Computing Gaussian mixture models with EM using equivalence constraints

Noam Shental, Aharon Bar-Hillel, Tomer Hertz, Daphna Weinshall

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Density estimation with Gaussian Mixture Models is a popular generative technique used also for clustering. We develop a framework to incorporate side information in the form of equivalence constraints into the model estimation procedure. Equivalence constraints are defined on pairs of data points, indicating whether the points arise from the same source (positive constraints) or from different sources (negative constraints). Such constraints can be gathered automatically in some learning problems, and are a natural form of supervision in others. For the estimation of model parameters we present a closed form EM procedure which handles positive constraints, and a Generalized EM procedure using a Markov net which handles negative constraints. Using publicly available data sets we demonstrate that such side information can lead to considerable improvement in clustering tasks, and that our algorithm is preferable to two other suggested methods using the same type of side information.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 17 - Proceedings of the 2003 Conference, NIPS 2003
PublisherNeural information processing systems foundation
ISBN (Print)0262201526, 9780262201520
StatePublished - 2004
Externally publishedYes
Event17th Annual Conference on Neural Information Processing Systems, NIPS 2003 - Vancouver, BC, Canada
Duration: 8 Dec 200313 Dec 2003

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258


Conference17th Annual Conference on Neural Information Processing Systems, NIPS 2003
CityVancouver, BC

Cite this