Mode-finding for mixtures of Gaussian distributions Export

@techreport{CarreiraPerpinan1999Modefinding, abstract = {I consider the problem of finding all the modes of a mixture of multivariate Gaussian distributions, which has applications in clustering and regression. I derive exact formulas for the gradient and Hessian and give a partial proof that the number of modes cannot be more than the number of components, and are contained in the convex hull of the component centroids. Then, I develop two exhaustive mode search algorithms: one based on combined quadratic maximisation and gradient ascent and the other one based on a fixed-point iterative scheme. Appropriate values for the search control parameters are derived by taking into account theoretical results regarding the bounds for the gradient and Hessian of the mixture. The significance of the modes is quantified locally (for each mode) by error bars, or confidence intervals (estimated using the values of the Hessian at each mode); and globally by the sparseness of the mixture, measured by its differential entropy (estimated through bounds). I conclude with some reflections about bump-finding.}, author = {Carreira-Perpi\~{n}\'{a}n, Miguel}, booktitle = {Technical Report CS-99-03}, citeulike-article-id = {2967118}, citeulike-linkout-0 = {http://www.dcs.shef.ac.uk/intranet/research/resmes/CS9903.pdf}, citeulike-linkout-1 = {http://www.cse.ogi.edu/~miguel/papers.html}, day = {31}, editor = {Dept}, institution = {Dept. of Computer Science, University of Sheffield, UK}, keywords = {algorithms, bars, bump, error, finding, gaussian, maximisation, mixtures, mode, sparseness}, month = {March}, posted-at = {2008-07-06 12:28:01}, priority = {2}, title = {Mode-finding for mixtures of Gaussian distributions}, url = {http://www.dcs.shef.ac.uk/intranet/research/resmes/CS9903.pdf}, year = {1999} }

TY - RPRT ID - CarreiraPerpinan1999Modefinding L3 - citeulike-article-id:2967118 N2 - I consider the problem of finding all the modes of a mixture of multivariate Gaussian distributions, which has applications in clustering and regression. I derive exact formulas for the gradient and Hessian and give a partial proof that the number of modes cannot be more than the number of components, and are contained in the convex hull of the component centroids. Then, I develop two exhaustive mode search algorithms: one based on combined quadratic maximisation and gradient ascent and the other one based on a fixed-point iterative scheme. Appropriate values for the search control parameters are derived by taking into account theoretical results regarding the bounds for the gradient and Hessian of the mixture. The significance of the modes is quantified locally (for each mode) by error bars, or confidence intervals (estimated using the values of the Hessian at each mode); and globally by the sparseness of the mixture, measured by its differential entropy (estimated through bounds). I conclude with some reflections about bump-finding. TI - Mode-finding for mixtures of Gaussian distributions T2 - Technical Report CS-99-03 KW - algorithms KW - bars KW - bump KW - error KW - finding KW - gaussian KW - maximisation KW - mixtures KW - mode KW - sparseness AU - Carreira-Perpiñán, Miguel A2 - Dept PY - 1999/03/31/revised August 4, 2000 UR - http://www.dcs.shef.ac.uk/intranet/research/resmes/CS9903.pdf ER -