Alexander Lorbert

Regularized hyperalignment of multi-set fMRI data

Inter-subject correspondence is an important aspect of multi-subject fMRI studies. Recently, a new approach, called hyperalignment, has shown very promising results in fMRI functional alignment. Hyperalignment is based on Procrustean rotations and is connected, mathematically, to canonical correlation analysis. We review the core details of each approach, relate them through an SVD analysis, and indicate why they can yield different levels of performance. We then examine the effectiveness of regularization in mediating between the extremes of these methods. An inter-subject classification experiment based on functional aligned fMRI datasets illustrates the resulting improved performance.

The Pairwise Elastic Net support vector machine for automatic fMRI feature selection

A support vector machine (SVM) regularized with the Pairwise Elastic Net (PEN) penalty is used to automatically select a sparse set of brain voxel clusters based on the fMRI responses to two stimuli classes. This requires solving the PEN-SVM quadratic program. We show how to design the PEN regularization to encode, in a graph-based fashion, the pairwise similarity structure of the voxel fMRI responses and how to control the spatial locality of the encoding using a voxel searchlight. The voxel similarity encoding is reflected in the sparse structure of the weights of trained PEN-SVM and these weights automatically select a sparse set of voxel clusters. We empirically demonstrate the effectiveness of the approach using a real-world, multi-subject fMRI dataset.

Level set estimation on the sphere

We investigate a technique for estimating level sets of functionals on the 2-sphere. The surface of the sphere is finely partitioned using a tree decomposition and a candidate level set is obtained by minimizing a regularized cost on the tree. A cycle spinning scheme, implemented as an ensemble classification method, is developed to decrease the variance of the tree-based estimate. Both constructions are compatible with many existing hierarchical discretizations of the 2-sphere, e.g. HEALPix and HTM. We present simulation results of a synthetic data set and an fMRI data set.

Collaborative denoising of multi-subject fMRI data

We propose a novel collaborative denoising scheme for multi-subject fMRI data. The scheme assumes that subjects experience a common, synchronous stimulus and uses the across-subject shared response structure to jointly denoise each subjects fMRI response along the spatial or voxel domain. Denoising is accomplished by learning subject-specfic orthonormal bases that yield sparse representations in a common transform domain. We provide empirical results using a real-world, multi-subject fMRI dataset.

The Rotational Lasso

This paper presents a sparse approach of solving the one-sided Procrustes problem with special orthogonal constraint. By leveraging a planar decomposition common to all rotation matrices, a new constraint is introduced into this classical problem in the form of a sparsity-inducing norm. We call the resulting optimization problem the Rotational Lasso. Experimental results are presented from a synthetic dataset.