Riemannian multi-manifold modeling and clustering in brain networks

Konstantinos Slavakis; Shiva Salsabilian; David S. Wack; Sarah F. Muldoon; Henry E. Baidoo-Williams; Jean M. Vettel; Matthew Cieslak; Scott T. Grafton

doi:10.1117/12.2274405

24 August 2017 Riemannian multi-manifold modeling and clustering in brain networks

Konstantinos Slavakis, Shiva Salsabilian, David S. Wack, Sarah F. Muldoon, Henry E. Baidoo-Williams, Jean M. Vettel, Matthew Cieslak, Scott T. Grafton

Author Affiliations +

Proceedings Volume 10394, Wavelets and Sparsity XVII; 103940B (2017) https://doi.org/10.1117/12.2274405
Event: SPIE Optical Engineering + Applications, 2017, San Diego, California, United States

Abstract

This paper introduces Riemannian multi-manifold modeling in the context of brain-network analytics: Brainnetwork time-series yield features which are modeled as points lying in or close to a union of a finite number of submanifolds within a known Riemannian manifold. Distinguishing disparate time series amounts thus to clustering multiple Riemannian submanifolds. To this end, two feature-generation schemes for brain-network time series are put forth. The first one is motivated by Granger-causality arguments and uses an auto-regressive moving average model to map low-rank linear vector subspaces, spanned by column vectors of appropriately defined observability matrices, to points into the Grassmann manifold. The second one utilizes (non-linear) dependencies among network nodes by introducing kernel-based partial correlations to generate points in the manifold of positivedefinite matrices. Based on recently developed research on clustering Riemannian submanifolds, an algorithm is provided for distinguishing time series based on their Riemannian-geometry properties. Numerical tests on time series, synthetically generated from real brain-network structural connectivity matrices, reveal that the proposed scheme outperforms classical and state-of-the-art techniques in clustering brain-network states/structures.

Citation Download Citation

Konstantinos Slavakis, Shiva Salsabilian, David S. Wack, Sarah F. Muldoon, Henry E. Baidoo-Williams, Jean M. Vettel, Matthew Cieslak, and Scott T. Grafton "Riemannian multi-manifold modeling and clustering in brain networks", Proc. SPIE 10394, Wavelets and Sparsity XVII, 103940B (24 August 2017); https://doi.org/10.1117/12.2274405

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available