When: Friday, October 13 at 4:00 pm. Where: Fascitelli 040

Abstract: Data imputation is an essential preprocessing step in statistical learning that is to be performed before any technical analysis is conducted on partially observed data. Data originating from natural phenomena is low-rank due to diverse natural dependencies that a low-rank technique should primarily emphasize during the imputation. Thus, we present an extended deep autoencoder for low-rank data imputation that we train only on the fully observed portion of the data by defining its loss function as the Hadamard product of a binary indicator matrix with the absolute difference between the outputs and the labels. This indicator matrix is of the same size as the data matrix, which has ones corresponding to the observed entries of the data matrix and zeros elsewhere. While low-rank data imputation is widely applicable across disciplines, here we focus on the reconstruction of fragmented trajectories of collective motion. Learning the dynamics of collectively moving agents such as fish or humans is an essential task in research. Due to natural 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. Thus, we defragment the trajectories using our Hadamard deep autoencoder (HDA) in which the observed and unobserved segments of the trajectories are treated as observed and unobserved portions of data, respectively. 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 HDA codes during its training. The performance of this HDA is compared with that of a matrix completion scheme in the context of low-rank data imputation.

Kelum Gajamannage is an Assistant Professor in the Department of Mathematics and Applied Mathematical Sciences at URI. His research

interests encompass the development of mathematical and statistical algorithms/methods for Machine Learning (ML), Computer Vision, and

Network Science. Dr. Kelum Gajamannage was awarded his Ph.D. in Mathematics in 2016 by Clarkson University, USA; and was awarded his

MS in Applied Statistics and BS in Mathematics by the University of Peradeniya, Sri Lanka. He was an Assistant Professor from 2019 to 2023 in the Department of Mathematics and Statistics at Texas A&M University – Corpus Christi, USA. He was a Postdoctoral Scholar from 2016 to 2019 in the Department of Mathematical Sciences at Worcester Polytechnic Institute, USA.