The MVN (MultiVariate Normal) Matlab/Octave toolbox implements diver- gences, centroids and algorithms (k-means, Self-Organizing Maps) to work with this non-vectorial of features.
Multivariate Gaussians are used in Music Similarity Algorithms, to represent timbre music features. Multivariate Gaussians and their attached Kullback- Leibler divergences are currently established as the de-facto standard method to compute music similarity. In this documentation we use Elias Pampalks music analysis (MA) Matlab toolbox to demonstrate how to use this toolbox (skip to Section 1.6 for some examples). Of course usage is not limited to music similarity models, any multivariate Gaussian features can be processed with this toolbox.
The centroid computing algorithms are implemented after Nielsen and Nock [NN09]. The k-means algorithms as it is described in Banjeree et al. [BMDG05], the Self-Organizing Maps algorithm for the Gaussians as in Schnitzer et al. [SFWG10].
We implement the following divergences for similarity computation of multivariate Gaussians/Normals:
We also include a k-means clustering method for the multivariate Gaussians and a method to compute native Self-Organizing maps for multivatiate Gaussians and their divergences.
The author uses the toolbox for Music Similarity estimation and experiments (as the features there are multivariate Gaussians), but its methods are of course not limited to that topic.
Documentation with usage Examples is available as PDF
Download Version 1 (August 31th, 2011) of the MVN Toolbox: mvn-1.0.tar.gz, Browse online
The MVN Toolbox is licensed under the GPL License, Version 3
[NN09] F. Nielsen and R. Nock. Clustering multivariate normal distributions. Emerging Trends in Visual Computing, pages 164-174, 2009.
[SFWG10] D. Schnitzer, A. Flexer, G. Widmer, and M. Gasser. Islands of Gaussians: The Self Organizing Map and Gaussian Music Similarity Features. In Proceedings of the 11th International Conference on Music Information Retrieval. ISMIR'10, 2010.
[BMDG05] A. Banerjee, S. Merugu, I. S. Dhillon, and J. Ghosh. Clustering with bregman divergences. The Journal of Machine Learning Research, 6:1705-1749, 2005.
Dominik Schnitzer, 8/25/2011