Spatio-Temporal Tensor Analysis for Whole-Brain fMRI Classification
Guixiang Ma
1∗
, Lifang He
2∗
, Chun-Ta Lu
1
, Philip S. Yu
1,3
, Linlin Shen
2†
, and Ann B. Ragin
4
1
University of Illinois at Chicago, Chicago, IL, USA, {gma4, clu29}@uic.edu
2
Shenzhen University, Shenzhen, China, {lifanghe, llshen}@szu.edu.cn
3
Tsinghua University, Beijing, China, psyu@uic.edu
4
Northwestern University, Chicago, IL, USA, ann-ragin@northwestern.edu
Abstract
Owing to prominence as a research and diagnostic tool
in human brain mapping, whole-brain fMRI image anal-
ysis has been the focus of intense investigation. Con-
ventionally, input fMRI brain images are converted into
vectors or matrices and adapted in kernel based classi-
fiers. fMRI data, however, are inherently coupled with
sophisticated spatio-temporal tensor structure (i.e., 3D
space × time). Valuable structural information will be
lost if the tensors are converted into vectors. Further-
more, time series fMRI data are noisy, involving time
shift and low temporal resolution. To address these
analytic challenges, more compact and discriminative
representations for kernel modeling are needed. In this
paper, we propose a novel spatio-temporal tensor kernel
(STTK) approach for whole-brain fMRI image analysis.
Specifically, we design a volumetric time series extrac-
tion approach to model the temporal data, and propose
a spatio-temporal tensor based factorization for feature
extraction. We further leverage the tensor structure to
encode prior knowledge in the kernel. Extensive ex-
periments using real-world datasets demonstrate that
our proposed approach effectively boosts the fMRI clas-
sification performance in diverse brain disorders (i.e.,
Alzheimer’s disease, ADHD and HIV).
1 Introduction
Many neurological disorders (e.g., Alzheimer’s disease
[1], neuro-AIDS [2]) are characterized in the early stages
by latent ongoing brain injury. As a forefront Neu-
roimaging technique, functional Magnetic Resonance
Imaging (fMRI) has been widely used for noninvasive
interrogation of the brain. During the course of an fMRI
experiment, a series of brain images are obtained in the
resting state or while the subject performs a task tai-
lored to activate a specific cognitive function. Over the
last decade, machine learning classifiers, especially ker-
∗
Authors have equal contributions.
†
Corresponding author.
nel method, e.g., Support Vector Machines (SVM), have
been successfully employed on fMRI images for analysis
of neurological status and diagnosis [3, 4].
In this paper, we study the fMRI classification prob-
lem in the context of kernel modeling. Most work on
fMRI classification focuses on analysis of specific brain
regions of interest(ROI) [5]. However, ROI analysis is
usually based on certain assumptions and may ignore
additional valuable information in the image. Compar-
atively, whole-brain fMRI images provide comprehen-
sive structural and functional information of the human
brain, thus having higher exploratory power and lower
bias [6, 7]. Typically, as shown in Fig. 1(a), a whole-
brain fMRI image sample consists of a discrete time
series of 3D image volumes (scans), where each volume
consists of hundreds of thousands of voxels. Each voxel
contains an intensity value that is proportional to the
strength of the Nuclear Magnetic Resonance (NMR) sig-
nal emitted at the corresponding location in the brain
volume [8]. Therefore, an fMRI brain image sample can
be naturally represented as a fourth-order tensor with
3D space × time. How to appropriately utilize the infor-
mation from such sophisticated spatio-temporal struc-
ture is a main issue in the kernel modeling task.
Most of conventional kernel methods convert a
tensor to a vector (or a matrix), which is then adapted
in the kernel modeling [9, 10]. However, voxels are often
highly correlated with the surrounding voxels in the
brain volume. For example, the adjacent voxels, marked
with red and blue colors in Fig. 1(b), exhibit similar
patterns in Fig. 1(c). This kind of tensor-to-vector
(or tensor-to-matrix) conversion would cause the loss of
structural information such as the spatial arrangement
of voxel-based features, particularly given that fMRI
data has high spatial resolution [11].
A common solution is to focus on the 3D spatial
domain of the fMRI brain images [7, 12]. For instance,
in [12], the original 4D tensor of fMRI data is converted
to a 3D tensor by averaging over the time dimension.
Then the obtained 3D tensor is utilized in the kernel for
Copyright © by SIAM
Unauthorized reproduction of this article is prohibited.
819
Downloaded 01/03/19 to 222.200.111.211. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php