Fuzzy Membership Functions for Nonparametric Signal and Data Modeling
The nonparametric form of fuzzy modeling can be promising, however, not analytically studied to compete with the Gaussian processes based Bayesian framework in statistics and machine learning. This work builds a fuzzy membership functions based signal and data modeling framework where a nonlinear mapping is assumed as uncertain and its uncertainty is being represented by an infinite-dimensional fuzzy membership function as a deterministic fuzzy analogous of a probabilistic Gaussian process. The membership functions are intended to be determined via maximizing the over uncertainties averaged log-membership values of the observed data around an initial guess. The maximization problem is partially analytically solved using variational optimization. The intractability problem of the analytical optimization based solution is circumvented by carefully and sensibly constraining the solution space to develop a practical algorithmic solution which is competitive in the modeling performance and computationally remarkably faster. The argument is sufficiently supported by the presented experimental results.
- W. Zhang, M. Kumar, J. Yang, Y. Wang, Y. Zhou, and J. Liu, "Fuzzy Membership Functions for Nonparametric Signal and Data Modeling," Future Generation Computer Systems, under-review, 2018.