The learning process in lots of machine learning algorithms is based on the similarity of the training data. Some kinds of specific similarity measures for two different categories of structural and vector data exist. In many cases, Euclidean distance, which is applied for the vector data, is not a suitable criterion for determining the similarity among input data. In distance metric learning , the new projected space is extracted in such a way that the new Euclidean distance well illustrates the similarity of the data. A considerable number of unsupervised and supervised metric learning algorithms exist. In unsupervised metric learning algorithms, the linear or nonlinear suace of the data is learned regardless of the data In this dissertation, we focus on the unsupervised metric learning with real world application in clustering. In unsupervised clustering, the objective is to find a set of clusters, where each cluster only contains the same In this dissertation, two different linear and nonlinear algorithms are introduced in this area. Dis-FCM is a linear method in which, unlike most available methods that apply k-means clustering, a new formulation is presented in which the benefits of FCM clustering are applied for obtaining the estimated align=left Keywords : Machine Learning, Pattern Recognition, Metric Learning, Clustering, Probabilistic Graphical Model, Gaussian Process
