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Poster
A Statistical Recurrent Model on the Manifold of Symmetric Positive Definite Matrices
Rudrasis Chakraborty · Chun-Hao Yang · Xingjian Zhen · Monami Banerjee · Derek Archer · David Vaillancourt · Vikas Singh · Baba C Vemuri

Tue Dec 04 02:00 PM -- 04:00 PM (PST) @ Room 210 #33
in Tue Poster Session B »

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several recent papers have shown how convolutional neural networks (CNNs) can be extended to learn with graph-based data. In this work, we study the setting where the data (or measurements) are ordered, longitudinal or temporal in nature and live on a Riemannian manifold -- this setting is common in a variety of problems in statistical machine learning, vision and medical imaging. We show how recurrent statistical recurrent network models can be defined in such spaces. We give an efficient algorithm and conduct a rigorous analysis of its statistical properties. We perform extensive numerical experiments demonstrating competitive performance with state of the art methods but with significantly less number of parameters. We also show applications to a statistical analysis task in brain imaging, a regime where deep neural network models have only been utilized in limited ways.

Keywords: Recurrent Networks · Computer Vision · Frequentist Statistics · Brain Imaging · Activity and Event Recognition
[ Paper] 

Author Information

Rudrasis Chakraborty (University of Florida)
Chun-Hao Yang (University of Florida)
Xingjian Zhen (UW-Madison)
Monami Banerjee (University of Florida)
Derek Archer (University of Florida)
David Vaillancourt (University of Florida)
Vikas Singh (UW-Madison)
Baba C Vemuri (University of Florida, USA)

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