Feature Extraction for Change-Point Detection Using Stationary Subspace Analysis

Abstract

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.

Stationary subspace analysis of nonstationary processes

“…For ISSA and ASSA, a sequential likelihood ratio test as in Blythe et al. is implemented to select d . Their sensitivity to the choice of number of epochs N is also illustrated.…”

“… and Blythe et al. , a sequential likelihood ratio test is used to determine the dimension of the stationary subspace d when the observations are independent and normally distributed. We rely on a sequential test of second‐order stationarity to determine d without the independence assumption, and study the consistency of the estimated d using the asymptotic distribution of the test statistic under the alternative hypothesis of local stationarity of the time series (Dahlhaus, ).…”

Independent Component Analysis

“…The observed time series x(t) is generated as a linear mixture of stationary source s s (t) and nonstationary source s n (t) with a time-constant mixing matrix A, (14.32) and the objective is to recover these two groups of underlying sources given only samples from x(t). Stationary subspace analysis can be used for change-point detection in high-dimensional time series [14]. The dimensionality of the data can be reduced to the most nonstationary directions, which are most informative for detecting state changes in the time series.…”

Removal of EOG Artifacts from EEG Recordings Using Stationary Subspace Analysis

“…Subsequently, artifacts can be concentrated in only a few components. To the best of our knowledge, SSA has not been applied to EEG signals for removing artifacts thus far, even though it has been shown to have interesting applications in robust motor imagery prediction for Brain-Computer Interface [15, 17], geophysical data analysis [16], WiFi localisation [18], computer vision [19], and change-point detection [20]. Experiments on both simulated data and real EEG recordings are conducted, and the results show that the proposed method can effectively improve the artifact correction on raw EEG recordings.…”