A Validity Index Based on Symmetry: Application to Satellite Image Segmentation
Some existing cluster validity indices are discussed in this chapter. Thereafter a newly developed symmetry-based cluster validity index, named Sym-index, is described in detail, and an intuitive explanation of how the different components of Sym-index compete with each other to identify a proper clustering is provided. A mathematical justification of the new index is derived by establishing its relationship with the well-known Dunn’s index. Experimental results show that Sym-index is able to detect the appropriate number of clusters from a given data set as long as the clusters possess the property of point-based symmetry, irrespective of their geometrical shape and convexity. The point symmetry-based distance is incorporated into eight existing cluster validity indices. These indices exploit the property of point symmetry to indicate both the appropriate number of clusters as well as the appropriate partitioning. Finally, an application of Sym-index in conjunction with the GAPS clustering technique is described for satellite image segmentation.
KeywordsValidity Index Proper Number Cluster Validity Index Silhouette Index Davies Bouldin Index
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