A New Line Symmetry Distance and Its Application to Data Clustering

In this paper, at first a new line-symmetry-based distance is proposed. The properties of the proposed distance are then elaborately described. Kd-tree-based nearest neighbor search is used to reduce the complexity of computing the proposed line-symmetry-based distance. Thereafter an evolutionary clustering technique is developed that uses the new line-symmetry-based distance measure for assigning points to different clusters. Adaptive mutation and crossover probabilities are used to accelerate the proposed clustering technique. The proposed GA with line-symmetry-distance-based (GALSD) clustering technique is able to detect any type of clusters, irrespective of their geometrical shape and overlapping nature, as long as they possess the characteristics of line symmetry. GALSD is compared with the existing well-known K-means clustering algorithm and a newly developed genetic point-symmetry-distance-based clustering technique (GAPS) for three artificial and two real-life data sets. The efficacy of the proposed line-symmetry-based distance is then shown in recognizing human face from a given image.