Fixed step size recursive algorithms for the covering problem

  • Authors:

  • J. A. Bucklew;W. A. Sethares

  • Affiliations:

  • Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI;Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI

  • Venue:
  • ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: digital speech processing - Volume III
  • Year:
  • 1993

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Abstract

This paper presents a family of techniques called Adaptive Cowering Algorithms, which solve a particular covering problem - how to best cover a target shape using a set of simply parameterized elements. The algorithms, inspired by adaptive filtering techniques, provide a computationally simple, robust, and efficient alternative to more traditional methods such as Bayesian approaches, convex hulls, and multi-layer perceptrons. The paper develops a theoretical understanding of the adaptive covering algorithms by relating their behavior to the evolution of a deterministic ordinary differential equation. Stability and instability of the ODE can be interpreted in terms of local stability/instability of the algorithm. In terms of the covering problem, candidate coverings tend to improve as more data is gathered whenever the ODE is stable. Several examples are given which demonstrate the ideas, and which verify that the analysis accurately predicts the true behavior of the algorithms.