1. Uncertainty in the 2001 Output Area Classification for the Census of England and Wales Peter Fisher Department of Geography, University of Leicester GISRUK , University College, London, 15th April 2010

2. Outline Output area classification Uncertainty reporting Transforming uncertainty Fuzzy c Means Possibilistic c Means Results Conclusion

3. Output Area Classification ONS OAC Hard Classification Based on 41 census variables Using the k Means classification Three levels recognised Super-Groups – 7 classes Groups – 21 classes Sub-Groups – 52 classes

4. Super-Groups Blue Collar Communities City Living Countryside Prospering Suburbs Constrained by Circumstances Typical Traits Multicutural

5. Each is characterised by variables Blue Collar Multicultural Typical Traits From Vickers, Rees and Birkin, (2005) WP 05/2 School of Geography, University of Leeds

6. Uncertainty Hardly anywhere could be a perfect example of any such class How many cultures are required for an area to be multicultural? How many white collar (or pale blue collar) workers are allowed in a blue collar community? Can you have prosperous suburbs in the country or in the city? What are “Typical traits”? Similar questions could be asked of other classifications

7. Uncertainty Reporting Uniquely among geodemographic classifications ONS OAC reports uncertainty Distance to cluster centres is reported for ALL classes at all levels of classification These distances could be derived from: the original data and the cluster centroids

8. Fuzzy c Means Fuzzy membership is given by: Subject to the conditions that: for all i and j for all i, and for all i.

9. Possibilistic c Means Relax condition 3 to simply for all j. Using

10. Where … m is the fuzziness as in FCM ηi is found iteratively from It can be different for each class

11. Study area: Leicester

14. Entropy – Degree of confusion FCM 0-1 Single class to more classes PCM 0-<c

15. Confusion The same number of cases in each OA Class as in the actual OAC Different α-cut for each class

16. PCM FCM

17. Conclusion Possibilistic c-Means offers a alternative to the usual Fuzzy c-Means Abandons constrain of memberships summing to 1 Makes more sense ? But the total class areas do not sum to 100% of the study area (usually greater)? Treatment of the uncertainty offers more satisfying (?) outcomes of the OAC But this treatment is only possible for the OAC

18. Questions ? Email: pff1@le.ac.uk