Some Line Symmetry Distance-Based Clustering Techniques

Abstract

In this chapter the concept of point symmetry is extended to line symmetry-based distances, and some genetic algorithm-based clustering techniques using these distances are described. A moment-based approach is first used for defining the distance; it is applicable only for two-dimensional data sets. Analogous to GAPS, a genetic clustering technique with line symmetry distance (GALSD) is developed. The GALSD clustering technique can cluster data sets with the property of line symmetry successfully. A technique for face detection that uses GALSD as the underlying approach is discussed in detail. Thereafter, in this chapter a second line symmetry-based distance is described which measures the total amount of symmetry of a point with respect to the first principal axis of a cluster. It is applicable for data sets of any number of dimensions. A genetic clustering technique using this line symmetry-based distance is also described. Experimental results show the efficacy of this technique over other competing ones.