Exact Indexing for Massive Time Series Databases under Time Warping Distance

Among many existing distance measures for time series data, Dynamic Time Warping (DTW) distance has been recognized as one of the most accurate and suitable distance measures due to its flexibility in sequence alignment. However, DTW distance calculation is computationally intensive. Especially in very large time series databases, sequential scan through the entire database is definitely impractical, even with random access that exploits some index structures since high dimensionality of time series data incurs extremely high I/O cost. More specifically, a sequential structure consumes high CPU but low I/O costs, while an index structure requires low CPU but high I/O costs. In this work, we therefore propose a novel indexed sequential structure called TWIST (Time Warping in Indexed Sequential sTructure) which benefits from both sequential access and index structure. When a query sequence is issued, TWIST calculates lower bounding distances between a group of candidate sequences and the query sequence, and then identifies the data access order in advance, hence reducing a great number of both sequential and random accesses. Impressively, our indexed sequential structure achieves significant speedup in a querying process by a few orders of magnitude. In addition, our method shows superiority over existing rival methods in terms of query processing time, number of page accesses, and storage requirement with no false dismissal guaranteed.

Learning DTW Global Constraint for Time Series Classification

1-Nearest Neighbor with the Dynamic Time Warping (DTW) distance is one of the most effective classifiers on time series domain. Since the global constraint has been introduced in speech community, many global constraint models have been proposed including Sakoe-Chiba (S-C) band, Itakura Parallelogram, and Ratanamahatana-Keogh (R-K) band. The R-K band is a general global constraint model that can represent any global constraints with arbitrary shape and size effectively. However, we need a good learning algorithm to discover the most suitable set of R-K bands, and the current R-K band learning algorithm still suffers from an 'overfitting' phenomenon. In this paper, we propose two new learning algorithms, i.e., band boundary extraction algorithm and iterative learning algorithm. The band boundary extraction is calculated from the bound of all possible warping paths in each class, and the iterative learning is adjusted from the original R-K band learning. We also use a Silhouette index, a well-known clustering validation technique, as a heuristic function, and the lower bound function, LB_Keogh, to enhance the prediction speed. Twenty datasets, from the Workshop and Challenge on Time Series Classification, held in conjunction of the SIGKDD 2007, are used to evaluate our approach.