I propose a learning algorithm for learning hierarchical models for object recognition. The model architecture is a compositional hierarchy that represents part-whole relationships: parts are described in the local context of substructures of the object. The focus of this report is learning hierarchical models from data, i.e. inducing the structure of model prototypes from observed exemplars of an object. At each node in the hierarchy, a probability distribution governing its parameters must be learned. The connections between nodes reflects the structure of the object. The formulation of substructures is encouraged such that their parts become conditionally independent. The resulting model can be interpreted as a Bayesian Belief Network and also is in many respects similar to the stochastic visual grammar described by Mjolsness. 1 INTRODUCTION Model-based object recognition solves the problem of invariant recognition by relying on stored prototypes at unit scale positioned at the ori...

We apply the Expectation Maximization (EM) algorithm to an assignment problem where in addition to binary assignment variables analog parameters must be estimated. As an example, we use the problem of part labelling in the context of model based object recognition where models are stored in from of a compositional hierarchy. This problem has been formulated previously as a graph matching problem and stated in terms of minimizing an objective function that a recurrent neural network solves [11, 12, 5, 8, 22]. Mjolsness [9, 10] has introduced a stochastic visual grammar as a model for this problem; there the matching problem arises from an index renumbering operation via a permutation matrix. The optimization problem w.r.t the match variables is difficult and Mean Field Annealing techniques are used to solve it. Here we propose to model the part labelling problem in terms of a mixture of distributions, each describing the parameters of a part. Under this model, the match variables corres...

angements of symbols that are possible a priori from a mere combinatorial point of view are illegitimate as linguistic constructions. The number of character strings of length 1,000 that make up a proper English text is vanishingly small when compared to the number of all possible strings of such length. Thus, while infinitely productive, language is at the same time severely constrained. When observed from the "surface," the composition mechanism in language appears simple. Individual characters are assembled into syllables, which are themselves assembled into words, further composed into phrases, sentences, etc. One text differs from another text in the same language only by the relative positioning (relations) among the constituents (symbols) , and not for instance by the frequencies of occurrence of each symbol; these frequencies are about the same for any sufficiently long text. Yet, encoded within this apparently simple Elie Bienenstock an

In this report, we propose a cascade fuzzy ART (CFART) neural network which can function as an extensible database in a model-based object recognition system. The proposed CFART network contains multiple layers. It preserves the prominent characteristics of a fuzzy ART network and extends fuzzy ART's capability toward hierarchical representation of input patterns. The learning process of the proposed network is unsupervised and self-organizing, and includes a top-down searching process and a bottom-up learning process. The top-down and bottom-up learning processes interact with each other in a closely coupled manner. Basically, the top-down searching guides the bottom-up learning whereas the bottom-up learning influences the top-down searching by changing its searching fuzzy boundary. In addition, a global searching tree is built to speed up the learning and recognition processes. The proposed CFART can accept both binary and analog inputs. With fast learning and categorization capabil...