Uncertainty in the 2001 Output Area Classification for the Census of England and Wales<br />Peter Fisher<br />Department o...
Outline<br />Output area classification <br />Uncertainty reporting<br />Transforming uncertainty<br />Fuzzy c Means<br />...
Output Area Classification<br />ONS OAC<br />Hard Classification<br />Based on 41 census variables<br />Using the k Means ...
Super-Groups<br />Blue Collar Communities<br />City Living<br />Countryside<br />Prospering Suburbs<br />Constrained by Ci...
Each is characterised by variables<br />Blue Collar<br />Multicultural<br />Typical Traits<br />From Vickers, Rees and Bir...
Uncertainty<br />Hardly anywhere could be a perfect example of any such class <br />How many cultures are required for an ...
Uncertainty Reporting<br />Uniquely among geodemographic classifications ONS OAC reports uncertainty<br />Distance to clus...
Fuzzy c Means<br />Fuzzy membership is given by:<br />Subject to the conditions that:<br />			for all i and j<br />for all...
Possibilistic c Means<br />Relax condition 3 to simply<br />for all j.<br />Using<br />
Where …<br />m is the fuzziness as in FCM<br />ηi is found iteratively from<br />It can be different for each class<br />
Study area: Leicester<br />
Entropy – Degree of confusion<br />FCM 0-1<br />Single class to more classes<br />PCM 0-<c<br />
Confusion<br />The same number of cases in each OA Class as in the actual OAC<br />Different α-cut for each class<br />
PCM<br />FCM<br />
Conclusion<br />Possibilistic c-Means offers a alternative to the usual Fuzzy c-Means<br />Abandons constrain of membershi...
Questions ?<br />Email:  pff1@le.ac.uk<br />
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4A_1_Uncertainty in the 2001 output area classification for the census of england and wales

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4A_1_Uncertainty in the 2001 output area classification for the census of england and wales

  1. 1. Uncertainty in the 2001 Output Area Classification for the Census of England and Wales<br />Peter Fisher<br />Department of Geography, University of Leicester<br />GISRUK , University College, <br />London, 15th April 2010<br />
  2. 2. Outline<br />Output area classification <br />Uncertainty reporting<br />Transforming uncertainty<br />Fuzzy c Means<br />Possibilistic c Means<br />Results<br />Conclusion<br />
  3. 3. Output Area Classification<br />ONS OAC<br />Hard Classification<br />Based on 41 census variables<br />Using the k Means classification<br />Three levels recognised<br />Super-Groups – 7 classes<br />Groups – 21 classes<br />Sub-Groups – 52 classes<br />
  4. 4. Super-Groups<br />Blue Collar Communities<br />City Living<br />Countryside<br />Prospering Suburbs<br />Constrained by Circumstances<br />Typical Traits<br />Multicutural<br />
  5. 5. Each is characterised by variables<br />Blue Collar<br />Multicultural<br />Typical Traits<br />From Vickers, Rees and Birkin, (2005) WP 05/2 School of Geography, University of Leeds<br />
  6. 6. Uncertainty<br />Hardly anywhere could be a perfect example of any such class <br />How many cultures are required for an area to be multicultural?<br />How many white collar (or pale blue collar) workers are allowed in a blue collar community?<br />Can you have prosperous suburbs in the country or in the city?<br />What are “Typical traits”?<br />Similar questions could be asked of other classifications<br />
  7. 7. Uncertainty Reporting<br />Uniquely among geodemographic classifications ONS OAC reports uncertainty<br />Distance to cluster centres is reported for ALL classes at all levels of classification<br />These distances could be derived from:<br /> the original data and the cluster centroids<br />
  8. 8. Fuzzy c Means<br />Fuzzy membership is given by:<br />Subject to the conditions that:<br /> for all i and j<br />for all i, and<br /> for all i.<br />
  9. 9. Possibilistic c Means<br />Relax condition 3 to simply<br />for all j.<br />Using<br />
  10. 10. Where …<br />m is the fuzziness as in FCM<br />ηi is found iteratively from<br />It can be different for each class<br />
  11. 11. Study area: Leicester<br />
  12. 12.
  13. 13.
  14. 14. Entropy – Degree of confusion<br />FCM 0-1<br />Single class to more classes<br />PCM 0-<c<br />
  15. 15. Confusion<br />The same number of cases in each OA Class as in the actual OAC<br />Different α-cut for each class<br />
  16. 16. PCM<br />FCM<br />
  17. 17. Conclusion<br />Possibilistic c-Means offers a alternative to the usual Fuzzy c-Means<br />Abandons constrain of memberships summing to 1<br />Makes more sense ?<br />But the total class areas do not sum to 100% of the study area (usually greater)?<br />Treatment of the uncertainty offers more satisfying (?) outcomes of the OAC<br />But this treatment is only possible for the OAC<br />
  18. 18. Questions ?<br />Email: pff1@le.ac.uk<br />

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