Hierarchical Mixtures of Experts and the EM Algorithm

We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's). Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain.

Recognition by Linear Combinations of Models

Visual object recognition requires the matching of an image with a set of models stored in memory. In this paper we propose an approach to recognition in which a 3-D object is represented by the linear combination of 2-D images of the object. If M = {M1,...Mk} is the set of pictures representing a given object, and P is the 2-D image of an object to be recognized, then P is considered an instance of M if P = Eki=aiMi for some constants ai. We show that this approach handles correctly rigid 3-D transformations of objects with sharp as well as smooth boundaries, and can also handle non-rigid transformations. The paper is divided into two parts. In the first part we show that the variety of views depicting the same object under different transformations can often be expressed as the linear combinations of a small number of views. In the second part we suggest how this linear combinatino property may be used in the recognition process.