{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/elastic-bands-across-the-path-a-new-framework","title":"Elastic bands across the path: A new framework and methods to lower bound DTW","arxiv_id":"1808.09617","date":"2018-08-29","proceeding":null,"authors":["Chang Wei Tan","Francois Petitjean","Geoffrey I. Webb"],"abstract":"There has been renewed recent interest in developing effective lower bounds\nfor Dynamic Time Warping (DTW) distance between time series. These have many\napplications in time series indexing, clustering, forecasting, regression and\nclassification. One of the key time series classification algorithms, the\nnearest neighbor algorithm with DTW distance (NN-DTW) is very expensive to\ncompute, due to the quadratic complexity of DTW. Lower bound search can speed\nup NN-DTW substantially. An effective and tight lower bound quickly prunes off\nunpromising nearest neighbor candidates from the search space and minimises the\nnumber of the costly DTW computations. The speed up provided by lower bound\nsearch becomes increasingly critical as training set size increases. Different\nlower bounds provide different trade-offs between computation time and\ntightness. Most existing lower bounds interact with DTW warping window sizes.\nThey are very tight and effective at smaller warping window sizes, but become\nlooser as the warping window increases, thus reducing the pruning effectiveness\nfor NN-DTW. In this work, we present a new class of lower bounds that are\ntighter than the popular Keogh lower bound, while requiring similar computation\ntime. Our new lower bounds take advantage of the DTW boundary condition,\nmonotonicity and continuity constraints to create a tighter lower bound. Of\nparticular significance, they remain relatively tight even for large windows. A\nsingle parameter to these new lower bounds controls the speed-tightness\ntrade-off. We demonstrate that these new lower bounds provide an exceptional\nbalance between computation time and tightness for the NN-DTW time series\nclassification task, resulting in greatly improved efficiency for NN-DTW lower\nbound search.","url_abs":"http://arxiv.org/abs/1808.09617v3","url_pdf":"http://arxiv.org/pdf/1808.09617v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"elastic-bands-across-the-path-a-new-framework","repo_url":"https://github.com/moradisten/KNN-LB","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"dynamic-time-warping","task_name":"Dynamic Time Warping"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"},{"task_slug":"time-series-classification","task_name":"Time Series Classification"}],"methods":[{"method_slug":"dtw","method_name":"DTW"},{"method_slug":"pruning","method_name":"Pruning"},{"method_slug":"speed","method_name":"SPEED"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}