## Rough Sets in Spatio-Temporal Data Mining (0)

Venue: | International Workshop on Temporal, Spatial, and Spatio-Temporal Data Mining, volume 2007 of Lecture |

Citations: | 4 - 2 self |

### BibTeX

@INPROCEEDINGS{Bittner_roughsets,

author = {Thomas Bittner},

title = {Rough Sets in Spatio-Temporal Data Mining},

booktitle = {International Workshop on Temporal, Spatial, and Spatio-Temporal Data Mining, volume 2007 of Lecture},

year = {},

pages = {89--104},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

. In this paper I define spatio-temporal regions as pairs consisting of a spatial and a temporal component and I define topological relations between them. Using the notion of rough sets I define approximations of spatio-temporal regions and relations between those approximations. Based on relations between approximated spatio-temporal regions configurations of spatio-temporal objects can be characterized even if only approximate descriptions of the objects forming them are available. 1 Introduction Rough set theory [Paw82] provides a way of approximating subsets of a set when the set is equipped with a partition or equivalence relation. Rough sets were extensively used in the context of Data Mining, e.g., [Lin95,LC97]. So far, however, they were used mainly in non spatio-temporal contexts, for example, in order to classify and analyze phenomena, like diseases, given a finite number of observations or symptoms, e.g., [NSR92,BNSNT + 95]. It is the purpose of this paper to apply rough...

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Citation Context ...ply them to temporal and spatio-temporal regions afterwards. 3.1 Relations between regions of (2D) space Given two regions x and y the boundary insensitive binary topological relation (RCC5 relations =-=[RCC92]-=-) between them can be determined by considering the triple of boolean values [BS00]: (x ^ y 6= ?; x ^ y = x; x ^ y = y): 3 This implies an ontology of absolute space and time, i.e., regions do not cha... |

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Citation Context ...spatio-temporal regions configurations of spatio-temporal objects can be characterized even if only approximate descriptions of the objects forming them are available. 1 Introduction Rough set theory =-=[Paw82]-=- provides a way of approximating subsets of a set when the set is equipped with a partition or equivalence relation. Rough sets were extensively used in the context of Data Mining, e.g., [Lin95,LC97].... |

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Citation Context ...ject and the case of the object covering a region which intuitively implies the region to be smaller than the object. 2 Notice that this implies a four dimensional ontology of spatio-temporal objects =-=[Sim87]-=- 2-dimensional plane. In the remainder I concentrate on regions of time and space and topological relations between them. Spatio-temporal objects may be at rest, i.e., being located in the same region... |

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Citation Context ...ns they occupy. Unfortunately, it is often impossible to identify the region of space and time those objects exactly occupy, i.e., the exact location of spatio-temporal objects is often indeterminate =-=[BF95]-=-. [Bit99] argued that often approximate location of spatial objects is known. The notion of approximate location is based on the notion of rough sets, i.e., the approximation of (exact) location with ... |

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Citation Context ... of the underlying definitions. In order to generate all remaining pairs approximations of time intervals in regional partitions consisting of at least three elements need to be considered. A Haskell =-=[Tho99]-=- program generating all remaining pairs of relations between approximations with respect to a partition consisting of three intervals can be found at [Bit00b]. 5.3 Semantic generalization of relations... |

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Citation Context ...regions. In the domain of approximation functions the meet operation between regions is approximated by pairs of greatest minimal, ^ , and least maximal, ^ , meet operations on approximation mappings =-=[BS98]-=-. Consider the operations ^ and ^ on the set 3 = ffo; po; nog that are defined as follows: ^ no po fo no no no no po no no po fo no po fo ^ no po fo no no no no po no po po fo no po fo These operation... |

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Citation Context ...ferent regions of space at each moment of time 3 . Spatial change may be continuous, i.e., regions of consecutive moments of time are topologically close as in the case of change of bona-fide objects =-=[SV97]-=- like cars, planets, and human beings, or discontinuous, as (sometimes) in the case of change of fiat objects [SV97] like land property. Consider an object at rest. I assume that the exact region of a... |

22 |
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Citation Context ...ns they occupy. Unfortunately, it is often impossible to identify the region of space and time those objects exactly occupy, i.e., the exact location of spatio-temporal objects is often indeterminate =-=[BF95]-=-. [Bit99] argued that often approximate location of spatial objects is known. The notion of approximate location is based on the notion of rough sets, i.e., the approximation of (exact) location with ... |

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(Show Context)
Citation Context ... spatio-temporal objects Binary topological relations between regions such as overlap, contained/containing, disjoint, are well known in the spatial reasoning community, e.g., [EF91,RCC92]. Recently, =-=[BS00]-=- proposed a specific style that allows to define binary topological relations between regions exclusively based on constraints regarding the outcome of the meet (intersection) operation, denoted by ^,... |

7 |
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Citation Context ...occupy. Unfortunately, it is often impossible to identify the region of space and time those objects exactly occupy, i.e., the exact location of spatio-temporal objects is often indeterminate [BF95]. =-=[Bit99]-=- argued that often approximate location of spatial objects is known. The notion of approximate location is based on the notion of rough sets, i.e., the approximation of (exact) location with respect t... |

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6 |
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Citation Context ...bounded by the time instances (points) t 1 and t 2 . Since time is a totally ordered set of time points (the set of all possible boundaries of time intervals) forming a directed one-dimensional space =-=[Gea66]-=-, we have t 1s2 . In this paper time is modeled as a one dimensional directed line and space is modeled as a 1 We say that the object x is located in the (spatial, temporal or spatio-temporal) region ... |

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1 |
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(Show Context)
Citation Context ... elements need to be considered. A Haskell [Tho99] program generating all remaining pairs of relations between approximations with respect to a partition consisting of three intervals can be found at =-=[Bit00b]-=-. 5.3 Semantic generalization of relations between temporal intervals At the semantic level we consider how syntactically generated pairs, (R 9 (X; Y ); R 9 (X; Y )) 7 , relate to relations between th... |

1 | Assessment of scene similarity - Egenhofer, Flewelling, et al. - 1997 |