Self-organizing maps with a single neuron

Self-organization is explored with a single complex-valued quadratic neuron. The output is the complex plane. A virtual grid is used to provide desired outputs for each input. Experiments have shown that training is fast. A quadratic neuron with the new training algorithm has been shown to have clustering properties. Data that are in a cluster in the input space tend to cluster on the complex plane. The speed of training and operation allows for efficient high-dimensional data exploration and for real-time critical applications.