The Behavior Language; User's Guide

The Behavior Language is a rule-based real-time parallel robot programming language originally based on ideas from [Brooks 86], [Connell 89], and [Maes 89]. It compiles into a modified and extended version of the subsumption architecture [Brooks 86] and thus has backends for a number of processors including the Motorola 68000 and 68HCll, the Hitachi 6301, and Common Lisp. Behaviors are groups of rules which are activatable by a number of different schemes. There are no shared data structures across behaviors, but instead all communication is by explicit message passing. All rules are assumed to run in parallel and asynchronously. It includes the earlier notions of inhibition and suppression, along with a number of mechanisms for spreading of activation.

Notes on PCA, Regularization, Sparsity and Support Vector Machines

We derive a new representation for a function as a linear combination of local correlation kernels at optimal sparse locations and discuss its relation to PCA, regularization, sparsity principles and Support Vector Machines. We first review previous results for the approximation of a function from discrete data (Girosi, 1998) in the context of Vapnik"s feature space and dual representation (Vapnik, 1995). We apply them to show 1) that a standard regularization functional with a stabilizer defined in terms of the correlation function induces a regression function in the span of the feature space of classical Principal Components and 2) that there exist a dual representations of the regression function in terms of a regularization network with a kernel equal to a generalized correlation function. We then describe the main observation of the paper: the dual representation in terms of the correlation function can be sparsified using the Support Vector Machines (Vapnik, 1982) technique and this operation is equivalent to sparsify a large dictionary of basis functions adapted to the task, using a variation of Basis Pursuit De-Noising (Chen, Donoho and Saunders, 1995; see also related work by Donahue and Geiger, 1994; Olshausen and Field, 1995; Lewicki and Sejnowski, 1998). In addition to extending the close relations between regularization, Support Vector Machines and sparsity, our work also illuminates and formalizes the LFA concept of Penev and Atick (1996). We discuss the relation between our results, which are about regression, and the different problem of pattern classification.