Scale-Based Clustering with Latent Variables

The use of clustering systems is very important in those real-word applications where an efficient, both accurate and economical, representation of the data to be processed is necessary. When dealing with statistical models, such a problem is usually related to the estimate of their parameters in the Maximum Likelihood context. At this regard, we propose an EM-based algorithm that uses a hierarchical growing approach, based on a given splitting procedure, to determine in an efficient way the parameters of a mixture of Gaussian clusters. The splitting procedure and the determination of the correct number of clusters are based on a scale-based approach, which imitates the human perception of images. Moreover, each cluster is modelled by means of latent variables, which also ensure a local linear dimension reduction of the data being processed.