Applying Deep Bidirectional LSTM and Mixture Density Network for Basketball Trajectory Prediction

Data analytics helps basketball teams to create tactics. However, manual data collection and analytics are costly and ineffective. Therefore, we applied a deep bidirectional long short-term memory (BLSTM) and mixture density network (MDN) approach. This model is not only capable of predicting a basketball trajectory based on real data, but it also can generate new trajectory samples. It is an excellent application to help coaches and players decide when and where to shoot. Its structure is particularly suitable for dealing with time series problems. BLSTM receives forward and backward information at the same time, while stacking multiple BLSTMs further increases the learning ability of the model. Combined with BLSTMs, MDN is used to generate a multi-modal distribution of outputs. Thus, the proposed model can, in principle, represent arbitrary conditional probability distributions of output variables. We tested our model with two experiments on three-pointer datasets from NBA SportVu data. In the hit-or-miss classification experiment, the proposed model outperformed other models in terms of the convergence speed and accuracy. In the trajectory generation experiment, eight model-generated trajectories at a given time closely matched real trajectories

Folded Recurrent Neural Networks for Future Video Prediction

Future video prediction is an ill-posed Computer Vision problem that recently received much attention. Its main challenges are the high variability in video content, the propagation of errors through time, and the non-specificity of the future frames: given a sequence of past frames there is a continuous distribution of possible futures. This work introduces bijective Gated Recurrent Units, a double mapping between the input and output of a GRU layer. This allows for recurrent auto-encoders with state sharing between encoder and decoder, stratifying the sequence representation and helping to prevent capacity problems. We show how with this topology only the encoder or decoder needs to be applied for input encoding and prediction, respectively. This reduces the computational cost and avoids re-encoding the predictions when generating a sequence of frames, mitigating the propagation of errors. Furthermore, it is possible to remove layers from an already trained model, giving an insight to the role performed by each layer and making the model more explainable. We evaluate our approach on three video datasets, outperforming state of the art prediction results on MMNIST and UCF101, and obtaining competitive results on KTH with 2 and 3 times less memory usage and computational cost than the best scored approach.Comment: Submitted to European Conference on Computer Visio