Issue No.04 - April (1983 vol.5)
pp: 410-416
Keinosuke Fukunaga , FELLOW, IEEE, School of Electrical Engineering, Purdue University, West Lafayette, IN 47907.
Given a general n-dimensional bimodal Gaussian mixture, this paper shows how unknown parameters may be found by the method of moments. Three cases are considered-equal modal probabilities, known but not necessarily equal probabilities, and all parameters unknown. The solution involves sample moments no higher than fourth order. For Gaussian mixtures where the number of modes is unknown, fourth-order moments can be used to count them, provided all modes have the same covariance matrix, and their multiplicity is not greater than data dimensionality. Examples of mode-counting and the determination of bimodal parameters are included.
Keinosuke Fukunaga, "Estimation of the Parameters of a Gaussian Mixture Using the Method of Moments", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.5, no. 4, pp. 410-416, April 1983, doi:10.1109/TPAMI.1983.4767410