Quantum Theory: The unified framework for FCM and QC algorithm

Clustering aims to study the instance distribution in scale-space. Its characteristics are very similar to the particle world in quantum mechanism. The probability wave function describes the distribution of particle, and the Schrodinger equation is the major methodology of solving for wave function when restricted boundary condition is given.Once wave function is confirmed, and the quantum potential serves as the clustering objective function to determine the location of particle distribution. In machine learning, this quantum mechanism implies that we can discover the grouping structures inherent in data. This is the key of quantum clustering, and is the same as the mechanism used in FCM algorithm. In FCM, via the key fuzzy similarity parameter is deduced by the wave function, a important predictability is proposed, which a cryptical wave function is found existing in FCM, finally, a quantum theory interpretation about FCM is presented in this paper.