https://inria.hal.science/inria-00321022v2Verbeek, JakobJakobVerbeekLEAR - Learning and recognition in vision - GRAVIR - IMAG - Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble - UJF - UniversitÃ© Joseph Fourier - Grenoble 1 - Inria - Institut National de Recherche en Informatique et en Automatique - INPG - Institut National Polytechnique de Grenoble - CNRS - Centre National de la Recherche Scientifique - Inria Grenoble - RhÃ´ne-Alpes - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche ScientifiqueNunnink, JanJanNunninkIvI - Instituut voor Informatica - UvA - Universiteit van AmsterdamVlassis, NikosNikosVlassisIvI - Instituut voor Informatica - UvA - Universiteit van AmsterdamAccelerated EM-based clustering of large data setsHAL CCSD2006Gaussian mixturesEM algorithmFree energykd-treesLarge data sets[INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG]Verbeek, Jakob2011-04-11 11:19:302023-03-24 14:52:542011-04-11 11:31:52enJournal articleshttps://inria.hal.science/inria-00321022v2/document10.1007/s10618-005-0033-3https://inria.hal.science/inria-00321022v1application/pdf2Motivated by the poor performance (linear complexity) of the EM algorithm in clustering large data sets, and inspired by the successful accelerated versions of related algorithms like k-means, we derive an accelerated variant of the EM algorithm for Gaussian mixtures that: (1) offers speedups that are at least linear in the number of data points, (2) ensures convergence by strictly increasing a lower bound on the data log-likelihood in each learning step, and (3) allows ample freedom in the design of other accelerated variants. We also derive a similar accelerated algorithm for greedy mixture learning, where very satisfactory results are obtained. The core idea is to define a lower bound on the data log-likelihood based on a grouping of data points. The bound is maximized by computing in turn (i) optimal assignments of groups of data points to the mixture components, and (ii) optimal re-estimation of the model parameters based on average sufficient statistics computed over groups of data points. The proposed method naturally generalizes to mixtures of other members of the exponential family. Experimental results show the potential of the proposed method over other state-of-the-art acceleration techniques.