Large number of machine learning algorithms, strongly depend on the underlying distance metric for representing the important relationships among the observed data points. Distance metric learning is defined as learning a good similarity measure or distance metric for input data. There are several deterministic and probabilistic approaches for supervised and unsupervised distance metric learning. In this thesis, we focus on unsupervised metric learning algorithms. Most of existing unsupervised methods are based on dimensionality reduction and there is not enough work in which the large separability between different clusters to be satisfied. We propose a probabilistic approach for this problem in which we formulate metric learning and fuzzy c-means clustering simultaneously to obtain large separability between different clusters in projected space. We use Markov Chain Monte Carlo (MCMC) algorithms to infer the latent variables in our probability model. Our approach can also reduce the dimensionality of data automatically without getting the number of reduced dimensions as input. The experimental results on real-world data sets demonstrated the effectiveness of the proposed algorithm. Keywords: 1. Distance Metric Learning 2. Fuzzy C-Means 3. Unsupervised Learning 4. Probabilistic Graphical Models 5. Markov Chain Monte Carlo
