Support vector machine learning-based fMRI data group analysis

Abstract

To explore the multivariate nature of fMRI data and to consider the inter-subject brain response discrepancies, a multivariate and brain response model-free method is fundamentally required. Two such methods are presented in this paper by integrating a machine learning algorithm, the support vector machine (SVM), and the random effect model. Without any brain response modeling, SVM was used to extract a whole brain spatial discriminance map (SDM), representing the brain response difference between the contrasted experimental conditions. Population inference was then obtained through the random effect analysis (RFX) or permutation testing (PMU) on the individual subjects' SDMs. Applied to arterial spin labeling (ASL) perfusion fMRI data, SDM RFX yielded lower false-positive rates in the null hypothesis test and higher detection sensitivity for synthetic activations with varying cluster size and activation strengths, compared to the univariate general linear model (GLM)-based RFX. For a sensory-motor ASL fMRI study, both SDM RFX and SDM PMU yielded similar activation patterns to GLM RFX and GLM PMU, respectively, but with higher t values and cluster extensions at the same significance level. Capitalizing on the absence of temporal noise correlation in ASL data, this study also incorporated PMU in the individual-level GLM and SVM analyses accompanied by group-level analysis through RFX or group-level PMU. Providing inferences on the probability of being activated or deactivated at each voxel, these individual-level PMU-based group analysis methods can be used to threshold the analysis results of GLM RFX, SDM RFX or SDM PMU.

Figure 1

Illustration of a separating hyperplane (solid line) with a maximal margin determined by a linear SVM. Dashed lines are the boundary hyperplanes of the separated classes and the circled symbols are the support vectors.

Figure 2

Diagram of individual SVM classification with or without permutation testing based group analysis. All subjects’ functional images were properly preprocessed and only the within voxels were considered. L, S, E, and X are the number of images per subject, original functional data matrix, decomposition matrix consisting of eigen vectors of S, and representing coefficients matrix respectively.

Figure 3

GLM RFX results of the null hypothesis resting CBF data. The t threshold is arbitrarily chosen to be 3.

Figure 4

SDM RFX results of the null hypothesis resting CBF data. The t threshold is the same as in Fig. 3.

Figure 5

Mean t values of the group analysis t maps of GLM RFX and SDM RFX for all simulations.

Figure 6

ROC analysis results. A) ROC curves of the GLM parametric map and the SDM of a representative subject’s synthetic data. The artificial activations were inserted into one ROI of 113 voxels with 5 percent of signal change. B) averaged (7 subjects) AUCs of GLM and SDM based analyses on the synthetic functional data with various percentage signal changes within two ROIs. The error bars mean the standard deviations. C) AUCs of the GLM RFX and SDM RFX on the same synthetic data as in B).

Figure 7

SDM extraction variations A) of the whole brain, B) within the hypothesized activation regions illustrated by the correlation coefficient between the SDM of the whole dataset and the SDM of a new dataset after randomly excluding an image from the baseline and the task condition. For B), the corrections were calculated within the hypothesized regions. The mean correlation coefficient of each subject is significantly greater than 0.975 (P < 0.00001) in A) and 0.986 (P < 0.0005) in B).

Figure 8

Suprathresholded A) multi-subject SDMrPM, B) multi-subject SDM, C) GLM RFX t map, and D) SDM RFX t map, superimposed on the MNI single subject’s template. The threshold is P < 0.001 (corresponding to rP> 0.999) for A); SDM> 14 for B), which is comparable to that used for A). Threshold for C) and D) is P < 0.001 (corresponding to t > 4.3).

Figure 9

Suprathresholded t maps of A) GLMrPM RFX and B) SDMrPM RFX, using a threshold of P < 0.01(t > 11.69) (FWE corrected). The display window is 11.69 ~ 100.

Figure 10

Suprathresholded group level permutation pseudo-t maps of A) GLM PMU and B) SDM PMU. The threshold is P < 0.05 (FWE corrected, corresponding to pseudo-t > 5.8), and the display window is 0 ~ ±10.