Methods for the supervised classification of signals generally aim to assign a signal to one class for its entire time span. In this paper we present an alternative formulation for multivariate signals where the class membership is permitted to change over time. Our aim therefore changes from classifying the signal as a whole to classifying the signal at each time point to one of a fixed number of known classes. We assume that each class is characterised by a different stationary generating process, the signal as a whole will however be nonstationary due to class switching. To capture this nonstationarity we use the recently proposed Multivariate Locally Stationary Wavelet model. To account for uncertainty in class membership at each time point our goal is not to assign a definite class membership but rather to calculate the probability of a signal belonging to a particular class. Under this framework we prove some asymptotic consistency results. This method is also shown to perform well when applied to both simulated and accelerometer data. In both cases our method is able to place a high probability on the correct class for the majority of time points.
|Original language||English (US)|
|Number of pages||12|
|State||Published - Mar 11 2018|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors are grateful to the anonymous reviewers for their constructive comments and suggestions that have significantly improved the quality of this manuscript. Park gratefully acknowledges funding from the EPSRC-funded STOR-i Centre for Doctoral Training and Unilever Research. Eckley’s work was supported by the Engineering and Physical Sciences Research Council under grant EP/I01697X/1, whilst Ombao gratefully acknowledges funding from NSF DMS and NSF SES.