Encoder-X: Solving Unknown Coefficients Automatically in Polynomial Fitting by Using an Autoencoder
Author(s): Wang, GJ (Wang, Guojun); Li, WJ (Li, Weijun); Zhang, LP (Zhang, Liping); Sun, LJ (Sun, Linjun); Chen, P (Chen, Peng); Yu, LN (Yu, Lina); Ning, X (Ning, Xin)
Source: IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS DOI: 10.1109/TNNLS.2021.3051430 Early Access Date: JAN 2021
Abstract: Modeling, prediction, and recognition tasks depend on the proper representation of the objective curves and surfaces. Polynomial functions have been proved to be a powerful tool for representing curves and surfaces. Until now, various methods have been used for polynomial fitting. With a recent boom in neural networks, researchers have attempted to solve polynomial fitting by using this end-to-end model, which has a powerful fitting ability. However, the current neural network-based methods are poor in stability and slow in convergence speed. In this article, we develop a novel neural network-based method, called Encoder-X, for polynomial fitting, which can solve not only the explicit polynomial fitting but also the implicit polynomial fitting. The method regards polynomial coefficients as the feature value of raw data in a polynomial space expression and therefore polynomial fitting can be achieved by a special autoencoder. The entire model consists of an encoder defined by a neural network and a decoder defined by a polynomial mathematical expression. We input sampling points into an encoder to obtain polynomial coefficients and then input them into a decoder to output the predicted function value. The error between the predicted function value and the true function value can update parameters in the encoder. The results prove that this method is better than the compared methods in terms of stability, convergence, and accuracy. In addition, Encoder-X can be used for solving other mathematical modeling tasks.
Accession Number: WOS:000732326200001
PubMed ID: 33497343
Author Identifiers:
Author Web of Science ResearcherID ORCID Number
Zhang, Liping ABC-7060-2021 0000-0001-6508-3757
Ning, Xin M-9479-2018 0000-0001-7897-1673
Wang, Guojun 0000-0002-1317-3694
Li, Weijun 0000-0001-9668-2883
ISSN: 2162-237X
eISSN: 2162-2388
Full Text: https://ieeexplore.ieee.org/document/9336312