## Iterative deepening dynamic time warping for time series (2002)

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Venue: | In Proc 2 nd SIAM International Conference on Data Mining |

Citations: | 34 - 8 self |

### BibTeX

@INPROCEEDINGS{Chu02iterativedeepening,

author = {Selina Chu and Eamonn Keogh and David Hart},

title = {Iterative deepening dynamic time warping for time series},

booktitle = {In Proc 2 nd SIAM International Conference on Data Mining},

year = {2002}

}

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### Abstract

Time series are a ubiquitous form of data occurring in virtually every scientific discipline and business application. There has been much recent work on adapting data mining algorithms to time series databases. For example, Das et al. attempt to show how association rules can be learned from time series [7]. Debregeas and Hebrail [8]

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Citation Context ...d. A method that allows this elastic shifting of the X-axis is desired in order to detect similar shapes with different phases. Such a technique has long been known in the speech processing community =-=[29, 26]-=-. The technique, Dynamic Time Warping (DTW), was † Department of Information and Computer Science, University of California, Irvine, California 92697, {selina, dhart, pazzani}@ics.uci.edu. ‡ Departmen... |

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Citation Context ... This maps nicely on to our intuitions of similarity. 2.1.3 Mining Association Rules Although the discovery of association rules in discrete sequences is an area that has attracted extensive research =-=[3]-=-, less work has been done on the discovery of association rules in time series. The most frequently referenced work in this area is by Das et al. [7], so we have implemented this method for our experi... |

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Citation Context ...d. A method that allows this elastic shifting of the X-axis is desired in order to detect similar shapes with different phases. Such a technique has long been known in the speech processing community =-=[29, 26]-=-. The technique, Dynamic Time Warping (DTW), was † Department of Information and Computer Science, University of California, Irvine, California 92697, {selina, dhart, pazzani}@ics.uci.edu. ‡ Departmen... |

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Citation Context ...mon data mining tasks, classification, clustering and the discovery of association rules. In each example we compare DTW to Euclidean distance, the most commonly used distance measure for time series =-=[2, 7, 8, 10, 15]-=-. 2.1.1 Classification There has been much work on classification of time series. The most commonly studied benchmark dataset is Cylinder-Bell-Funnel, a synthetic dataset introduced in [28] and used b... |

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Citation Context ...mon data mining tasks, classification, clustering and the discovery of association rules. In each example we compare DTW to Euclidean distance, the most commonly used distance measure for time series =-=[2, 7, 8, 10, 15]-=-. 2.1.1 Classification There has been much work on classification of time series. The most commonly studied benchmark dataset is Cylinder-Bell-Funnel, a synthetic dataset introduced in [28] and used b... |

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Citation Context ...ve lethargy, various modifications to the algorithm have been suggested. Yi et al. proposed a technique that maps the data into Euclidean space such that their DTW distance is approximately preserved =-=[33]-=-. Unfortunately the method allows false dismissals, and more importantly, does not allow user to have direct control over the quality of the results returned. Rafiei and Mendelzon proposed an extensio... |

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Citation Context ...fornia, Riverside, California 92521, eamonn@cs.ucr.edu. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited 195introduced to the data mining community by Berndt and Clifford =-=[4]-=-. Although they demonstrate the utility of the approach, they acknowledge that the algorithm’s time complexity is a problem and that “…performance on very large databases may be a limitation”. Despite... |

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Citation Context ...(t) = (6+η) • X[a,b](t) • (b-a)/(b-t) + ε(t) X[a,b] = { 1, if a ≤ t ≤ b, else 0 } Where η and ε(t) are drawn from a standard normal distribution N(0,1), a is an integer drawn uniformly from the range =-=[16, 32]-=- and (b-a) is an integer drawn uniformly from the range [32, 96]. Figure 2 shows an example from each class. C ylinder Bell Funnel Figure 2: Examples of the Cylinder-Bell-Funnel dataset. We performed ... |

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Citation Context ...bregeas and Hebrail [8] demonstrate a technique for scaling up time series clustering algorithms to massive datasets. Keogh and Pazzani introduced a new, scalable time series classification algorithm =-=[16]-=-. Almost all algorithms that operate on time series data need to compute the similarity between them. Euclidean distance, or some extension or modification thereof, is typically used. However as we wi... |

