Advertisement

Many Connected Components

Chapter
  • 820 Downloads
Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)

Abstract

This chapter presents different ways of handling the first challenge of summarizing spatial network data, i.e., the large number of k-subsets of connected components in the network. This challenge is conceptualized as the spatial network activity summarization problem (SNAS) where given a spatial network, a collection of activities and their locations (e.g., placed on a node or an edge), and a desired number of paths k, SNAS finds a set of k shortest paths that maximizes the sum of activities on the paths (counting activities that are on overlapping paths only once) and a partitioning of activities across the paths.

Keywords

Short Path Active Node Transportation Planning Computational Structure Spatial Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Oliver, D., Shekhar, S., Kang, J. M., Laubscher, R., Carlan, V., & Bannur, A. (2014). A k-main routes approach to spatial network activity summarization. IEEE Transactions on Knowledge and Data Engineering, 26(6), 1464–1478.CrossRefGoogle Scholar
  2. 2.
    Eck, J., Chainey, S., Cameron, J., & Wilson, R. (2005). Mapping crime: Understanding hotspots, National Institute of Justice.Google Scholar
  3. 3.
    Matthews, D. A., Effler, S. W., Driscoll, C. T., ODonnell, S. M., & Matthews, C. M. (2008). Electron budgets for the hypolimnion of a recovering urban lake, 1989–2004: Response to changes in organic carbon deposition and availability of electron acceptors”. Limnology and Oceanography, 53(2), 743–759.CrossRefGoogle Scholar
  4. 4.
    Chicago Tribune, Metra argues for delay of ‘fail-safe’ rail system. https://goo.gl/3bxuw0.
  5. 5.
    Huffington Post, Hungary: Snowstorm strands thousands in their cars. http://www.huffingtonpost.com/huff-wires/20130315/eu-europe-snow.
  6. 6.
    Brantingham, P. J., & Brantingham, P. L. (Eds.) (1981). Environmental criminology (pp. 27–54). Beverly Hills: Sage Publications.Google Scholar
  7. 7.
    Levine, N. (2006). Crime mapping and the Crimestat program. Geographical analysis, 38(1), 41–56.CrossRefGoogle Scholar
  8. 8.
    Scott, M. S., & Dedel, K. (2006). Assaults in and around bars (2nd ed.). Washington, DC: Office of Community Oriented Policing Services.Google Scholar
  9. 9.
    Cohen, L. E., & Felson, M. (1979). Social Change and Crime Rate Trends: A Routine. American sociological review (pp. 588–608)Google Scholar
  10. 10.
    Brantingham, P. J., & Brantingham, P. L. (1993). Environment, routine and situation: Toward a pattern theory of crime. Advances in criminological theory, 5, 259–294.Google Scholar
  11. 11.
    MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, 1(14), 281–297.MathSciNetzbMATHGoogle Scholar
  12. 12.
    Kaufman, L., & Rousseeuw, P. J. (2009). Finding groups in data: An introduction to cluster analysis (Vol. 344). Wiley.Google Scholar
  13. 13.
    Ng, R.T. & Han, J. (1994). Efficient and effective clustering methods for spatial data mining. Proceedings of the International Conference on Very Large Databases.Google Scholar
  14. 14.
    Resende, M. G., & Werneck, R. F. (2004). A hybrid heuristic for the p-median problem. Journal of Heuristics, 10(1), 59–88.CrossRefzbMATHGoogle Scholar
  15. 15.
    D’Andrade, R. G. (1978). U-statistic hierarchical clustering. Psychometrika, 43(1), 59–67.CrossRefzbMATHGoogle Scholar
  16. 16.
    Celik, M., Shekhar, S., George, B., Rogers, J. P., & Shine, J. A. (2007). Discovering and Quantifying Mean Streets: A Summary of Results, Technical Report 07–025. Computer Science and Engineering: University of Minnesota.Google Scholar
  17. 17.
    Buchin, K., Cabello, S., Gudmundsson, J., Löffler, M., Luo, J., & Rote, G. et al. (2009). Detecting hotspots in geographic networks, (pp. 217–231). Berlin: Springer.Google Scholar
  18. 18.
    Roach, S. A., & Roach, S. A. (1968). The theory of random clumping. London: Methuen.zbMATHGoogle Scholar
  19. 19.
