Error and Anomaly Detection for Intra-Participant Time-Series Data

Abstract

Identification of errors or anomalous values, collectively considered outliers, assists in exploring data or through removing outliers improves the statistical analysis. In biomechanics, outlier detection methods have explored the ‘shape’ of the entire cycles, although exploring fewer points using a ‘moving-window’ may be advantageous. Hence, the aim was to develop a moving-window based method for detecting trials with outliers in intra-participant time-series data. The test data were the angles and displacements for the strides or cycles (mean 38 cycles) from treadmill running, with outliers detected through two-stages. Stage-1 was a one-dimensional (spatial) outlier detection at each time-point, where any data-value of a scaled median-absolute-deviation away from the median at that time-point led to removing that cycle. Stage-2 was a two-dimensional (spatial-temporal) outlier detection of a moving-window-standard-deviation (mwSD) across cycles and across the moving-window size (size of ± 0, 1, 2 or 3 time-points), where any data-value greater than the scaled mwSD led to removing that cycle. Scaling was performed using the t-statistic for three significance levels of 0.01, 0.001 or 0.0001. Fewer cycles were removed with smaller scaling and smaller window size. Appropriate settings were stage-1 scaling of 0.0001 (mean 3.5 cycles removed) and stage-2 scaling of 0.01 with a moving-window size of 1 (mean 2.6 cycles removed). Settings in the supplied Matlab code should be customised to each data set, and trials with outliers assessed to justify whether to retain or remove those trials. The method provides an effective method to identify trials with outliers in intra-participant time-series data.