Development of Quantum Local Potential Function Networks Based on Quantum Assimilation and Subspace Division

The centers and radii of radial basis functions (RBFs) greatly affect the approximation capability of RBF networks (RBFNs). Traditional statistics-based approaches are widely used, but they may lack adaptivity to different data structures. Quantum clustering (QC), derived from quantum mechanics and the Schrödinger equation, demonstrates excellent capability in finding the structure and conformity toward data distribution. In this paper, a novel neural networks model called quantum local potential function networks (QLPFNs) is proposed. The QLPFN inherits the outstanding properties of QC by constructing the waves and the potential functions, and the level of data concentration can be discovered to obtain the inherent structures of the given data set. The local potential functions form the basic components of the QLPFN structure, which are automatically generated from the subsets of training data following specific subspace division procedures. Therefore, the QLPFN model in fact incorporates the level of data concentration as a computation technique, which is different from the classical RBFN model that exhibits radial symmetry toward specific centers. Some application examples are given in this paper to show the effectiveness of the QLPFN model.