Name
Abstract | ||
|---|---|---|
In this paper we formulate a homotopy approach for solving for the weights of a network by smoothly transforming a linear single layer network into a nonlinear perceptron network. While other researchers have reported potentially useful numerical results based on heuristics related to this approach, the work presented here provides the first rigorous exposition of the deformation process. Results include a complete description of how the weights relate to the data space, a proof of the global convergence and validity of the method, and a rigorous formulation of the generalized orthogonality theorem to provide a geometric perspective of the solution process. This geometric interpretation clarifies conditions resulting in the appearance of local minima and infinite weights in network optimization procedures, and the similarities of and differences between optimizing the weights in a nonlinear network and optimizing the weights in a linear network. The results provide a strong theoretical foundation for quantifying performance bounds on finite neural networks and for constructing globally convergent optimization approaches on finite data sets. |
Year | DOI | Venue |
|---|---|---|
1996 | 10.1109/72.485634 | IEEE transactions on neural networks / a publication of the IEEE Neural Networks Council |
Keywords | Field | DocType |
nonlinear single-layer network,network optimization procedure,linear network,finite neural network,natural homotopy,data space,convergent optimization approach,linear single layer network,nonlinear perceptron network,nonlinear network,finite data set,deformation process,neural network,kalman filters,linear systems,neural networks,neural nets,time series analysis,pattern analysis,pattern recognition,local minima | Convergence (routing),Mathematical optimization,Nonlinear system,Linear system,Computer science,Orthogonality,Maxima and minima,Artificial intelligence,Homotopy,Artificial neural network,Perceptron,Machine learning | Journal |
Volume | Issue | ISSN |
7 | 2 | 1045-9227 |
Citations | PageRank | References |
5 | 0.60 | 10 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Frans Coetzee | 1 | 370 | 28.76 |
| V. L. Stonick | 2 | 17 | 3.16 |