Reconstruction of Fragmented Trajectories of Collective Motion using Hadamard Deep Autoencoders

TL;DR

This paper introduces Hadamard Deep Autoencoders (HDA), a novel method for reconstructing fragmented trajectories of collective motion by leveraging low-rank patterns and training only on fully observed segments.

Contribution

The paper presents a new deep autoencoder approach that uses Hadamard products and low-rank assumptions to improve trajectory reconstruction in collective motion scenarios.

Findings

HDA outperforms low-rank matrix completion in trajectory reconstruction.

HDA effectively utilizes low-rank structures in collective motion data.

Training on fully observed segments enhances reconstruction accuracy.

Abstract

Learning dynamics of collectively moving agents such as fish or humans is an active field in research. Due to natural phenomena such as occlusion and change of illumination, the multi-object methods tracking such dynamics might lose track of the agents where that might result fragmentation in the constructed trajectories. Here, we present an extended deep autoencoder (DA) that we train only on 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 trajectories 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 our HDA is compared with that of a low-rank matrix completion scheme in the context of fragmented trajectory reconstruction.