By Yves Chauvin (ed.), David E. Rumelhart (ed.)
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Kolmogorov, A. N. (1991). Selected Works of A. N. Kolmogorov, Dordrecht; Boston; Kluwer Academic. , Boser, Y. , Denke, J. , Henderson, R. D , Howard, R. , & Jackel, L. D. (1990). In D. S. ), Handwritten digit recognition with a back-propagation network (Vol. 2). San Mateo, CA: Morgan Kaufmann. McCullagh, P. & Nelder, J. A. (1989). Generalized linear models. London: Chapman and Hall. Mitchison, G. , & Durbin, R. M. (1989). Bounds on the learning capacity of some multi-layer networks. Biological Cybernetics, 60, 345-356.
We can imagine a single output unit which is to classify the input vectors (stimuli) as being in one or the other of these classes. A simple perceptron will be able to solve this problem if the stimuli are linearly separable; that is, we can draw a line which puts all of the A stimuli on one side of the line and all of the B stimuli on the other side. This is illustrated in part (a) of Figure 8. In part (b) we see that replacing the sharp line of the threshold function with a "fuzzy" line of the sigmoid causes little trouble.
Adaptive mixtures of local experts. Neural Computation, 3(1). Jordan, M. , & Rumelhart, D. E. (1992). Forward models: Supervised learning with a distal teacher. Cognitive Science, 16, pp. 307-354. Keeler, J. , Rumelhart, D. , & Loew, W. (1991). Integrated segmentation and recognition of hand-printed numerals. In R. P. Lippmann, J. E. Moody, and D. S. ), Neural information processing systems (Vol. 3). San Mateo, CA: Morgan Kaufmann. Kolmogorov, A. N. (1991). Selected Works of A. N. Kolmogorov, Dordrecht; Boston; Kluwer Academic.