    Okabe, A., Okunuki, K. I., & Shiode, S. (2006). SANET: A toolbox for spatial analysis on a network. Geographical Analysis, 38(1), 57–66.CrossRefGoogle Scholar
  20. 20.
    Shiode, S., & Okabe, A. (2004). Network variable clumping method for analyzing point patterns on a network. Unpublished paper presented at the Annual Meeting of the Associations of American Geographers. Philadelphia, Pennsylvania.Google Scholar
  21. 21.
    Aerts, K., Lathuy, C., Steenberghen, T., & Thomas, I. (2006). Refining spatial clustering of traffic accidents using distances along the network. In Proceedings of 19th workshop of the international cooperation on theories and concepts in traffic safety.Google Scholar
  22. 22.
    Spooner, P. G., Lunt, I. D., Okabe, A., & Shiode, S. (2004). Spatial analysis of roadside Acacia populations on a road network using the network K-function. Landscape Ecology, 19(5), 491–499.CrossRefGoogle Scholar
  23. 23.
    Steenberghen, T., Dufays, T., Thomas, I., & Flahaut, B. (2004). Intra-urban location and clustering of road accidents using GIS: A Belgian example. International Journal of Geographical Information Science, 18(2), 169–181.CrossRefGoogle Scholar
  24. 24.
    Yamada, I., & Thill, J. C. (2007). Local indicators of networkconstrained clusters in spatial point patterns. Geographical Analysis, 39(3), 268–292.CrossRefGoogle Scholar
  25. 25.
    Shiode, S., & Shiode, N. (2009). Detection of multiscale clusters in network space. International Journal of Geographical Information Science, 23(1), 75–92.CrossRefGoogle Scholar
  26. 26.
    Shekhar, S., & Liu, D. R. (1997). CCAM: A connectivity-clustered access method for networks and network computations. IEEE Transactions on Knowledge and Data Engineering, 9(1), 102–119.CrossRefGoogle Scholar
  27. 27.
    Meehan, Bill. (2013). Modeling electric distribution with GIS. Redlands: Esri Press.Google Scholar
  28. 28.
    Cormen, T. H. (2001). Introduction to algorithms. MIT press.Google Scholar
  29. 29.
    Michael, R. G., & David, S. J. (1979). Computers and intractability: A guide to the theory of NP-completeness. San Francisco: W.H. Freeman.zbMATHGoogle Scholar
  30. 30.
    Hochbaum, D. S. (1996). Approximating covering and packing problems: set cover, vertex cover, independent set, and related problems. In Approximation algorithms for NP-hard problems (pp. 94–143). PWS Publishing Co.Google Scholar
  31. 31.
    Levine, N. (2008). CrimeStat: A spatial statistics program for the analysis of crime incident locations, vol 3.1, Houston, TX: Ned Levine and Associates; and Washington, DC: The National Institute of Justice.Google Scholar
  32. 32.
    Fatality Analysis Reporting System (FARS) Encyclopedia, National Highway Traffic Safety Administration (NHTSA), http://www.nhtsa.gov/FARS.
  33. 33.
    Borah, S., & Ghose, M. K. (2009). Performance analysis of AIM-K-means and K-means in quality cluster generation. ArXiv preprint arXiv:0912.3983.
  34. 34.
    Barakbah, A. R., & Kiyoki, Y. (2009). A pillar algorithm for k-means optimization by distance maximization for initial centroid designation. In IEEE Symposium on Computational intelligence and data mining, 2009. CIDM’09 (pp. 61–68). IEEE (2009).Google Scholar
  35. 35.
    Khan, S. S., & Ahmad, A. (2004). Cluster center initialization algorithm for K-means clustering. Pattern recognition letters, 25(11), 1293–1302.CrossRefGoogle Scholar
  36. 36.
    Pelleg, D., & Moore, A. W. (2000). X-means: Extending K-means with efficient estimation of the number of clusters. In ICML (Vol. 1).Google Scholar
  37. 37.
    Bradley, P. S., & Fayyad, U. M. (1998). Refining initial points for K-means clustering. ICML, 98, 91–99.Google Scholar
  38. 38.
    Ernst, M., Lang, M., & Davis, S. (2011). Dangerous by design: Solving the epidemic of preventable pedestrian deaths, Transportation for America: Surface Transportation Policy Partnership, Washington, DC.Google Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.ESRIRedlandsUSA

Personalised recommendations