## Efficient time series matching by wavelets (1999)

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Venue: | Proc. of 15th Int'l Conf. on Data Engineering |

Citations: | 217 - 1 self |

### BibTeX

@INPROCEEDINGS{Chan99efficienttime,

author = {Kin-pong Chan and Ada Wai-chee Fu},

title = {Efficient time series matching by wavelets},

booktitle = {Proc. of 15th Int'l Conf. on Data Engineering},

year = {1999},

pages = {126--133}

}

### Years of Citing Articles

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### Abstract

Time series stored as feature vectors can be indexed by multidimensional index trees like R-Trees for fast retrieval. Due to the dimensionality curse problem, transformations are applied to time series to reduce the number of dimensions of the feature vectors. Different transformations like Discrete Fourier Transform (DFT), Discrete Wavelet Transform (DWT), Karhunen-Loeve (K-L) transform or Singular Value Decomposition (SVD) can be applied. While the use of DFT and K-L transform or SVD have been studied in the literature, to our knowledge, there is no in-depth study on the application of DWT. In this paper, we propose to use Haar Wavelet Transform for time series indexing. The major contributions are: (1) we show that Euclidean distance is preserved in the Haar transformed domain and no false dismissal will occur, (2) we show that Haar transform can outperform DFT through experiments, (3) a new similarity model is suggested to accommodate vertical shift of time series, and (4) a two-phase method is proposed for efficient-nearest neighbor query in time series databases. 1.

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(Show Context)
Citation Context ...is used to support efficient retrieval and matching of time series. Some important factors have to be considered: The first factor is dimensionality reduction. Many multi-dimensional indexing methods =-=[13, 7, 5, 20]-=- such as the R-Tree and R*-Tree [20, 5, 11] scale exponentially for high dimensionalities, eventually reducing the performance to that of sequential scanning or worse. Hence, transformation is applied... |

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Citation Context ...is used to support efficient retrieval and matching of time series. Some important factors have to be considered: The first factor is dimensionality reduction. Many multi-dimensional indexing methods =-=[13, 7, 5, 20]-=- such as the R-Tree and R*-Tree [20, 5, 11] scale exponentially for high dimensionalities, eventually reducing the performance to that of sequential scanning or worse. Hence, transformation is applied... |

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Citation Context ...tem by Haar [21] is an important milestone. Haar basis is still a foundation of modern wavelet theory. Another significant advance is the introduction of a nonorthogonal basis by Dennis Gabor in 1946 =-=[16]-=-. In this work we shall advocate the use of the Haar wavelets in the problem of time series retrieval. 3. The Proposed Approach Following a trend in the disciplines of signal and image processing, we ... |

543 | The X-Tree: An Index Structure for High-Dimensional Data
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Citation Context ...is used to support efficient retrieval and matching of time series. Some important factors have to be considered: The first factor is dimensionality reduction. Many multi-dimensional indexing methods =-=[13, 7, 5, 20]-=- such as the R-Tree and R*-Tree [20, 5, 11] scale exponentially for high dimensionalities, eventually reducing the performance to that of sequential scanning or worse. Hence, transformation is applied... |

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Citation Context ...or Query For nearest neighbor query, we propose a two-phase evaluation as follows. ffl Phase 1 In the first phase, n nearest neighbors of query ~q are found in the R-Tree index using the algorithm in =-=[25]-=-. The Euclidean distances D in time domain (full dimension) are computed between the query sequence and all n nearest neighbors obtained which are D(~q; ~ nn 1 i ), where ~ nn 1 i denotes the nearest ... |

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Citation Context ... dynamically adjusts the range by the property of Euclidean distance preservation of the wavelet transformation. 2. Related Work Discrete Fourier Transform (DFT) is often used for dimension reduction =-=[2, 15]-=- to achieve efficient indexing. An index built by means of DFT is also called an F-index [2]. Suppose the DFT of a time sequence~x is denoted by ~ X . For many applications such as stock data, the low... |

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Citation Context ...es leads to other problems. While large pieces reduce the power of multi-resolution, small pieces has weakness in modeling low frequencies. Wavelet Transform (WT), or Discrete Wavelet Transform (DWT) =-=[9, 18]-=- has been found to be effective in replacing DFT in many applications in computer graphics, image [26], speech [1] , and signal processing [6, 4]. We propose to apply this technique in time series for... |

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Citation Context ...ature of the time series. It is believed that only brown noise or random walks exists in real signals. In particular, stock movements and exchange rates can be modeled successfully as random walks in =-=[10]-=-, for which a skewed energy spectrum can be obtained. Discrete Fourier Transform (DFT) has been one of the most commonly used techniques. One problem with DFT is that it misses the important feature o... |

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Citation Context ...st with DFT where only frequency components are considered. The origin of wavelets can be traced to the work of Karl Weierstrass [27] in 1873. The construction of the first orthonormal system by Haar =-=[21]-=- is an important milestone. Haar basis is still a foundation of modern wavelet theory. Another significant advance is the introduction of a nonorthogonal basis by Dennis Gabor in 1946 [16]. In this wo... |

