Efficient fuzzy clustering of multi-spectral images

Abstract

Cluster analysis involves the use of a class of algorithms that aim to partition a data set into a number of disjoint groups. These groups have the property that members within a group are more similar to each other than members from different groups. Cluster analysis is used to examine underlying patterns or groupings in data. In remote sensing it can be used to determine the natural spectral classes in a data set and hence to select representative training samples for classification. A feature of many data sets in the Earth sciences is the presence of observations that exhibit characteristics of more than one class. While this may be overcome by collecting data at a higher resolution, it is not always feasible or possible to do this. An example of this problem is mixed pixels in satellite imagery. Fuzzy clustering is a variant of conventional clustering that overcomes the limitations of samples being committed wholly to one group. In fuzzy clustering, a fuzzy set is used to represent a sample's multiple group membership. Each element of the set is the degree of belonging of the sample to a particular group. This is a numerical value with range [0,1] such that the sum of all group memberships for a sample is exactly 1. This paper presents two operational improvements that can reduce the execution time of a standard fuzzy clustering algorithm, the Fuzzy c-Means (FCM) algorithm. The original and improved algorithms are compared by application to a SPOT multi-spectral image. An FCM algorithm is an iterative partitioning method that produces optimal c-partitions. A fuzzy partition is an array of N fuzzy membership sets that are created when a set of N samples in n-space are fuzzy clustered into c groups.