FANCFIS: Fast adaptive neuro-complex fuzzy inference system

Abstract

Large-scale multivariate time series forecasting is an increasingly important problem, with sensor networks pouring out sampled data at unprecedented rates, trillions of dollar's worth of stock trades made every data, and zettabytes of traffic transmitted over the Internet every year. While they are only examples of the much larger domain of general data streams, the uniformly-sampled time series still remains a very large and important subdomain. Extensive research has shown that machine-learning algorithms can often be very effective forecasting models, but many of these algorithms do not scale well. The Adaptive Neuro-Complex-Fuzzy Inferential System is one such approach; built to leverage complex fuzzy sets, it is both an accurate and parsimonious forecasting algorithm. However, its scaling is poor due to a relatively slow training algorithm (gradient descent hybridized with chaotic simulated annealing). Before the algorithm can be used for large-scale forecasting, a fast training algorithm that preserves the system's accuracy and compactness must be developed.We propose the Fast Adaptive Neuro-Complex Fuzzy Inference System, which is designed for fast training of a compact, accurate forecasting model. We use the Fast Fourier Transform algorithm to identify the dominant frequencies in a time series, and then create complex fuzzy sets to match them as the antecedents of complex fuzzy rules. Consequent linear functions are then learned via recursive least-squares. We evaluate this algorithm on both univariate and multivariate time series, finding that this incremental-learning algorithm is as accurate and compact as its slower predecessor, and can be trained much more quickly.