A Wavelet-Based Approach for Similar Pattern Detection in Time Series

Abstract

Pierpaolo Massoli

The analysis of randomness in time series is crucial for extracting relevant pat- terns from noisy data. Noise can obscure underlying dynamics, posing challenges in various research fields such as financial analysis, biomedical signal processing, and environmental monitoring. This study proposes a novel method for detecting similar patterns in large- scale time series datasets. The approach employs a denoising technique based on the Morlet wavelet transform to enhance pattern recognition. The similarity-search method leverages Locality Sensitive Hashing in order to detect denoised similar patterns embedded within time series. A significant reduction in entropy in the reconstructed data reveals hidden patterns that were previously masked by noise. This study avails of entropy as a measure of detection accuracy, incorporating a well-known technique from the Conformal Prediction framework. The pre-defined confidence level is closely related to the minimum cosine similarity of the detected patterns which exchange high values of mutual information as a consequence of the noise removal as demonstrated in the case study.

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