ALGeNet: Adaptive Log-Euclidean Gaussian embedding network for time series forecasting

Time series prediction has attracted much attention as various issues can be formulated as such a task. It is one of the critical challenges to extract the intrinsic information for estimating future trends from historical data. Long Short-Term Memory Network (LSTM) shows excellent performance in this assignment. Probabilistic information extraction, which is demonstrated effective in object recognition in recent years, has not been introduced in time series prediction. To our knowledge, there has not been any work on plugging trainable probability distributions into LSTM as feature representation in an end-to-end manner. In this work we put forward an Adaptive Log-Euclidean Gaussian embedding Network (ALGeNet) to take one step further on solving this problem. The core of the network is capturing statistical information through the Gaussian Distribution with LSTM for end-to-end learning. As the space of Gaussian Distribution is a manifold, we try to embed Gaussian layer into LSTM through mapping Gaussian space into a linear space based on the Lie group and logarithm operation. We introduce four descriptors of Gaussian, two descriptors performing direct logarithm and the others performing indirect logarithm. All of them can extract first-order and second-order statistical features while utilizing the structures of geometry and smooth group of Gaussians. Furthermore, our adaptive mechanism merges the advantages of each descriptor and works well. Experimental results on a real-world wind speed data set and a system-level electricity load dataset show that the proposed adaptive network outperforms some state-of-the-art algorithms. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This work introduces an Adaptive Log-Euclidean Gaussian embedding Network (ALGeNet) to extract probabilistic information from time series data and combines it with LSTM for end-to-end learning to better predict future trends. Experimental results show that the adaptive network outperforms some state-of-the-art algorithms on real-world datasets.