Pattern recognition by hierarchy of attracting sets

Summary form only given, as follows. A concept for pattern recognition based upon a hierarchy of attracting sets in phase space is proposed. The first group of attracting sets represents different classes of patterns, the second group different subclasses, etc. so that a new pattern is recognized in sequential steps starting with the identification of global characteristics and proceeding to finer and finer details. The approach exploits the phenomenology of nonlinear dynamics for creating an appropriate hierarchy of attracting sets. Special attention is paid to unsupervised learning based upon examples introduced to the neural network. Each example is considered an interpolation node of the velocity field in the phase space. The velocities at these nodes are selected such that all the streamlines diverge to an attracting set imbedded in the subspace occupied by the cluster of examples. The synaptic interconnections are found from the minimization of the strength energy, while the node velocities play the role of constraints. For faster convergence the higher order interconnection and terminal attractors are applied.<>