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Citation Context ...es leads to other problems. While large pieces reduce the power of multi-resolution, small pieces has weakness in modeling low frequencies. Wavelet Transform (WT), or Discrete Wavelet Transform (DWT) =-=[9, 18]-=- has been found to be effective in replacing DFT in many applications in computer graphics, image [26], speech [1] , and signal processing [6, 4]. We propose to apply this technique in time series for... |

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Citation Context ...oints themselves. When a query arrives, all MBRs that intersect the query region are retrieved and their trails are matched. New similarity models are applied to F-index based time series matching in =-=[24]-=-. It achieves time warping, moving average, and reversing by applying transformations to feature points in the frequency domain. Given a query ~q, a new index is built by applying a transformation to ... |

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Citation Context ...kness in modeling low frequencies. Wavelet Transform (WT), or Discrete Wavelet Transform (DWT) [9, 18] has been found to be effective in replacing DFT in many applications in computer graphics, image =-=[26]-=-, speech [1] , and signal processing [6, 4]. We propose to apply this technique in time series for dimension reduction and content-based search. DWT is a discrete version of WT for numerical signal. A... |

108 | Efficiently supporting ad hoc queries in large datasets of time sequences
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Citation Context ...que in time series for dimension reduction and content-based search. DWT is a discrete version of WT for numerical signal. Although the potential application of DWT in this problem was pointed out in =-=[22]-=-, no further investigation has been reported to our knowledge. Hence, it is of value to conduct studies and evaluations on time series retrieval and matching by means of wavelets. The advantage of usi... |

95 |
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Citation Context ...sequence and simple coding, and (3) it preserves Euclidean distance (see Section 3.3). The formal definition of Haar wavelets is given in Appendix A. Concrete mathematical foundations can be found in =-=[9, 19]-=- and related implementations in [14]. Haar transform can be seen as a series of averaging and differencing operations on a discrete time function. We compute the average and difference between every t... |

92 |
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Citation Context ...t Transform (WT), or Discrete Wavelet Transform (DWT) [9, 18] has been found to be effective in replacing DFT in many applications in computer graphics, image [26], speech [1] , and signal processing =-=[6, 4]-=-. We propose to apply this technique in time series for dimension reduction and content-based search. DWT is a discrete version of WT for numerical signal. Although the potential application of DWT in... |

29 | Abbadi, "Efficient Retrieval for Browsing Large Image Databases
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(Show Context)
Citation Context ...se Haar wavelet transform and DWT interchangeably throughout this paper, unless specified particularly. Another method that has been employed for dimension reduction is Karhunen-Loeve (K-L) transform =-=[28]-=-. (This method is also known as Singular Value Decomposition (SVD) [22], and is called Principle Component analysis in statistical literature.) Given a collection of n-dimensional points, we project t... |

15 | Discrete wavelet transforms: Theory and implementation
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(Show Context)
Citation Context ...preserves Euclidean distance (see Section 3.3). The formal definition of Haar wavelets is given in Appendix A. Concrete mathematical foundations can be found in [9, 19] and related implementations in =-=[14]-=-. Haar transform can be seen as a series of averaging and differencing operations on a discrete time function. We compute the average and difference between every two adjacent values of f(x). The proc... |

10 |
Arun Swami â€œEfficient similarity search in sequence databases
- Agrawal, Faloutsos
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(Show Context)
Citation Context ...for efficient n-nearest neighbor query in time series databases. 1. Introduction Time series data are of growing importance in many new database applications, such as data warehousing and data mining =-=[3, 8, 2, 12]-=-. A time series (or time sequence) is a sequence of real numbers, each number representing a value at a time point. Typical examples include stock prices or currency exchange rates, biomedical measure... |

8 |
Enhanced nearest neighbor search on the R-tree
- Cheung, Fu
- 1998
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Citation Context ...ching of time series. Some important factors have to be considered: The first factor is dimensionality reduction. Many multi-dimensional indexing methods [13, 7, 5, 20] such as the R-Tree and R*-Tree =-=[20, 5, 11]-=- scale exponentially for high dimensionalities, eventually reducing the performance to that of sequential scanning or worse. Hence, transformation is applied to map the time sequences to a new feature... |

3 |
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(Show Context)
Citation Context ...ling low frequencies. Wavelet Transform (WT), or Discrete Wavelet Transform (DWT) [9, 18] has been found to be effective in replacing DFT in many applications in computer graphics, image [26], speech =-=[1]-=- , and signal processing [6, 4]. We propose to apply this technique in time series for dimension reduction and content-based search. DWT is a discrete version of WT for numerical signal. Although the ... |

2 |
An efficient hashbased algorithm for sequencedata searching
- Chu, Lam, et al.
- 1999
(Show Context)
Citation Context ...for efficient n-nearest neighbor query in time series databases. 1. Introduction Time series data are of growing importance in many new database applications, such as data warehousing and data mining =-=[3, 8, 2, 12]-=-. A time series (or time sequence) is a sequence of real numbers, each number representing a value at a time point. Typical examples include stock prices or currency exchange rates, biomedical measure... |