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Citation Context ...r work on similarity searching to allow shifting and scaling of the time axis; however their method only handles global scaling of the time axis, and not the more general case of (local) time warping =-=[27]-=-. In previous work we introduced piecewise dynamic time warping (PDTW), a modification of DTW that performs warping on a reduced dimensionality representation of the data [17]. (Chan and Fu [6] later ... |

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Citation Context ...ry large databases may be a limitation”. Despite this shortcoming of DTW, it is still widely used in various fields. In bioinformatics, Aach and Church successfully applied DTW to RNA expression data =-=[1]-=-. In chemical engineering, it has been used for the synchronization and monitoring of batch processes in polymerization [14]. DTW has been successfully used to align biometric data, such as gait, sign... |

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Citation Context ... has been used for the synchronization and monitoring of batch processes in polymerization [14]. DTW has been successfully used to align biometric data, such as gait, signatures and even fingerprints =-=[11, 14, 22, 19]-=-. Several researchers including Vullings et al. [30] and Caiani et al. [5] have demonstrate the use of DTW for ECG pattern matching. Finally in robotics, Oates et al. demonstrated that DTW may be used... |

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Citation Context ... disclaimer greatly understates the problem with their approach, which rarely finds a true best match to a query. Perng et al proposed the Landmark Model for pattern querying in time series databases =-=[25]-=-. This model does not rely on Euclidean distance. Rather it identifies features of landmarks that are invariant under the several transformations. Instead of working directly with raw data, they propo... |

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Citation Context ..., 7, 8, 10, 15]. 2.1.1 Classification There has been much work on classification of time series. The most commonly studied benchmark dataset is Cylinder-Bell-Funnel, a synthetic dataset introduced in =-=[28]-=- and used by [21, 13, 9] and others. The dataset consists of a 3-class problem, with the classes generated by the following equations: c(t) = (6+η) • X[a,b](t) + ε(t) b(t) = (6+η) • X[a,b](t) • (t-a)/... |

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Citation Context ... of (local) time warping [27]. In previous work we introduced piecewise dynamic time warping (PDTW), a modification of DTW that performs warping on a reduced dimensionality representation of the data =-=[17]-=-. (Chan and Fu [6] later introduced a similar technique that operates on a different, but logically equivalent representation [15].) We demonstrated that this approach allows dramatic speedup with low... |

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Citation Context ...2.1.1 Classification There has been much work on classification of time series. The most commonly studied benchmark dataset is Cylinder-Bell-Funnel, a synthetic dataset introduced in [28] and used by =-=[21, 13, 9]-=- and others. The dataset consists of a 3-class problem, with the classes generated by the following equations: c(t) = (6+η) • X[a,b](t) + ε(t) b(t) = (6+η) • X[a,b](t) • (t-a)/(b-a) + ε(t) f(t) = (6+η... |

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Citation Context ...at it is only defined in the special case where the two sequences have the same length. The time complexity of DTW is O(nm). This review of DTW is necessarily brief; we refer the interested reader to =-=[20]-=- for a more detailed treatment. 2.3 Why Dynamic Time Warping is Resistant to Optimization Because similarity measurement can be computationally expensive, we would like to optimize the calculations as... |

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Citation Context ... has been used for the synchronization and monitoring of batch processes in polymerization [14]. DTW has been successfully used to align biometric data, such as gait, signatures and even fingerprints =-=[11, 14, 22, 19]-=-. Several researchers including Vullings et al. [30] and Caiani et al. [5] have demonstrate the use of DTW for ECG pattern matching. Finally in robotics, Oates et al. demonstrated that DTW may be used... |

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Citation Context ...o be set, and it is not clear how best to choose them. Park et al. introduced a time warping measure that uses a symbolic representation that is itself obtained from a piecewise linear representation =-=[24]-=-. They demonstrate that this approach can be indexed in a suffix tree. However they only report the speedup for the indexing scheme (which is relatively small), and there is no comparison in terms of ... |

