Calculating the matrix profile from noisy data

The matrix profile (MP) is a data structure computed from a time series which encodes the data required to locate motifs and discords, corresponding to recurring patterns and outliers respectively. When the time series contains noisy data then the conventional approach is to pre-filter it in order to remove noise but this cannot apply in unsupervised settings where patterns and outliers are not annotated. The resilience of the algorithm used to generate the MP when faced with noisy data remains unknown. We measure the similarities between the MP from original time series data with MPs generated from the same data with noisy data added under a range of parameter settings including adding duplicates and adding irrelevant data. We use three real world data sets drawn from diverse domains for these experiments Based on dissimilarities between the MPs, our results suggest that MP generation is resilient to a small amount of noise being introduced into the data but as the amount of noise increases this resilience disappears