On-line Learning on Temporal Manifolds

We formulate an online learning algorithm that exploits the temporal smoothness of data evolving on trajectories in a temporal manifold. The learning agent builds an undirected graph whose nodes store the information provided by the data during the input evolution. The agent's behavior is based on a dynamical system that is derived from the temporal coherence assumption for the prediction function. Moreover, the graph connections are developed in order to implement a regularization process in both the spatial and temporal dimensions. The algorithm is evaluated on a benchmark based on a temporal sequence obtained from the MNIST dataset by generating a video from the original images. The proposed approach is compared with standard methods when the number of supervisions decreases.