Soft partition of FCM clustering results: A case study on the clustering of urban underlying surface from remotely sensed imagery

ZHOU Zi-min[1], ZHOU Jian-hua[2]

1. 1. School of Geographic Sciences, East China Normal University, Shanghai 200241, China; 2. Key Lab of Geographical Information Science, Ministry of Education, East China Normal University, Shanghai 200241, China.
• Received:2015-06-17 Online:2016-07-25 Published:2016-09-29

Abstract:

FCM is one of the most widely used fuzzy clustering methods. Being different from the distinct clustering, the fuzzy clustering provides variations of membership of entity. The variations serve as useful references for adjusting centroids and allocating clusters during and after the clustering respectively. It is a commonly used way in FCM applications to allocate a pixel according to the maximum of memberships of this pixel owns. Such "hard partition" will likely allocate the pixel to an inappropriate class. Therefore, a soft partition approach, called as SPFCM, has been investigated in this paper. The soft partition depends on both the dispersion degree of the memberships (represented by the standard deviation between the memberships) and the spatial dependence of pixels (indicated by the density of neighborhood pixels). There are four steps to conduct the soft partition：1) Get a membership matrix by FCM clustering. 2) Calculate the standard deviation of class membership for each pixel from the membership matrix. 3) Compute the density of neighboring elements for each class in the pixel’s neighbor and these elements are weighted by their membership. 4) Take the results from step 2 and 3 as references to allocate the centre pixel. To release from manual operation, some important adjustable parameters (e.g. neighborhood window size, etc.) are determined by adaptive calculation. Experiments indicate that the average area of clustering patches can be applied to derive the base number of window size for calculating the density of neighboring elements. MATLAB simulation tests show that the accuracy of allocation by SPFCM is 9% higher than that by the hard one involved with the maximum membership.