| Content | Supervised learning problems using streamed data (a path) as input are important due to various applications in computer vision, e.g. automatic character identification based on the pen trajectory (online handwritten character recognition) and gesture recognition in videos. Recurrent neural networks (RNN) are one kind of very popular neural networks, which have strength in supervised learning on the path space and have been a success in various computer vision applications like gesture recognition. Stochastic differential equations (SDEs) are the foundational building blocks in the derivatives pricing theory, an area of huge financial impact. Motivated by the numerical approximation theory of SDEs, we propose a novel and effective algorithm (Logsig-RNN model) to tackle this problem by combining the log signature feature set and RNN. The log-signature serves a top-down description of data stream to capture its effects economically, which further improves the performance of RNN significantly as a feature set. Compared with a RNN based on raw data alone, the proposed method achieves better accuracy, efficiency and robustness on various data sets (synthetic data generated by a SDE, UCI Pen-Digit data and gesture recognition ChaLearn2013 data). In ChaLearn 2013 data (skeleton data only), the proposed method achieves state-of-the-art classification accuracy. |