gmm_diag and gmm_full: C++ classes for multi-threaded Gaussian mixture models and Expectation-Maximisation

• The gmm_diag and gmm_full classes are included in recent versions of the Armadillo C++ library.

• Documentation for the gmm_diag and gmm_full classes is available online: http://arma.sourceforge.net/docs.html#gmm_diag.

• The gmm_diag and gmm_full classes provide multi-threaded (parallelised) implementations of Gaussian mixture models (GMMs) and the associated k-means and Expectation-Maximisation (EM) training algorithms.

• The gmm_diag class is specifically tailored for diagonal covariance matrices (all entries outside the main diagonal in each covariance matrix are assumed to be zero), while the gmm_full class is tailored for full covariance matrices. The gmm_diag class is typically much faster to train and use than the gmm_full class, at the potential cost of some reduction in modelling accuracy.

• The interface for the gmm_diag and gmm_full classes allows the user full control over the parameters for GMM fitting, as well as easy and flexible access to the trained model. Specifically, the two classes contain functions for likelihood evaluation, vector quantisation, histogram generation, data synthesis, and parameter modification, in addition to training (learning) the GMM parameters via the EM algorithm. The classes use several techniques to improve numerical stability and promote convergence of EM based training, such as keeping as much as possible of the internal computations in the log domain, and ensuring the covariance matrices stay positive-definite.

• To achieve multi-threading, the k-means and EM training algorithms have been reformulated into a MapReduce-like framework and implemented with the aid of OpenMP pragma directives. As such, the EM algorithm runs much quicker on multi-core machines when OpenMP is enabled during compilation (use the -fopenmp option in GCC and clang compilers).