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## Discovering similar multidimensional trajectories (2002)

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### Other Repositories/Bibliography

Venue: | In ICDE |

Citations: | 260 - 6 self |

### Citations

4843 |
Pattern Classification and Scene Analysis
- Duda, Hart
- 1973
(Show Context)
Citation Context ...utomatic classification of trajectories using Nearest Neighbor Classification. It has been shown that the one nearest neighbor rule has asymptotic error rate that is at most twice the Bayes error rate=-=[12]-=-. So, the problem is: given a database ¦ of trajectories and a query § (not already in the database), we want to find the trajectory that is closest § to . We need to define the following: 1. A realis... |

787 | Dynamic programming algorithm optimization for spoken word recognition
- Salkoe, Chiba
- 1978
(Show Context)
Citation Context ...ended and indexed this distance metric [2, 37, 18, 14, 10, 32, 10, 20, 24, 23]. Another approach is based on the time warping technique that first has been used to match signals in speech recognition =-=[33]-=-. Berndt and Clifford [5] proposed to use this technique to measure the similarity of time-series data in data mining. Recent works have also used this similarity measure [25, 28]. A similar technique... |

641 | Similarity search in high dimensions via hashing. In
- Gionis, Indyk, et al.
- 1999
(Show Context)
Citation Context ...���§� ¨§¦ � ¨¤£ ¤©¨�� ¨�© ¤ � � � ¤ � � � . For © it is the well known Euclidean distance and fors� the Manhattan distance. Various approaches have used, �s� extended and indexed this distance metric =-=[2, 37, 18, 14, 10, 32, 10, 20, 24, 23]-=-. Another approach is based on the time warping technique that first has been used to match signals in speech recognition [33]. Berndt and Clifford [5] proposed to use this technique to measure the si... |

623 | A quantitative analysis and performance study for similarity-search methods in high dimensional spaces, in:
- Weber, Schek, et al.
- 1998
(Show Context)
Citation Context ...ing power increases along with the database size. ity of the trajectories have almost the same distance to the query. This behavior follows again the same pattern of high dimensional indexing methods =-=[6, 36]-=-. The last experiment evaluates the index performance, over sets of trajectories with increasing cardinality. We indexed from � to ����� �¢¡ trajectories. The pruning power ����� of the inequality is ... |

533 | Fast sub-sequence matching in time-series databases”.
- Faloutsos, Ranganathan, et al.
- 1994
(Show Context)
Citation Context ...ximate methods to compute the similarity. In another recent work, Lee et al. [27] propose methods to index sequences of multidimensional points. They extend the ideas presented by Faloutsos et al. in =-=[15]-=- and the similarity model is based on the Euclidean distance. A recent work that proposes a method to cluster trajectory data is due to Gaffney and Smyth [16]. They use a variation of the EM (expectat... |

515 | Efficient similarity search in sequence databases
- Agrawal, Faloutsos, et al.
- 1993
(Show Context)
Citation Context ...���§� ¨§¦ � ¨¤£ ¤©¨�� ¨�© ¤ � � � ¤ � � � . For © it is the well known Euclidean distance and fors� the Manhattan distance. Various approaches have used, �s� extended and indexed this distance metric =-=[2, 37, 18, 14, 10, 32, 10, 20, 24, 23]-=-. Another approach is based on the time warping technique that first has been used to match signals in speech recognition [33]. Berndt and Clifford [5] proposed to use this technique to measure the si... |

502 | FastMap: A fast algorithm for indexing, data-mining and visualization of traditional and multimedia databases
- Faloutsos, Lin
- 1995
(Show Context)
Citation Context ...���§� ¨§¦ � ¨¤£ ¤©¨�� ¨�© ¤ � � � ¤ � � � . For © it is the well known Euclidean distance and fors� the Manhattan distance. Various approaches have used, �s� extended and indexed this distance metric =-=[2, 37, 18, 14, 10, 32, 10, 20, 24, 23]-=-. Another approach is based on the time warping technique that first has been used to match signals in speech recognition [33]. Berndt and Clifford [5] proposed to use this technique to measure the si... |

408 | When is ”nearest neighbor” meaningful?,
- Beyer, Goldstein, et al.
- 1999
(Show Context)
Citation Context ...of clusters increased the performance of the algorithm improved considerably. This behavior is expected and it is similar to the behavior of recent proposed index structures for high dimensional data =-=[9, 6, 21]-=-. On the other hand if the dataset has no clusters, the performance of the algorithm degrades, since the majorAv. Correct Clusterings (out of 45) 45 30 14 10 1 0.95 0.9 Sample size 0.85 0.8 0.75 0.4 0... |

