Optimal Nonlinear Training in the Multi-Class Proximity Problem
D Bollé, G Jongen, GM Shim - International Journal of Neural …, 1996 - World Scientific
D Bollé, G Jongen, GM Shim
International Journal of Neural Systems, 1996•World ScientificUsing a signal-to-noise analysis, the effects of nonlinear modulation of the Hebbian learning
rule in the multi-class proximity problem are investigated. Both random classification and
classification provided by a Gaussian and a binary teacher are treated. Analytic expressions
are derived for the learning and generalization rates around an old and a new prototype. For
the proximity problem with binary inputs but Q′-state outputs, it is shown that the optimal
modulation is a combination of a hyperbolic tangent and a linear function. As an illustration …
rule in the multi-class proximity problem are investigated. Both random classification and
classification provided by a Gaussian and a binary teacher are treated. Analytic expressions
are derived for the learning and generalization rates around an old and a new prototype. For
the proximity problem with binary inputs but Q′-state outputs, it is shown that the optimal
modulation is a combination of a hyperbolic tangent and a linear function. As an illustration …
Using a signal-to-noise analysis, the effects of nonlinear modulation of the Hebbian learning rule in the multi-class proximity problem are investigated. Both random classification and classification provided by a Gaussian and a binary teacher are treated. Analytic expressions are derived for the learning and generalization rates around an old and a new prototype. For the proximity problem with binary inputs but Q′-state outputs, it is shown that the optimal modulation is a combination of a hyperbolic tangent and a linear function. As an illustration, numerical results are presented for the two-class and the Q′=3 multi-class problem.
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