Data-Driven Fuzzy Transform

The Fuzzy transform is applied mainly to 1-D signals and 2-D data organized as a regular grid (e.g., images), thus, limiting its potential application arbitrary in terms of dimensionality structure. This article defines analyzes the properties data-driven F-transform, with focus on construction class membership functions, which are multiscale, local, linearly independent, intrinsic, robust discretization. Data-driven functions defined by applying filter Laplace–Beltrami operator, encodes geometric topological input data. Then, we address efficient computation F-transform through polynomial or rational approximation filter. In this way, independent evaluation at any point domain reduces solution small set sparse symmetric linear systems. Finally, efficiently evaluated large data, dimensionality, structure, size.