389 | Indexing the positions of continuously moving objects.
- Saltenis, Jensen, et al.
- 2000
(Show Context)
Citation Context ...c models which are not easy to find and describe in real datasets. Lately, there has been some work on indexing moving objects to answer spatial proximity queries (range and nearest neighbor queries) =-=[26, 1, 34]-=-. Also in [30], Pfoser et al. present index methods to answer topological and navigational queries in a database that stores trajectories of moving objects. However these works do not consider a globa... |

316 | Locally adaptive dimensionality reduction for indexing large time series databases.
- Keogh, Chakrabarti, et al.
- 2001
(Show Context)
Citation Context |

281 |
Using Dynamic Time Warping to Find Patterns in Time Series.
- Berndt, Clifford
- 1994
(Show Context)
Citation Context ...ing algorithm � in � � time. However we only allow matchings when the ¨�� difference in the indices is � at most , and this allows the use of a faster algorithm. The following lemma has been shown in =-=[5]-=-, [11]. Lemma 1 Given two � trajectories � and , � ������� with � ����� � and , we can finds¡¤£ £ � � ��¨�������� the in � � ¨���¨�� ��� time. � � If is small, the dynamic programming algorithm is ver... |

236 | Fast Similarity Search in the Presence of Noise, Scaling and Translation in Time-Series Databases.
- Agrawal, Lin, et al.
- 1995
(Show Context)
Citation Context ... also used this similarity measure [25, 28]. A similar technique is to find the longest common subsequence (s¡¤£¥£ ) of two sequences and then define the distance using the length of this subsequence =-=[3, 7, 11]-=-. The shows how well the two sequences can match one ¡¤£¥£sanother if we are allowed to stretch them but we cannot rearrange the sequence of values. Since the values are real numbers, we typically all... |

217 | On Indexing Mobile Objects.
- Kollios, Gunopulos, et al.
- 1999
(Show Context)
Citation Context ...c models which are not easy to find and describe in real datasets. Lately, there has been some work on indexing moving objects to answer spatial proximity queries (range and nearest neighbor queries) =-=[26, 1, 34]-=-. Also in [30], Pfoser et al. present index methods to answer topological and navigational queries in a database that stores trajectories of moving objects. However these works do not consider a globa... |

184 | Indexing moving points.
- Agarwal, Arge, et al.
- 2000
(Show Context)
Citation Context ...c models which are not easy to find and describe in real datasets. Lately, there has been some work on indexing moving objects to answer spatial proximity queries (range and nearest neighbor queries) =-=[26, 1, 34]-=-. Also in [30], Pfoser et al. present index methods to answer topological and navigational queries in a database that stores trajectories of moving objects. However these works do not consider a globa... |

183 |
Fast Time Sequence Indexing for Arbitrary Lp Norms.
- Yi, Faloutsos
- 2000
(Show Context)
Citation Context |

135 |
Novel approaches in query processing for moving object trajectories.
- Pfoser, Jensen, et al.
- 2000
(Show Context)
Citation Context ...t easy to find and describe in real datasets. Lately, there has been some work on indexing moving objects to answer spatial proximity queries (range and nearest neighbor queries) [26, 1, 34]. Also in =-=[30]-=-, Pfoser et al. present index methods to answer topological and navigational queries in a database that stores trajectories of moving objects. However these works do not consider a global similarity m... |

123 | Trajectory clustering with mixtures of regression models.
- Gaffney, Smyth
- 1999
(Show Context)
Citation Context ...he ideas presented by Faloutsos et al. in [15] and the similarity model is based on the Euclidean distance. A recent work that proposes a method to cluster trajectory data is due to Gaffney and Smyth =-=[16]-=-. They use a variation of the EM (expectation maximization) algorithm to cluster small sets of trajectories. However, their method is a model based approach that usually has scalability problems. Also... |

119 | Local dimensionality reduction: A new approach to indexing high dimensional spaces
- Chakrabarti, Mehrotra
(Show Context)
Citation Context ...of clusters increased the performance of the algorithm improved considerably. This behavior is expected and it is similar to the behavior of recent proposed index structures for high dimensional data =-=[9, 6, 21]-=-. On the other hand if the dataset has no clusters, the performance of the algorithm degrades, since the majorAv. Correct Clusterings (out of 45) 45 30 14 10 1 0.95 0.9 Sample size 0.85 0.8 0.75 0.4 0... |

