Abstract
In this paper, we observe a new approach to learn non-linearly separable problems using a single multi-valued neuron. It is shown that a k-valued problem, which is non-linearly separable in the n-dimensional space can be projected into an m-valued (where m = kl) linearly separable problem in the same space. This projection can be utilized through a periodic activation function for the multi-valued neuron. Then the initial problem can be learned by a single multi-valued neuron using its learning algorithm. This approach is illustrated by the examples of such problems as XOR, Parity n, mod k addition of n variables and some benchmarks using a single multi-valued neuron.
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Aizenberg, I. (2011). On the Projection of k-Valued Non-linearly Separable Problems into m-Valued Linearly Separable Problems. In: Madani, K., Correia, A.D., Rosa, A., Filipe, J. (eds) Computational Intelligence. IJCCI 2009. Studies in Computational Intelligence, vol 343. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20206-3_15
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DOI: https://doi.org/10.1007/978-3-642-20206-3_15
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