and efficiently detect abrupt change from large-scale bioelectric signals. Currently, most of the existing methods, like Kolmogorov-Smirnov (KS) statistic and so forth, are time-consuming, especially for large-scale datasets. In this paper, we propose a fast framework for abrupt change detection based on binary search trees (BSTs) and a modified KS statistic, named BSTKS (binary search trees and Kolmogorov statistic). In this method, first, two binary search trees, termed as BSTcA and BSTcD, are constructed by multilevel Haar Wavelet Transform (HWT); second, three search criteria are introduced in terms of the statistic and variance fluctuations in the diagnosed time series; last, an optimal search path is detected from the root to leaf nodes of two BSTs. The studies on both the synthetic time series samples and the real electroencephalograph (EEG) recordings indicate that the proposed BSTKS can detect abrupt change more quickly and efficiently than KS,t-statistic (t), and Singular-Spectrum Analyses (SSA) methods, with the shortest computation time, the highest hit rate, the smallest error, and the highest accuracy out of four methods. This study suggests that the proposed BSTKS is very helpful for useful information inspection on all kinds of bioelectric time series signals.

Distribution of Variables Extracted from Spectral EEG-Analysis

For 1000 variables extracted from auto- and cross-spectra of two 12-channel montages, the empirical density function is investigated. Only a small group of them may be considered to have a univariate normal distribution. Another important group including the absolute and the relative power in the four classical frequency bands has distribution functions that may be more or less accurately approximated by gamma-type functions.A third group including some of the peak frequencies shows distribution functions with two peaks not assignable to any natural classification of the EEG.The power of discrimination between the four samples is investigated for each variable by means of Bayes-classification and by a quasi-Kolmogorov-statistic. Its quality is demonstrated using linear discriminant analysis.Correlations were computed to complete basic statistical information.