Skip to main content
SpringerLink
Log in

Quantitative Expressions of Spatial Similarity in Multi-scale Map Spaces

  • Conference paper
  • First Online:
Advances in Cartography and GIScience (ICACI 2017)

Part of the book series: Lecture Notes in Geoinformation and Cartography ((ICA))

Included in the following conference series:

  • 1963 Accesses

Abstract

Spatial similarity plays an important role in automated map generalization , spatial computations, spatial reasoning , spatial retrieval and the construction of multi-scale spatial databases. Nevertheless, the features of spatial similarity relations have never been investigated systematically, yet. To fill the gap, this paper focuses on quantitative expressions of the features of spatial similarity relations in map spaces . It firstly summarizes and analyzes the features of similarity in other fields, such as computer science, psychology and geography; then it proposes a number of features of spatial similarity relations in map spaces, i.e., equality, minimality, auto-similarity, symmetry (reflectivity), non-transitivity, triangle inequality, and scale dependency. Mathematical expressions of the features are presented and explained. Finally, potential research issues in spatial similarity relations are reviewed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Belohlavek, R. (2000). Similarity relations in concept lattices. Journal of Logic and Computation, 10(6), 823–845.

    Article  Google Scholar 

  • Bronstein, A. M., Bronstein, M. M., Bruckstein, A. M., & Kimmel, R. (2009). Partial similarity of objects, or how to compare a centaur to a horse. International Journal of Computer Vision, 84(2), 163–183.

    Article  Google Scholar 

  • Cilibrasi, R., Vitanyi, P. (2006). Similarity of objects and the meaning of words. In Proceedings of the 3rd Annual Conference on Theory and Applications of Models of Computation (TAMC’06) (Vol. 3959, pp. 21–45). Lecture Notes in Computer Science.

    Google Scholar 

  • Douglas, D. H., & Peucker, T. K. (1973). Algorithms for the reduction of the number of points required to represent a digitised line or its caricature. Canadian Cartographer, 10(2), 112–122.

    Article  Google Scholar 

  • Du, S. H., Qin, Q. M., Wang, Q., & Ma, H. J. (2008). Reasoning about topological relations between regions with broad boundaries. International Journal of Approximate Reasoning, 47(2), 219–232.

    Article  Google Scholar 

  • Egenhofer, M., & Franzosa, R. (1991). Point-set topological spatial relations. International Journal of Geographical Information Systems, 5(2), 161–174.

    Article  Google Scholar 

  • Goldstone, R. L. (1994). Similarity, interactive activation and mapping. Journal of Experimental Psychology. Learning, Memory, and Cognition, 20(1), 3–28.

    Article  Google Scholar 

  • Goldstone, R. L. (2004). Similarity. In R. A. Wilson & F. C. Keil (Eds.), MIT encyclopedia of the cognitive sciences. MIT Press.

    Google Scholar 

  • Goyal, R. K. (2000). Similarity assessment for cardinal directions between extended spatial objects. PHD thesis, The University of Maine, USA.

    Google Scholar 

  • Hahn, U., Chater, N., & Richardson, L. B. (2003). Similarity as transformation. Cognition, 87(1), 1–32.

    Article  Google Scholar 

  • Hong, J. (1994). Qualitative distance and direction reasoning in geographic space. PHD thesis, University of Maine, USA.

    Google Scholar 

  • Larkey, L. B., & Markman, A. B. (2005). Processes of similarity judgment. Cognitive Science, 29, 1061–1076.

    Article  Google Scholar 

  • Li, B., & Fonseca, F. T. (2006). TDD—a comprehensive model for qualitative spatial similarity assessment. Spatial Cognition and Computation, 6(1), 31–62.

    Article  Google Scholar 

  • Markman, A. B. (1997). Constraints on analogical inference. Cognitive Science, 21(4), 373–418.

    Article  Google Scholar 

  • Medin, D. L., Goldstone, R. L., & Gentner, D. (1993). Respects for similarity. Psychological Review, 100(2), 254–278.

