On principle axis based line symmetry clustering techniques

In this paper, at first a new line symmetry (LS) based distance is proposed which calculates the amount of symmetry of a point with respect to the first principal axis of a data set. The proposed distance uses a recently developed point symmetry (PS) based distance in its computation. Kd-tree based nearest neighbor search is used to reduce the complexity of computing the closest symmetric point. Thereafter an evolutionary clustering technique is described that uses this new principal axis based LS distance for assignment of points to different clusters. The proposed GA with line symmetry distance based (GALS) clustering technique is able to detect any type of clusters, irrespective of their geometrical shape, size or convexity as long as they possess the characteristics of LS. GALS is compared with the existing genetic algorithm based K-means clustering technique, GAK-means, existing genetic algorithm with PS based clustering technique, GAPS, spectral clustering technique, and average linkage clustering technique. Five artificially generated data sets having different characteristics and seven real-life data sets are used to demonstrate the superiority of the proposed GALS clustering technique. In a part of experiment, utility of the proposed genetic LS distance based clustering technique is demonstrated for segmenting the satellite image of the part of the city of Kolkata. The proposed technique is able to distinguish different landcover types in the image. In the last part of the paper genetic algorithm is used to search for the suitable line of symmetry of each cluster.