Independent vector analysis for common subspace analysis: Application to multi-subject fMRI data yields meaningful subgroups of schizophrenia

Abstract

The extraction of common and distinct biomedical signatures among different populations allows for a more detailed study of the group-specific as well as distinct information of different populations. A number of subspace analysis algorithms have been developed and successfully applied to data fusion, however they are limited to joint analysis of only a couple of datasets. Since subspace analysis is very promising for analysis of multi-subject medical imaging data as well, we focus on this problem and propose a new method based on independent vector analysis (IVA) for common subspace extraction (IVA-CS) for multi-subject data analysis. IVA-CS leverages the strength of IVA in identification of a complete subspace structure across multiple datasets along with an efficient solution that uses only second-order statistics. We propose a subset analysis approach within IVA-CS to mitigate issues in estimation in IVA due to high dimensionality, both in terms of components estimated and the number of datasets. We introduce a scheme to determine a desirable size for the subset that is high enough to exploit the dependence across datasets and is not affected by the high dimensionality issue. We demonstrate the success of IVA-CS in extracting complex subset structures and apply the method to analysis of functional magnetic resonance imaging data from 179 subjects and show that it successfully identifies shared and complementary brain patterns from patients with schizophrenia (SZ) and healthy controls group. Two components with linked resting-state networks are identified to be unique to the SZ group providing evidence of functional dysconnectivity. IVA-CS also identifies subgroups of SZs that show significant differences in terms of their brain networks and clinical symptoms.

Keywords: Functional magnetic resonance imaging; Heterogeneity of schizophrenia; Independent vector analysis; Multi-subject medical imaging data; Subspace analysis.

Figure 1:

IVA model and an example of two unseparable α-SCVs.

Figure 2:

The definition of common subspace and other two sets of SCVs in signal space (a) and the subset analysis and common subspace identification of IVA-CS (b). The number of SCVs in each of the three sets in (a) are denoted by N_C, N_G and N_D separately.

Figure 3:

Correlation matrices of true SCVs (a)–(h) and the estimated ones from IVA-G (i)–(p) and MCCA-GENVAR (q)–(v) in simulation. GT means ground truth.

Figure 4:

Boxplots of the correlation values between the estimates and the ground truth for IVA-G in blue and IVA-L-SOS in magenta for the four cases. Statistics are calculated from 100 independent runs with different initialization. The box plot displays the median, the 25th and 75th percentiles of the correlation values with whiskers extending to the 99.3% confidence interval using the default settings.

Figure 5:

Plot of joint-ISI as a function of the number of subjects when performing IVA-G on the hybrid data. The mean and standard deviation calculated from the results of 20 runs are shown.

Figure 6:

Smoothed distribution of the correlation values of the fifth subset of SZs (a) and the second subset of HCs (b). The red crosses and the green squares denote the mean and median. Two ratios q and $\tilde{q}$ are plotted in yellow and purple. Two vertical red lines denotes the margins between different groups of SCVs. Blue and magenta horizontal lines denotes 0.6 and 0.2 which are used for a comparison of the three groups of SCVs.

Figure 7:

Spatial maps of the common components in six categories: Motor; COG, cognitive control; DM, default mode; AUD, auditory, VIS, visual; CB, cerebellum. (a)-(d) for SZ group and (e)-(h) for HC group. The number of independent components (ICs) that are composited in each subfigure is listed and different colors refer to the spatial maps of individual components. The anatomical regions of the activation in the common components are provided in the supplementary materials.

Figure 8:

The clustering and modularization processes of the correlation matrices of group-specific SCVs and the two clusters that yield clear subgroups of patients (a-c). Subgroup 1, 2, and 3 are labeled by orange, magenta, and red squares separately. The differences of spatial activation patterns across subgroups in Cluster I (d) and Cluster II (e) are represented by the t-statistic from a two sample t-test with FDR (≤ 0.05) control and the associated confidence interval (CI) is reported. The brain regions that show significant subgroup (SG) differences including: posterior cingulate gyrus (PCG), BA31, secondary visual cortex (SVC), anterior cingulate gyrus (ACG), primary somatosensory and motor cortex (SSM), angular gyrus (Ang), inferior frontal gyrus (IFG), and BA30.

Figure 9:

The median (connected by solid lines), minimum, and maximum (connected by dash lines) values of each PANSS score of subgroups in Cluster I (a) and Cluster II (c), and the dominant (bright orange, magenta, and cyan) and absent (fade orange, magenta, and cyan) symptoms of each subgroup in Cluster I (b) and Cluster II (d). In (b) and (d), the bold symptoms refer to those that are unique for a subgroup and the translucent symptoms refer to those that are absent from all three subgroups.