100 | Mobile computing and databases - a survey.
- Barbara
- 1999
(Show Context)
Citation Context ...ces in mobile computing, sensor and GPS technology have made it possible to collect large amounts of spatiotemporal data and there is increasing interest to perform data analysis tasks over this data =-=[4]-=-. For example, in mobile computing, users equipped with George Kollios Boston University gkollios@cs.bu.edu Dimitrios Gunopulos UC Riverside dg@cs.ucr.edu mobile devices move in space and register the... |

100 | Finding Similar Time Series.
- Das, Gunopulos, et al.
- 1997
(Show Context)
Citation Context ...lgorithm � in � � time. However we only allow matchings when the ¨�� difference in the indices is � at most , and this allows the use of a faster algorithm. The following lemma has been shown in [5], =-=[11]-=-. Lemma 1 Given two � trajectories � and , � ������� with � ����� � and , we can finds¡¤£ £ � � ��¨�������� the in � � ¨���¨�� ��� time. � � If is small, the dynamic programming algorithm is very effi... |

91 | Landmarks: a New Model for Similarity-based Pattern Querying in Time Series Databases.
- Perng, Wang, et al.
- 2000
(Show Context)
Citation Context .... In [7, 11] fast probabilistic algorithms to compute thes¡¤£¥£ of two time series are presented. Other techniques to define time series similarity are based on extracting certain features (Landmarks =-=[29]-=- or signatures [13]) from each time-series and then use these features to define the similarity. An interesting approach to represent a time series using the direction of the sequence at regular time ... |

84 | Scaling up Dynamic Time Warping for Datamining Applications. In
- Keogh, Pazzani
- 2000
(Show Context)
Citation Context ... Y parameters and collected 5 recordings of the following 10 words: ’Norway’, ’cold’, ’crazy’, ’eat’, ’forget’, ’happy’, ’innocent’, ’later’, ’lose’, ’spend’. This is the experiment conducted also in =-=[25]-=- (but there only one dimension was used). Examples of this dataset can be seen in figure 6. � http://kdd.ics.uci.edusDistance Function Time (sec) Correct Clusterings (out of 10) Complete Linkage Eucli... |

74 | Similaritybased queries.
- Jagadish, Mendelzon, et al.
- 1995
(Show Context)
Citation Context ...interesting alternative approach for sequence similarity that is based on probabilistic matching. A domain independent framework for defining queries in terms of similarity of objects is presented in =-=[22]-=-. Note that all the above work deals mainly with one dimensional time-series. The most related paper to our work is the Bozkaya et al. [8]. They discuss how to define similarity measures for sequences... |

72 | Deformable markov model templates for time-series pattern matching,’ in KDD,
- Smyth
- 2000
(Show Context)
Citation Context ...d then use these features to define the similarity. An interesting approach to represent a time series using the direction of the sequence at regular time intervals is presented in [31]. Ge and Smyth =-=[17]-=- present an interesting alternative approach for sequence similarity that is based on probabilistic matching. A domain independent framework for defining queries in terms of similarity of objects is p... |

60 | Similarity Search for Multidimensional Data Sequences.
- Lee, Chun, et al.
- 2000
(Show Context)
Citation Context ...on sequences of feature vectors extracted from images and not trajectories and they do not discuss transformations or approximate methods to compute the similarity. In another recent work, Lee et al. =-=[27]-=- propose methods to index sequences of multidimensional points. They extend the ideas presented by Faloutsos et al. in [15] and the similarity model is based on the Euclidean distance. A recent work t... |

57 | Variable length queries for time series data. In
- Kahveci, Singh
- 2001
(Show Context)
Citation Context |

56 |
Fast Time-Series Searching with Scaling and Shifting.
- Chu, Wong
- 1999
(Show Context)
Citation Context |

49 | Efficient Searches for Similar Subsequences of Different Lengths in Sequence Databases.
- Park, Chu, et al.
- 2000
(Show Context)
Citation Context ...ls in speech recognition [33]. Berndt and Clifford [5] proposed to use this technique to measure the similarity of time-series data in data mining. Recent works have also used this similarity measure =-=[25, 28]-=-. A similar technique is to find the longest common subsequence (s¡¤£¥£ ) of two sequences and then define the distance using the length of this subsequence [3, 7, 11]. The shows how well the two sequ... |

