Finite convergence of the learning algorithms for a modified multi-valued neuron

The multi-valued neuron (MVN) has a strong multi-classification ability. However, the MVN learning algorithms require the complex-valued learning rate and depends on the unknown optimal weights. To address this issue, we introduce a modified MVN that centers the neuron state in each sector. The learning algorithms of the modified MVN are able to reuse the real-valued learning rate and eliminate the dependencies on the optimal weights. We prove the convergence of the modified MVN learning algorithms with real-valued learning rate.