No abstract

Temporal prediction is a still difficult task due to the chaotic behavior, non-Markovian characteristics, and nonstationary noise of temporal signals. Handwriting prediction is also challenging because of uncertainty arising from inter-class bifurcation structures, in addition to the above problems. For example, the classes '0' and '6' are very similar in terms of their beginning parts; therefore it is nearly impossible to predict their subsequent parts from the beginning part. In other words, '0' and '6' have a bifurcation structure due to ambiguity between classes, and we cannot make a long-term prediction in this context. In this paper, we propose a temporal prediction model that can deal with this bifurcation structure. Specifically, the proposed model learns the bifurcation structure explicitly as a Gaussian mixture model (GMM) for each class as well as the posterior probability of the classes. The final result of prediction is represented as the weighted sum of GMMs using the class probabilities as weights. When multiple classes have large weights, the model can handle a bifurcation and thus avoid an inaccurate prediction. The proposed model is formulated as a neural network including long short-term memories and is thus trained in an end-to-end manner. The proposed model was evaluated on the UNIPEN online handwritten character dataset, and the results show that the model can catch and deal with the bifurcation structures.