Non-intrusive loading monitoring (NILM) provides a smart solution to the problem of electrical energy monitoring of households at the appliance level. In blind disaggregation, the power level of each appliance is not known a priori. In this paper, we propose an event-based blind disaggregation algorithm that uses Gaussian mixture models (GMM) for clustering to automatically detect two-state appliances from the aggregate data. The benefit of using Gaussian mixture models over other clustering methods is that they can automatically learn the statistical distributions present in the data. This is beneficial, especially when the appliances have similar power consumptions. Since Gaussian mixture models do not determine the number of clusters automatically, we use Bayesian information criteria (BIC) to determine the number of clusters. The blind disaggregation method is tested with data from a real house collected by a smart meter which samples the aggregate consumption at 3.4 kHz and also from Reference Energy Disaggregation Dataset (REDD) public data, sampled at a frequency of 1 Hz. We compared the performance of our algorithm with other unsupervised methods and found comparable performance. We also compared the Gaussian mixture model with mean shift clustering in a blind disaggregation. We saw an improved performance by using Gaussian mixture models instead of mean-shift clustering in various accuracy measures.