An introduction to multiscale defined systems: self-organising IFS fractal networks

Deterministic multiscale defined representational forms have found a significant role in the theory and application of signal processing. The most widely important form for signal and system modelling is likely to be multiscale defined wavelets. Another class of multiscale representation which has attracted consistent interest is the group of signal models defined in terms of iterated function systems (IFS). This paper is concerned with widening the IFS application to include system modelling, particularly of neural network-like structures. We introduce an interpolating IFS model as a form of self-organising map with global fractal constraints. Symbolic addressing is employed to discretize the attractor into pseudo-network nodes. We present in detail an online gradient based algorithm for training. This particular model is intended for efficient pattern recognition in complex environments, for example, with multifractal sources such as those seen in network traffic and general turbulence