K-means Algorithm Based on Particle Swarm Optimization for the Identification of Rock Discontinuity Sets

List of Symbols a Dip direction ( ) b Dip angle ( ) cj Center of the jth cluster h Deviation angle from the mean orientation angle D Dimension of the search space Ds Discontinuity data set d Search direction ei Unit normal vector of the ith discontinuity f Cost function (fitness value) iter Iteration number K Number of clusters n Normalized eigenvector M Orientation cosine matrix l1, l2 Learning factors N Population size of particles n Total number of discontinuities nj Number of discontinuities in the jth cluster Pi Personal best position of the ith particle Pg Global best position of the swarm POP Population of particles r1, r2 Random variables ranging from 0 to 1 Sj Discontinuity set Vi Velocity of the ith particle v Ray–Turi index w Inertia weight Xi Position of the ith particle

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