Using multi-scale histograms to answer pattern existence and shape match queries over time series data

Similarity-based querying of time series data can be categorized as pattern existence queries and shape match queries. Pattern existence queries find the time series data with certain patterns while shape match queries look for the time series data that have similar movement shapes. Existing proposals address one of these or the other. In this paper, we propose multi-scale time series histograms that can be used to answer both types of queries, thus offering users more flexibility. Multiple histogram levels allow querying at various precision levels. Most importantly, the distances of time series histograms at lower scale are lower bounds of the distances at higher scale, which guarantees that no false dismissals will be introduced when a multi-step filtering process is used in answering shape match queries. We further propose to use averages of time series histograms to reduce the dimensionality and avoid computing the distances of full time series histograms. The experimental results show that multi-scale histograms can effectively find the patterns in time series data and answer shape match queries, even when the data contain noise, time shifting and scaling, or amplitude shifting and scaling.