In this work we have applied two different ensemble classification methods to analyze differences in functional connectivity across gender. RF is a well know technique in bioinformatics while the ELRC has been introduced here. This last approach combines the sparsity property of lasso regression with the concept of ensemble learning. The former will perform feature selection by forcing many predictors’ coefficients to be zero while the latter will allow defining importance scores for each variable by estimating the frequency of its appearance across all the models defining the members of the ensemble. These machine learning methodologies allow performing group analyses of brain networks without previous selection of thresholds.
The final result in both cases is a set of edges that carry discriminative information between the two groups of networks. In the case of the ELRC we used a very fast implementation of lasso regression provided by the library GLMNET that allowed us to use permutation testing not only for assessing the significance of accuracy but also for the importance of selected features.
The results produced by both methodologies were consistent in terms of the levels of classification accuracy and statistical significance. While the levels of classification accuracy were very similar the statistical significance of the results in both cases was the same. Despite very different underlying mechanisms, both methods detected common edges and nodes as more discriminative which are the more robust findings in this study. Our results suggest that the ELRC detected more discriminative edges than RF. Simulations necessary to confirm this finding were out of the scope of this work, as they are very time consuming and our focus was mainly on finding sex differences in R-fMRI brain networks. In addition, ELRC provides useful information about the association of the detected edges to classification as male or female. But this is a general advantage of linear classifiers over non-linear ones. Very often non-linear classifiers in high dimensional problems do not produce improvements while being at the same time more difficult to interpret because the linear classifiers generate weights for each predictor that can be used as a measure of their importance within the estimated model [72
]. Because RF is a highly non-linear classifier it does not provide this type of information.
There are some limitations in the ELRC methodology. There is a lack of a method to select optimal values of the number of classifiers of the ensemble (Nc
) and the fraction of samples used to generate each member of the ensemble. This is a common problem with previous approaches [30
]. Here via trial and error we have chosen the value of the fraction of samples that leads to higher values of average overall accuracy computed across all members of the ensembles. This amounts to performing lasso regression Nc
times with different CV partitions.
Although RF is a highly nonlinear classifier and, therefore, unable to provide information about the association of discriminative edges and sex, many of the discriminative edges identified using this technique overlap with discriminative edges associated with classification as male according to the ELRC analysis. Specifically, both the RF and ELRC methods identify key discriminative edges between: 1. left middle cingulum and right postcentral gyrus, 2. right para-hippocampal gyrus and right fusiform gyrus, as well as, 3. left calcarine fissure and right crus of the cerebellum (Tables
). These gender-discriminative differences are consistent with findings described in other studies investigating sexual dimorphism of network connectivity using graph theoretical methods [76
]. Wang and colleagues demonstrated lower nodal efficiency in females compared to males in the left middle cingulum and right parahippocampal gyrus. In addition, Tian and colleagues identified the left middle cingulate gyrus as an important hub node in males and females [77
]. The ELRC method identified additional nodes connected by gender discriminative edges in the present investigation that correspond to nodes that Wang et al.,
demonstrated to have gender-associated differences in efficiency, including frontal (left middle frontal gyrus), temporal (right superior temporal gyrus), and limbic/paralimbic regions (left hippocampus, right hippocampus, and left amygdala) [76
]. It is possible that gender-related differences in nodal efficiency [76
] may reflect sexually dimorphic variability in the nodes with which they connect, as demonstrated in the present study (Tables
). It is possible that differences in functional connectivity between males and females may also be related to gender-related differences in regional connectivity between hub nodes [77
In the present study, males demonstrated a greater proportion of gender-discriminative edges associated with sensory, motor and association regions than females, which may be related to known male gender performance differences in visuospatial tasks [44
]. As compared to males, females demonstrated a greater proportion of gender-discriminative edges associated with limbic regions, although both males and females had discriminative limbic-associated edges. In particular, there were distinct differences between males and females in specific limbic areas associated with gender-discriminative edges. For example, males but not females had a discriminative edge associated with the posterior cingulum and parahippocampal gyrus, which are known to be involved in visuospatial processing and formation of spatial memories, respectively [78
). Interestingly, men have demonstrated greater BOLD activation than women in posterior cingulum and parahippo-campal gyrus during performance of visuospatial navigation fMRI tasks [80
Other limbic areas, such as the anterior and middle cingulum, were identified in the present study as important nodes transmitting discriminative edges in both males and females (Tables
). Edges associated with the anterior and middle cingulum may be gender-discriminative because of the nodes with which they connect, which differ between males and females. For example, the anterior cingulum, known to be involved in affect processing [78
], is connected by a gender-discriminative edge to the right hippocampus in females, but to the triangular inferior frontal gyrus in males (Tables
). Similarly, the middle cingulum, which is known to be involved in response selection [78
], is connected by gender-discriminative edges to the vermis and right thalamus in females, but to the left and right posterior-central gyrus in males (Tables
). It is possible that these gender-associated differences in anterior and middle cingulate connectivity may contribute to known differences in cingulate BOLD activation associated with emotion-processing tasks between men and women that are correlated with fMRI task performance [82
Taken together, these data suggest that gender differences in brain function may be related to sexually dimorphic regional connectivity between specific critical nodes via gender-discriminative edges. Furthermore, such differences may be related to performance advantages of females on tasks such as verbal memory and selective attention [39
], and males on tasks of mental rotation and visuospatial ability [44
]. More work is necessary, however, to further investigate these possibilities.