## Fast and exact warping of time series using adaptive segmental approximations (2005)

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Venue: | Machine Learning, Vol |

Citations: | 6 - 0 self |

### BibTeX

@INPROCEEDINGS{Mamoulis05fastand,

author = {Nikos Mamoulis and David W. Cheung and Eamonn Keogh},

title = {Fast and exact warping of time series using adaptive segmental approximations},

booktitle = {Machine Learning, Vol},

year = {2005},

pages = {231--267}

}

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### Abstract

Abstract. Similarity search is a core module of many data analysis tasks, including search by example, classification, and clustering. For time series data, Dynamic Time Warping (DTW) has been proven a very effective similarity measure, since it minimizes the effects of shifting and distortion in time. However, the quadratic cost of DTW computation to the length of the matched sequences makes its direct application on databases of long time series very expensive. We propose a technique that decomposes the sequences into a number of segments and uses cheap approximations thereof to compute fast lower bounds for their warping distances. We present several, progressively tighter bounds, relying on the existence or not of warping constraints. Finally, we develop an index and a multi-step technique that uses the proposed bounds and performs two levels of filtering to efficiently process similarity queries. A thorough experimental study suggests that our method consistently outperforms state-of-the-art methods for DTW similarity search.

### Citations

1502 |
Fundementals of Speech Recognition
- Rabiner, Juang
- 1993
(Show Context)
Citation Context ...en sequences of different lengths. Based on these advantages, DTW has been widely used in different kinds of applications such as signature verification (Munich & Perona, 1999) and voice recognition (=-=Rabiner & Juang, 1993-=-). Recent studies (Berndt & Clifford, 1994; Chu, Keogh, and Pazzani, 2002; Keogh, 2002a; Kim, Park, and Chu, 2001; Yi, Jagadish, & Faloutsos, 1998; Zhu & Shasha, 2003) have adopted DTW for generic ana... |

1357 |
Finding Groups in Data: An Introduction to Cluster Analysis
- Kaufman, Rousseeuw
- 1990
(Show Context)
Citation Context ...eighbor search based classifiers assign class labels to a new sample according to its nearest neighbor in the samples of known labels. In addition, partitioning clustering algorithms, like k-medoids (=-=Kaufman & Rousseeuw, 1990-=-), assign a sample to the cluster corresponding to the nearest medoid. Similarity queries are classified into two categories. The first is whole sequence matching (Agrawal, Faloutsos, & Swami, 1993; K... |

984 | The r*-tree: An efficient and robust access method for points and rectangles
- Beckmann, Kriegel, et al.
- 1990
(Show Context)
Citation Context ...�s, for which Lb Kim(�q,�s) >ɛ(Kim, Park, and Chu, 2001). Based on Feature(�s), each sequence �s is mapped to a point in 4-dimensional space and inserted into a multi-dimensional index (e.g. R*-tree (=-=Beckmann et al., 1990-=-)). For a query sequence �q, Feature(�q) isfirst extracted and then a range query is performed to obtain candidate sequences for which Lb Kim(�q,�s) ≤ ɛ. The range query is defined by extending each d... |

488 | The R -tree: an efficient and robust access method for points and rectangles - Beckmann, Kriegel, et al. - 1990 |

447 | Dynamic programming algorithm optimization for spoken word recognition
- Sakoe, Chiba
- 1978
(Show Context)
Citation Context ...traint could be used to limit how far the warping path may stray from the diagonal. Two popular warping path constraints are the Sakoe-Chiba band and the Itakura Parallelogram (Rabiner & Juang, 1993; =-=Sakoe & Chiba, 1978-=-). In this work, we focus on Sakoe-Chiba band also used by Keogh (2002a) and Zhu & Shasha (2003). In Table 2, all but the faded-out cells correspond to a Sakoe-Chiba band which allows element qi to ma... |

424 | Fast subsequence matching in time-series databases
- Faloutsos, Ranganathan, et al.
- 1994
(Show Context)
Citation Context ... sales, sensor transmissions, telecommunication signals, medical and financial data. There is a need for efficient similarity search in databases of time sequences (Agrawal, Faloutsos, & Swami, 1993; =-=Faloutsos, Ranganathan, & Manolopoulos, 1994-=-; Goldin & Kanellakis, 1995; Moon, Whang, & Han, 2002; Keogh, 2002a; Kim, Park, and Chu, 2001; Yi, Jagadish, & Faloutsos, 1998; Zhu & Shasha, 2003), due to its wide use by data analysts. As a typical ... |

