Querying Time Series Data Based on Similarity

ÐWe study similarity queries for time series data where similarity is defined, in a fairly general way, in terms of a distance function and a set of affine transformations on the Fourier series representation of a sequence. We identify a safe set of transformations supporting a wide variety of comparisons and show that this set is rich enough to formulate operations such as moving average and time scaling. We also show that queries expressed using safe transformations can efficiently be computed without prior knowledge of the transformations. We present a query processing algorithm that uses the underlying multidimensional index built over the data set to efficiently answer similarity queries. Our experiments show that the performance of this algorithm is competitive to that of processing ordinary (exact match) queries using the index, and much faster than sequential scanning. We propose a generalization of this algorithm for simultaneously handling multiple transformations at a time, and give experimental results on the performance of the generalized algorithm. Index TermsÐSimilarity queries, time series retrieval, indexing time series, Fourier transform.