Application of the sequential matrix diagonalization algorithm to high-dimensional functional MRI data

Abstract

This paper introduces an adaptation of the sequential matrix diagonalization (SMD) method to high-dimensional functional magnetic resonance imaging (fMRI) data. SMD is currently the most efficient statistical method to perform polynomial eigenvalue decomposition. Unfortunately, with current implementations based on dense polynomial matrices, the algorithmic complexity of SMD is intractable and it cannot be applied as such to high-dimensional problems. However, for certain applications, these polynomial matrices are mostly filled with null values and we have consequently developed an efficient implementation of SMD based on a GPU-parallel representation of sparse polynomial matrices. We then apply our "sparse SMD" to fMRI data, i.e. the temporal evolution of a large grid of voxels (as many as 29,328 voxels). Because of the energy compaction property of SMD, practically all the information is concentrated by SMD on the first polynomial principal component. Brain regions that are activated over time are thus reconstructed with great fidelity through analysis-synthesis based on the first principal component only, itself in the form of a sequence of polynomial parameters.

Pooling random forest and functional data analysis for biomedical signals supervised classification: Theory and application to electrocardiogram data

“…1,2,[8][9][10] In addition, there is a constant development of novel applications and suggestions to answer particular dilemmas in singular contexts employing functional instruments. [11][12][13][14][15][16] Because FDA is widely appreciated as a valuable tool for analyzing biomedical data, research on curves' supervised classification is lively. 7,[17][18][19] However, functional data supervised classification using tree-based techniques is still little known and underdeveloped.…”

“…For these reasons, recently, we are witnessing an uninterrupted growth of methodological research on FDA that attempts to replicate, in a functional key, a large part of classical statistics 1,2,8‐10 . In addition, there is a constant development of novel applications and suggestions to answer particular dilemmas in singular contexts employing functional instruments 11‐16 …”

“… 1 , 2 , 8 , 9 , 10 In addition, there is a constant development of novel applications and suggestions to answer particular dilemmas in singular contexts employing functional instruments. 11 , 12 , 13 , 14 , 15 , 16 …”