418 | Efficient similarity search in sequence databases
- Agrawal, Faloutsos, et al.
- 1993
(Show Context)
Citation Context ... avariety of domains, e.g., product sales, sensor transmissions, telecommunication signals, medical and financial data. There is a need for efficient similarity search in databases of time sequences (=-=Agrawal, Faloutsos, & Swami, 1993-=-; Faloutsos, Ranganathan, & Manolopoulos, 1994; Goldin & Kanellakis, 1995; Moon, Whang, & Han, 2002; Keogh, 2002a; Kim, Park, and Chu, 2001; Yi, Jagadish, & Faloutsos, 1998; Zhu & Shasha, 2003), due t... |

293 | Distance browsing in spatial databases
- Hjaltason, Samet
- 1999
(Show Context)
Citation Context ...4 shows a pseudo-code for the neighbor search algorithm, which is processed by employing the same filter and refinement steps in combination with the incremental nearest neighbor search algorithm of (=-=Hjaltason & Samet, 1999-=-), as suggested by the multi-step paradigm of Seidl & Kriegel (1998). A priority queue is used to organize R*-tree node entries and sequences �s based on their lower bounding distance from �q computed... |

237 | Exact indexing of dynamic time warping - Keogh, Ratanamahatana - 2005 |

231 | Locally adaptive dimensionality reduction for indexing large time series databases
- Keogh, Chakrabarti, et al.
(Show Context)
Citation Context ...tion of an approximation scheme that can provide improved bounds for DTW distance. Each data sequence �s ∈ S is decomposed into a small number of segments, using a dimensionality reduction technique (=-=Keogh et al., 2001-=-). We then apply aversion of DTW on the segmented approximations of the data and query sequences to compute fast tight lower bounds for DTW distance. Our technique resembles the segmented dynamic time... |

176 | Efficient retrieval of similar time sequences under time warping
- Yi, Jagadish, et al.
- 1998
(Show Context)
Citation Context ...abases of time sequences (Agrawal, Faloutsos, & Swami, 1993; Faloutsos, Ranganathan, & Manolopoulos, 1994; Goldin & Kanellakis, 1995; Moon, Whang, & Han, 2002; Keogh, 2002a; Kim, Park, and Chu, 2001; =-=Yi, Jagadish, & Faloutsos, 1998-=-; Zhu & Shasha, 2003), due to its wide use by data analysts. As a typical application, consider an investor who is interested in finding stocks that have similar behavior to a certain query stock. Sim... |

173 |
Using dynamic time warping to find patterns in time series
- Berndt, Clifford
- 1994
(Show Context)
Citation Context ... on these advantages, DTW has been widely used in different kinds of applications such as signature verification (Munich & Perona, 1999) and voice recognition (Rabiner & Juang, 1993). Recent studies (=-=Berndt & Clifford, 1994-=-; Chu, Keogh, and Pazzani, 2002; Keogh, 2002a; Kim, Park, and Chu, 2001; Yi, Jagadish, & Faloutsos, 1998; Zhu & Shasha, 2003) have adopted DTW for generic analysis and mining tasks on time series. How... |

169 | Optimal multi-step k-nearest neighbor search
- Seidl, Kriegel
- 1998
(Show Context)
Citation Context ...efly summarize previous work related to similarity search in time series databases using DTW. Due to the expensive computation of DTW, most approaches employ the multi-step query processing strategy (=-=Seidl & Kriegel, 1998-=-). A computationally cheap lower bounding function Lb(�q,�s) for DTW distance is defined, such that Lb(�q,�s) ≤ Ddtw(�q,�s). Let ɛ be the distance threshold for range similarity search or distance of ... |

99 | On similarity queries for time-series data: constraint specification and implementation
- Goldin, Kanellakis
- 1995
(Show Context)
Citation Context ...n signals, medical and financial data. There is a need for efficient similarity search in databases of time sequences (Agrawal, Faloutsos, & Swami, 1993; Faloutsos, Ranganathan, & Manolopoulos, 1994; =-=Goldin & Kanellakis, 1995-=-; Moon, Whang, & Han, 2002; Keogh, 2002a; Kim, Park, and Chu, 2001; Yi, Jagadish, & Faloutsos, 1998; Zhu & Shasha, 2003), due to its wide use by data analysts. As a typical application, consider an in... |

