Compression rate distance measure for time series

In this work, we propose a Compression Rate Distance, a new distance measure for time series data. The main idea behind this distance is based on the Minimum Description Length (MDL) principle. The higher compression rate between two time series is, the closer they should be. Besides, we also propose a relaxed version of the new distance, called the Extended Compression Rate Distance. The Extended Compression Rate Distance can satisfy some crucial characteristics on time series such as Early Abandoning, Lower Bounding, and Relaxed-Triangular Inequality which help the new distance easily adapt with traditional indexing structures and searching methods. We tested our distances on classification problem with numerous datasets and compared the results with most of the commonly used distances in time series such as Euclidean Distance, Dynamic Time Warping, and a recently proposed Complexity-Invariant Distance. Experimental results reveal that our novel distances outperform several previous important distance measures in a vast majority of the datasets.