43 | Matching and Indexing Sequences of Different Lengths.
- Bozkaya, Yazdani, et al.
- 1997
(Show Context)
Citation Context ...ng queries in terms of similarity of objects is presented in [22]. Note that all the above work deals mainly with one dimensional time-series. The most related paper to our work is the Bozkaya et al. =-=[8]-=-. They discuss how to define similarity measures for sequences of multidimensional points using a restricted version of the edit distance which is equivalent to thes¢¡¤¡¤£ . Also, they present two eff... |

40 | TimeSeries Similarity Problems and Well-Separated Geometric Sets.
- Bollobas, Das, et al.
- 1997
(Show Context)
Citation Context ... also used this similarity measure [25, 28]. A similar technique is to find the longest common subsequence (s¡¤£¥£ ) of two sequences and then define the distance using the length of this subsequence =-=[3, 7, 11]-=-. The shows how well the two sequences can match one ¡¤£¥£sanother if we are allowed to stretch them but we cannot rearrange the sequence of values. Since the values are real numbers, we typically all... |

38 | Supporting Fast Search in Time Series for Movement Patterns in Multiple Scales.
- Qu, Wang, et al.
- 1998
(Show Context)
Citation Context ...each time-series and then use these features to define the similarity. An interesting approach to represent a time series using the direction of the sequence at regular time intervals is presented in =-=[31]-=-. Ge and Smyth [17] present an interesting alternative approach for sequence similarity that is based on probabilistic matching. A domain independent framework for defining queries in terms of similar... |

37 |
When is "nearest neighbor" meaningful
- Beyer, Goldstein, et al.
- 1998
(Show Context)
Citation Context ...of clusters increased the performance of the algorithm improved considerably. This behavior is expected and it is similar to the behavior of recent proposed index structures for high dimensional data =-=[9, 6, 21]-=-. On the other hand if the dataset has no clusters, the performance of the algorithm degrades, since the majority of the trajectories have almost the same distance to the query. This behavior follows ... |

36 | Signature technique for similarity-based queries.
- Faloutsos, Jagadish, et al.
- 1997
(Show Context)
Citation Context ...robabilistic algorithms to compute thes¡¤£¥£ of two time series are presented. Other techniques to define time series similarity are based on extracting certain features (Landmarks [29] or signatures =-=[13]-=-) from each time-series and then use these features to define the similarity. An interesting approach to represent a time series using the direction of the sequence at regular time intervals is presen... |

29 |
Contrast plots and psphere trees: Space vs. time in nearest neighbour searches.
- Goldstein, Ramakrishnan
- 2000
(Show Context)
Citation Context ...of clusters increased the performance of the algorithm improved considerably. This behavior is expected and it is similar to the behavior of recent proposed index structures for high dimensional data =-=[9, 6, 21]-=-. On the other hand if the dataset has no clusters, the performance of the algorithm degrades, since the majorAv. Correct Clusterings (out of 45) 45 30 14 10 1 0.95 0.9 Sample size 0.85 0.8 0.75 0.4 0... |

25 | Querying Time Series Data Based on Similarity.
- Rafiei, Mendelzon
- 2000
(Show Context)
Citation Context |

18 | The Camera Mouse: Preliminary investigation of automated visual tracking for computer access.
- Gips, Betke, et al.
- 2000
(Show Context)
Citation Context ... tracking data. The 2D time series obtained represent the X and Y position of a human tracking feature (e.g. tip of finger). In conjuction with a ”spelling program” the user can ”write” various words =-=[19]-=-. We used 3 recordings of 5 different words. The data correspond to the following words: ’athens’, ’berlin’, ’london’, ’boston’, ’paris’. The average length of the series is around 1100 points. The sh... |

11 |
On Similarity Queries for TimeSeries Data.
- Goldin, Kanellakis
- 1995
(Show Context)
Citation Context |

4 |
Indexing similar trajectories.
- Vlachos
- 2001
(Show Context)
Citation Context ...thes¢¡¤£¥£ � � on � � and . We can show that, with high probability, the result of the algorithm over the samples, is a good approximation of the actual value. We describe this technique in detail in =-=[35]-=-. 3.2 Computing the similarity function £¡sWe now consider the more complex similarity function £¡s. Here, given two ����� sequences , and ����� constants , we have to find the ��� � � translation tha... |