87 | Indexing multi-dimensional time-series with support for multiple distance measures
- Vlachos, Hadjieleftheriou, et al.
(Show Context)
Citation Context ...ueries, using the proposed bounds. 3.1. Sequence segmentation Our technique is based on the segmentation of each sequence into an Adaptive Piecewise Constant Approximation (APCA) (Keogh et al., 2001; =-=Vlachos et al., 2003-=-). APCA approximates a time sequence by a set of constant value segments of varying lengths such that their individual reconstruction errors are minimal. APCA is a better approximation than PAA, since... |

71 | Warping Indexes with Envelope Transforms for Query by Humming
- Zhu, Shasha
(Show Context)
Citation Context ..., Faloutsos, & Swami, 1993; Faloutsos, Ranganathan, & Manolopoulos, 1994; Goldin & Kanellakis, 1995; Moon, Whang, & Han, 2002; Keogh, 2002a; Kim, Park, and Chu, 2001; Yi, Jagadish, & Faloutsos, 1998; =-=Zhu & Shasha, 2003-=-), due to its wide use by data analysts. As a typical application, consider an investor who is interested in finding stocks that have similar behavior to a certain query stock. Similarity search is al... |

60 | Making time-series classification more accurate using learned constraints
- Ratanamahatana, Keogh
- 2004
(Show Context)
Citation Context ...osition in [i −x, i +x], where x =⌊w·max{|�q|, |�s|}⌋. Such constraints speed up the DTWs236 Y. SHOU, N. MAMOULIS AND D. W. CHEUNG distance calculation and prevent pathological warping (Keogh, 2002a; =-=Ratanamahatana & Keogh, 2004-=-), where a small section of one sequence maps onto a relatively large section of another. 2.2. Lower bounds and indices for DTW In this section, we briefly summarize previous work related to similarit... |

52 | Scaling up dynamic time warping to massive datasets - Keogh, Pazzani - 1999 |

47 |
The symmetric time warping algorithm: From continuous to discrete,” Time Warps
- Kruskall, Liberman
- 1983
(Show Context)
Citation Context ... �s of length m, dynamic time warping (DTW) aligns each element qi of �q to one or more elements s j of�s and vice versa. DTW is performed by applying dynamic programming on an n × m distance matrix (=-=Kruskall & Liberman, 1983-=-; Rabiner & Juang, 1993). Each cell (i, j)ofthe distance matrix DM contains the local distance d(qi, s j) = (qi − s j) 2 between elements qi of �q and s j of �s. Table 1 shows the distance matrix for ... |

46 | The UCR Time Series Data Mining Archive - Keogh, Folias |

40 | An Index-Based Approach for Similarity Search Supporting Time Warping in Large Sequence Databases
- Kim, Park, et al.
- 2001
(Show Context)
Citation Context ...t similarity search in databases of time sequences (Agrawal, Faloutsos, & Swami, 1993; Faloutsos, Ranganathan, & Manolopoulos, 1994; Goldin & Kanellakis, 1995; Moon, Whang, & Han, 2002; Keogh, 2002a; =-=Kim, Park, and Chu, 2001-=-; Yi, Jagadish, & Faloutsos, 1998; Zhu & Shasha, 2003), due to its wide use by data analysts. As a typical application, consider an investor who is interested in finding stocks that have similar behav... |

28 | Iterative deepening dynamic time warping for time series - Chu, Keogh, et al. - 2003 |

25 | Continuous dynamic time warping for translation-invariant curve alignment with applications to signature verification
- Munich, Perona
- 1999
(Show Context)
Citation Context ...re, it can be used to measure similarity between sequences of different lengths. Based on these advantages, DTW has been widely used in different kinds of applications such as signature verification (=-=Munich & Perona, 1999-=-) and voice recognition (Rabiner & Juang, 1993). Recent studies (Berndt & Clifford, 1994; Chu, Keogh, and Pazzani, 2002; Keogh, 2002a; Kim, Park, and Chu, 2001; Yi, Jagadish, & Faloutsos, 1998; Zhu & ... |

4 |
GeneralMatch: A Subsequence Matching Method in Time-Series Databases Based on Generalized Windows
- Moon, Whang, et al.
- 2002
(Show Context)
Citation Context ...ncial data. There is a need for efficient similarity search in databases of time sequences (Agrawal, Faloutsos, & Swami, 1993; Faloutsos, Ranganathan, & Manolopoulos, 1994; Goldin & Kanellakis, 1995; =-=Moon, Whang, & Han, 2002-=-; Keogh, 2002a; Kim, Park, and Chu, 2001; Yi, Jagadish, & Faloutsos, 1998; Zhu & Shasha, 2003), due to its wide use by data analysts. As a typical application, consider an investor who is interested i... |