Dynamic Time Warping Under Product Quantization, With Applications to Time-Series Data Similarity Search

Abstract

The similarity search on sensor data generated by a myriad of sensing devices is a frequently encountered problem in the era of the Internet of Things (IoT). This sensor data generally appear in the form of time series, a temporally ordered sequence of real numbers obtained regularly in time. It has been widely accepted that the dynamic time warping (DTW) currently is the most prevalent similarity measure in the time-series mining community, mainly due to its flexibility and broad applicability. However, calculating DTW between two time series has quadratic time complexity, leading to unsatisfactory efficiency when performing the similarity search over the large time-series data set. The main contribution of this article is to propose a method called product quantization (PQ)-based DTW (PQDTW) for fast time-series approximate similarity search under DTW. The PQ, a well-known approximate nearest neighbor search approach, is used in PQDTW. Nevertheless, the conventional PQ is developed with the Euclidean distance and is not designed for DTW. To solve this problem, the DTW barycenter averaging (DBA) technique is utilized to adapt the PQ for DTW before using it. We employ PQDTW along with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">filter-and-refine</i> framework to efficiently and accurately perform the time-series similarity search. Our method can reasonably reduce many DTW computations in the filtering phase; thus, the query process is accelerated. We compare PQDTW with related popular algorithms using public time-series data sets. Experimental results verify that the proposal achieves the best tradeoff between query efficiency and retrieval accuracy compared to the competitors.