IST Colloquium, Nov 11, 2005, 01:00PM - 02:30PM, Wachman 322
Automatic Adjustment of EM Components
Prof. Longin Jan Latecki, CIS Department, Temple University
We will provide a domain specific solution to one of the most challenging problems in statistical reasoning which is the estimation of the number of components of a statistical model.
Our solution is described in the framework of Expectation Maximization (EM). EM is a very popular and powerful method that allows simultaneous estimation of model parameters and assignment of data point to particular components of the model. However, EM produces an optimal solution only if the number of model components and the initial values of model parameters are well estimated. EM is guaranteed to produce only a locally optimal solution, which in particular means that it may get stuck in local optimum if the initial values of model parameters are not close to the global optimum.
Our domain of interest is polygonal approximation of data points with two specific applications in mind: (1) polygonal approximation of laser range data points obtained by a mobile robot and (2) grouping of edge pixels to object contours in digital images. When the number of lines (i.e., number of model components) and their initial positions (i.e., the initial parameters) are well estimated an optimal solution can be obtained in the EM framework. The proposed approach yields globally optimal solution independent of the initial number of lines and their initial parameters.