O(log n) bimodality analysis

Abstract The bimodality of a population P can be measured by dividing its range into two intervals so as to maximize the Fisher distance between the resulting two subpopulations P 1 and P 2 . If P is a mixture of two (approximately) Gaussian subpopulations, then P 1 and P 2 are good approximations to the original Gaussians, if their Fisher distance is great enough. Moreover, good approximations to P 1 and P 2 can be obtained by dividing P into small parts; finding the maximum-distance (MD) subdivision of each part; combining small groups of these subdivisions into (approximate) MD subdivisions of larger parts; and so on. This divide-and-conquer approach yields an approximate MD subdivision of P in O (log n ) computational steps using O ( n ) processors, where n is the size of P .