Improving Rehabilitative Assessment with Statistical and Shape Preserving Surrogate Data and Singular Spectrum Analysis

Abstract

Time series data are collected in temporal order and are widely used to train systems for prediction, modeling and classification to name a few. These systems require large amounts of data to improve generalization and prevent over-fitting. However there is a comparative lack of time series data due to operational constraints. This situation is alleviated by synthesizing data which have a suitable spread of features yet retain the distinctive features of the original data. These would be its basic statistical properties and overall shape which are important for short time series such as in rehabilitative applications or in quickly changing portions of lengthy data. In our earlier work synthesized surrogate time series were used to augment rehabilitative data. This gave good results in classification but the resulting waveforms did not preserve the original signal shape. To remedy this, we use singular spectrum analysis (SSA) to separate a signal into trends and cycles to describe the shape of the signal and low level components. In a novel way we subject the low level component to randomizing processes then recombine this with the original trend and cycle components to form a synthetic time series. We compare our approach with other methods, using statistical and shape measures and demonstrate its effectiveness in classification.