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From: janowsky@math.rutgers.edu (Steven Janowsky)
Newsgroups: sci.math,comp.ai.neural-nets
Subject: Re: Pseudo-inverse formula problem.  HELP!
Message-ID: <Apr.29.12.57.52.1991.23683@math.rutgers.edu>
Date: 29 Apr 91 16:57:53 GMT
References: <1991Apr27.213346.9351@serval.net.wsu.edu> <1991Apr28.050903.6084@wimsey.bc.ca>
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Organization: Rutgers Univ., New Brunswick, N.J.
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The need for linear independence of patterns in neural network learning
algorithms is vastly overestimated.  Typically a linearly dependent set will
produce the same results as any spanning linearly independent set.

See Berryman, Inchiosa, Jaffe and Janowsky:
"Convergence of an iterative neural network learning algorithm for linearly
dependent patterns"  J. Phys. A 23 L223-L228 (1990).

"Extending the Pseudo-Inverse Rule" in _Neural_Networks_and_Spin_Glasses_
(Proceedings, Porto Alegre 1989), W.K. Theumann and R. K\"oberle, eds.,
Teaneck: World Scientific, 1990.