Time Series Clustering Using Coherence
Time series clustering has drawn increasing attention with the rising popularity of machine learning and artificial intelligence. In this thesis, a new technique for clustering time series based on the coherence between time series in the frequency domain is proposed. Several comparisons between the proposed techniques and some classic clustering algorithms are performed using both simulated and real world data sets. To evaluate the cluster assignment accuracy, the Adjusted Rand Index is used as the performance evaluation criterion. We find that under certain restrictive conditions, namely the classic ``signal in noise'' case, the proposed method performs very well compared to the classic $k$-means clustering algorithm and a variation that focuses on clustering extracted features of the data. Through extensive simulation studies, we also present cases where the proposed methods perform poorly. The thesis concludes with a discussion of some ideas for future work in this area.