Extended Rayleigh-Ritz Autoencoder with Distribution-Free Statistics

This paper presents a detailed analysis of an extended Rayleigh-Ritz Autoencoder which uses distribution-free statistics to achieve stability with respect to non-Gaussian data. This provides consistent results for sensor data with both Gaussian and non-Gaussian perturbations. The necessity for handling non-Gaussian data in sensor applications is documented by the behavior of inclinometer sensors where the perturbations are characterized by Cauchy-Lorentz distribution. In such cases variance does not provide a reliable measure for uncertainty; consequently, 1-norm error measures are investigated thoroughly. Furthermore, the stability of the basis functions is improved via a new synthesis approach; enabling the use of single precision computations while achieving polynomials of higher degree. The concept of Lebesgue functions and constants is extended to constrained bases, yielding a theoretical upper bound on the interpolation error of the autoencoder.