    Article  Google Scholar 

  • Peuquet, D. (1986). The use of spatial relationships to aid spatial database retrieval. In Proceedings of the 2nd International Symposium on Spatial Data Handling (SDH), Zurich, Switzerland.

    Google Scholar 

  • Rodríguez, A., & Egenhofer, M. (2003). Determining semantic similarity among entity classes from different ontologies. IEEE Transactions on Knowledge and Data Engineering, 15(2), 442–456.

    Article  Google Scholar 

  • Rodríguez, A., & Egenhofer, M. (2004). Comparing geospatial entity classes: An asymmetric and context-dependent similarity measure. International Journal of Geographical Information Science, 18(3), 229–256.

    Article  Google Scholar 

  • Ruas, A. (1998). A method for building displacement in automated map generalization. International Journal of Geographical Information Science, 12(8), 789–803.

    Article  Google Scholar 

  • Ruas, A. (2001). Automating the generalization of geographical data. In Proceedings of the 20th International Cartographic Conference, Beijing, China, 1943–1953.

    Google Scholar 

  • Shepard, R. N. (1962). The analysis of proximities: Multidimensional scaling with an unknown distance function. International Psychometrika, 27(2), 125–140.

    Article  Google Scholar 

  • Tversky, A. (1977). Features of similarity. Psychological Review, 84(4), 327–352.

    Article  Google Scholar 

  • Wang, J. Y. (1993). Principles of general map generalization. Beijing: Surveying and Mapping Press. (in Chinese).

    Google Scholar 

  • Weibel, R., & Jones, C. B. (1998). Computational perspectives on map generalization. GeoInformatica, 2(4), 307–314.

    Article  Google Scholar 

  • Yan, H. W. (2010). Fundamental theories of spatial similarity relations in multi-scale map spaces. Chinese Geographical Sciences, 20(1), 18–22.

    Article  Google Scholar 

  • Yan, H. W. (2015). Quantitative relations of spatial similarity degree and map scale change of individual linear objects in multi-scale map spaces. GeoCarto International, 30(4), 472–482.

    Article  Google Scholar 

  • Yan, H. W., Chu, Y. D., Li, Z. L., & Guo, R. Z. (2006). A quantitative direction description model based on direction groups. Geoinformatica, 10(2), 177–196.

    Article  Google Scholar 

  • Yan, H. W., Li, J. (2014). Spatial similarity relations in multi-scale map spaces. Springer International Publishing Switzerland.

    Google Scholar 

  • Yan, H. W., Shen, Y. Z., & Li, J. (2016). Approach to calculating spatial similarity degrees of the same river basin networks on multi-scale maps. GeoCarto International, 31(7), 765–782.

    Article  Google Scholar 

Download references

Acknowledgements

The work described in this paper is funded by the Natural Science Foundation Committee, China (No. 41371435; No. 71563025).

Author information

Authors and Affiliations

  1. Department of GIS, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Haowen Yan, Liming Zhang & Zhonghui Wang

  2. Gansu Provincial Engineering Laboratory for National Geographic State Monitoring, Lanzhou, 730070, China

    Weifang Yang, Tao Liu & Liang Zhou

Authors
  1. Haowen Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liming Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhonghui Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Weifang Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Liang Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haowen Yan .

Editor information

Editors and Affiliations

  1. Department of Geography and Geology, University of Nebraska Omaha, Omaha, Nebraska, USA

    Michael P. Peterson

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Yan, H., Zhang, L., Wang, Z., Yang, W., Liu, T., Zhou, L. (2017). Quantitative Expressions of Spatial Similarity in Multi-scale Map Spaces. In: Peterson, M. (eds) Advances in Cartography and GIScience. ICACI 2017. Lecture Notes in Geoinformation and Cartography(). Springer, Cham. https://doi.org/10.1007/978-3-319-57336-6_28

Download citation

Publish with us

Policies and ethics

Search

Navigation