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Citation Context ...rping [27]. In previous work we introduced piecewise dynamic time warping (PDTW), a modification of DTW that performs warping on a reduced dimensionality representation of the data [17]. (Chan and Fu =-=[6]-=- later introduced a similar technique that operates on a different, but logically equivalent representation [15].) We demonstrated that this approach allows dramatic speedup with low probability of fa... |

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Citation Context ... al. [30] and Caiani et al. [5] have demonstrate the use of DTW for ECG pattern matching. Finally in robotics, Oates et al. demonstrated that DTW may be used for clustering an agent's sensory outputs =-=[23]-=-. A) B) 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 Figure 1: Note that while the sequences have an overall similar shape, they are not aligned in the time axis. Euclidean distance, which assumes the i... |

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Citation Context ... has been used for the synchronization and monitoring of batch processes in polymerization [14]. DTW has been successfully used to align biometric data, such as gait, signatures and even fingerprints =-=[11, 14, 22, 19]-=-. Several researchers including Vullings et al. [30] and Caiani et al. [5] have demonstrate the use of DTW for ECG pattern matching. Finally in robotics, Oates et al. demonstrated that DTW may be used... |

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Citation Context ... much recent work on adapting data mining algorithms to time series databases. For example, Das et al. attempt to show how association rules can be learned from time series [7]. Debregeas and Hebrail =-=[8]-=- demonstrate a technique for scaling up time series clustering algorithms to massive datasets. Keogh and Pazzani introduced a new, scalable time series classification algorithm [16]. Almost all algori... |

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Citation Context ...ion [14]. DTW has been successfully used to align biometric data, such as gait, signatures and even fingerprints [11, 14, 22, 19]. Several researchers including Vullings et al. [30] and Caiani et al. =-=[5]-=- have demonstrate the use of DTW for ECG pattern matching. Finally in robotics, Oates et al. demonstrated that DTW may be used for clustering an agent's sensory outputs [23]. A) B) 0 10 20 30 40 50 60... |

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Citation Context ...informatics, Aach and Church successfully applied DTW to RNA expression data [1]. In chemical engineering, it has been used for the synchronization and monitoring of batch processes in polymerization =-=[14]-=-. DTW has been successfully used to align biometric data, such as gait, signatures and even fingerprints [11, 14, 22, 19]. Several researchers including Vullings et al. [30] and Caiani et al. [5] have... |

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Citation Context ...2.1.1 Classification There has been much work on classification of time series. The most commonly studied benchmark dataset is Cylinder-Bell-Funnel, a synthetic dataset introduced in [28] and used by =-=[21, 13, 9]-=- and others. The dataset consists of a 3-class problem, with the classes generated by the following equations: c(t) = (6+η) • X[a,b](t) + ε(t) b(t) = (6+η) • X[a,b](t) • (t-a)/(b-a) + ε(t) f(t) = (6+η... |

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Citation Context ...2.1.1 Classification There has been much work on classification of time series. The most commonly studied benchmark dataset is Cylinder-Bell-Funnel, a synthetic dataset introduced in [28] and used by =-=[21, 13, 9]-=- and others. The dataset consists of a 3-class problem, with the classes generated by the following equations: c(t) = (6+η) • X[a,b](t) + ε(t) b(t) = (6+η) • X[a,b](t) • (t-a)/(b-a) + ε(t) f(t) = (6+η... |

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Citation Context ...application. There has been much recent work on adapting data mining algorithms to time series databases. For example, Das et al. attempt to show how association rules can be learned from time series =-=[7]-=-. Debregeas and Hebrail [8] demonstrate a technique for scaling up time series clustering algorithms to massive datasets. Keogh and Pazzani introduced a new, scalable time series classification algori... |

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ECG Segmentation Using Time-Warping. Advances in Intelligent Data Analysis. pp 275285. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited 211
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Citation Context ...rocesses in polymerization [14]. DTW has been successfully used to align biometric data, such as gait, signatures and even fingerprints [11, 14, 22, 19]. Several researchers including Vullings et al. =-=[30]-=- and Caiani et al. [5] have demonstrate the use of DTW for ECG pattern matching. Finally in robotics, Oates et al. demonstrated that DTW may be used for clustering an agent's sensory outputs [23]. A) ... |