Efficient Interval-focused Similarity Search under Dynamic Time Warping

Similarity search on time series from large temporal text corpora is interesting in many settings. Our use case is the Google Books Ngram corpus and historians interested in the changes of word frequencies over time. More specifically, users are interested in similarity search in a specific period of time, aka. interval-focused similarity search. Related work formalizes interval-focused similarity search, but the sparsely existing approaches are limited to metric distance measures, like the Euclidean distance. Most other approaches in this area, that address the usage of warping distance measures, focus on whole matching similarity search. In this work, we present a novel search tree that uses so-called time series envelopes to group objects. To speed up the tree traversal, our search tree approximates the envelopes based on the node height, i. e., envelopes are tighter further down in the tree. We combine this with various time series pruning techniques, mainly to reduce the number of expensive distance computations. Our experimental evaluation shows that this combination is worthwhile and indeed decisive for a significant speedup, compared to less sophisticated adaptations of known approaches. We, first, show that a combination of both pruning groups of time series and single time series outperforms the usage of a single pruning technique. Secondly, we compare the wall-clock run times of our data structure to existing approaches and determine a significant speed up for focused-interval similarity search queries on large temporal data sets, like the Google Books Ngram corpus.