Self-organizing hypercomplex-valued adaptive network

Abstract

A novel, unsupervised, artificial intelligence system is presented, whose input signals and trainable weights consist of complex or hypercomplex values. The system uses the effect given by the complex multiplication that the multiplicand is not only scaled but also rotated. The more similar an input signal and the reference signal are, the more likely the input signal belongs to the corresponding class. The data assigned to a class during training is stored on a generic layer as well as on a layer extracting special features of the signal. As a result, the same cluster can hold a general description and the details of the signal. This property is vital for assigning a signal to an existing or a new class. To ensure that only valid new classes are opened, the system determines the variances by comparing each input signal component with the weights and adaptively adjusts its activation and threshold functions for an optimal classification decision. The presented system knows at any time all boundaries of its clusters. Experimentally, it is demonstrated that the system is able to cluster the data of multiple classes autonomously, fast, and with high accuracy.