Reconstruction of fragmented trajectories of collective motion using Hadamard deep autoencoders

Abstract

Learning dynamics of collectively moving agents such as fish or humans is an essential task in research. Due to phenomena such as occlusion or change of illumination, the multi-object methods tracking such dynamics may lose the tracks of the agents which may result in fragmentations of trajectories. Here, we present an extended deep autoencoder (DA) that we train only on the fully observed segments of the trajectories by defining its loss function as the Hadamard product of a binary indicator matrix with the absolute difference between the outputs and the labels. The trajectory matrix of the agents practicing collective motion is low-rank due to mutual interactions and dependencies between the agents that we utilize as the underlying pattern that our Hadamard deep autoencoder (HDA) codes during its training. The performance of this HDA is compared with that of a low-rank matrix completion scheme in the context of fragmented trajectory reconstruction.