I. Introduction
With the development of data collection and storage, time series data is now commonly applied in a variety of domains, from voice recognition, the stock market, to solar activities, medical research, and many other scientific and engineering fields where measurements in the temporal sense are important. With more data, the need to effectively process and compare data is essential. Distance measures can be categorized as lock-step and elastic. Lock-step measures generally refer to Lp norms, meaning the i-th element in one sequence is always mapped to the i-th element in another sequence. While elastic measures allow for one-to-many, or even one-to-none mappings [1]. With the commonly seen temporal discrepancies in time series sequences, traditional lock-step measures are not as effective as elastic when identifying similarities [2].