A Statistical Recurrent Model on the Manifold of Symmetric Positive Definite Matrices

Autor:	Chakraborty, Rudrasis, Yang, Chun-Hao, Zhen, Xingjian, Banerjee, Monami, Archer, Derek, Vaillancourt, David, Singh, Vikas, Vemuri, Baba C.
Rok vydání:	2018
Předmět:	Computer Science - Machine Learning Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	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. Comment: Accepted in Thirty-second Conference on Neural Information Processing Systems (NIPS), 2018
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1805.11204 Zobrazit plný text záznamu View this record from Arxiv