Although the self has traditionally been viewed as a higher-order mental function by most theoretical frameworks, recent research advocates a fundamental self hypothesis, viewing the self as a baseline function of the brain embedded within its spontaneous activities. This hypothesis has been behaviorally established by observed self-biased effects, but its neural embeddedness remains uncorroborated. To provide a test, we investigated the association between spontaneous neural connectivity and robust self-prioritization in a perceptual matching task using task-irrelevant functional magnetic resonance imaging in 348 participants. By decoding whole-brain connectivity patterns, the support vector regression model successfully predicted the magnitude of behavioral self-prioritization, supporting the fundamental self hypothesis. The functional connectivity among default mode, cognitive control, and salience networks served as prominent neuromarkers of self-biased behavior. We further proposed a fundamental self-network model that portrays the brain mechanisms by which the self emerges internally and regulates responses to the external environment.
Article
Decoding individual differences in self-prioritization from the resting-state functional connectome
https://doi.org/10.21203/rs.3.rs-2204324/v1
This work is licensed under a CC BY 4.0 License
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published 01 Aug, 2023
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self-prioritization effect
resting state
functional magnetic resonance imaging
functional connectivity
machine learning
One of the most intriguing questions in science is how the brain generates a sense of the self. Previous philosophical, psychological, and neuroscientific discussions on this topic have yielded two competing views 1. The first, hereafter referred to as the higher-order self hypothesis, dates back to philosophers such as Descartes and Kant and regards the self as one of the brain’s highest functions and serves as a meta-representation of other lower-level functions such as perception, emotion, memory, and action 2, 3. However, recent theories have challenged this notion and advocated for an alternative fundamental self hypothesis, which depicts the self as a fundamental brain function that precedes and regulates other functions 1, 4, 5, 6, 7, 8. According to this viewpoint, the self is an intrinsic feature of the brain that is embedded within and continuously sustained in spontaneous activities of the brain 1. When an internal or external stimulus appears, the self network interacts with task-related networks to exert its influence on cognitive processing 1, 8.
The fundamental self hypothesis has been empirically supported by three lines of research. First, it has been well documented that our brain prioritizes processing stimuli related to ourselves, a phenomenon known as the self-prioritization effect (SPE) 9. The SPE manifests itself in a variety of cognitive processes including memory, attention, and perception 10. For instance, individuals can automatically notice the mention of their name in background noise 11 and recognize their own faces more quickly than other people’s faces 6. Even simple and meaningless geometric shapes (e.g., triangles or circles) are processed more quickly when associated with the self 9. The widespread manifestation of the SPE at various levels of cognitive processing lends support to the idea that the self is a fundamental mental function. Second, the spontaneous neural network, that is, the default mode network (DMN), which is active mainly during rest, overlaps significantly with the network activated when one thinks about oneself, both of which involve so-called cortical midline structures 12, 13, 14. This anatomical overlap implies the presence of self-related processing within the brain’s spontaneous activities 13, 14, but anatomical overlap does not guarantee functional overlap. More direct evidence was provided by a third line of work that directly tested the hypothesized link between resting-state activities and self-related behaviors. The processing of self-related stimuli has been shown to influence subsequent resting-state activity and vice versa 15, 16, 17. Resting-state activities can also be used to predict self-related personality traits such as self-consciousness 18 or self-reflectiveness 19.
Although these studies provide preliminary support for the rest-self relationship, there are still gaps in the current evidence base. First, the small number of studies that directly examined the rest-self link commonly employed measures of self-related behaviors that require higher-order processing (e.g., the explicit judgment of a stimulus’s self-relatedness or completing self-reported scales) and thus cannot fully test the hypothesis of the self at the fundamental level of the mental function hierarchy. Second, although existing studies have mostly focused on the DMN, the roles of other regions in the neural basis of the self are unclear. For example, the thalamus has been reported to be involved in self-referential processing 20, 21, but its exact role remains unclear.
As the fundamental self hypothesis stresses the stability of the self rather than the ebb and flow of thoughts or a specific aspect of the self, it is critical to examine this hypothesis based on self-related trait measurements. Therefore, the present study examined the hypothesis of the SPE in perceptual matching 9 from the resting-state connectome in a large sample of young and healthy participants (n = 348). The SPE has been shown to relate to different aspects of cognitive processing, reflecting the stability of self-processing across tasks and contexts 22. Compared with previous studies’ self-related tasks (higher-level behavioral tasks or self-reported measures), this task can more directly probe the self’s regulation of other mental functions, particularly low-level functions such as attention and perception and thus provide a more appropriate test of the fundamental self hypothesis 7, 8, 9. Moreover, in contrast to previous studies’ general linear model approach, we used a machine learning approach by building a linear support vector regression (SVR) model with whole-brain resting-state functional connectivity (rs-FC) as the input feature and the predicted magnitude of the SPE as the output. This approach leverages rich information on the spontaneous brain activity on rs-fMRI and the data-driven nature of machine learning to generate individualized predictions. It has been used successfully to identify neurobiological markers of individual difference variables such as demographics 23, traits 24, and performance in cognitive tasks 25, 26. A rigorous leave-one-out cross-validation (LOOCV) procedure was applied to ensure out-of-sample generalizability 27. The contributing FCs were further identified through analyses of model coefficients and computational lesions. Based on previous theoretical and empirical studies 1, 8, 28, 29, 30, 31, we hypothesized that the medial prefrontal cortex, posterior superior temporal sulcus, and dorsolateral prefrontal cortex would significantly contribute to the performance of the model. The roles of other regions were also examined using our data-driven approach.
Network definition. To test whether rs-FC can predict an individual’s magnitude of self-prioritization, we asked 348 participants to complete the perceptual matching task (see Fig. 1a) outside the scanner. Briefly, the participants were instructed to associate themselves and a stranger with different shapes (e.g., “a circle represents you, and a square represents a stranger”) and then continuously judge whether the label-shape combination displayed on the screen was correct. Participants’ tendency for self-prioritization was quantified as the difference in reaction time between the stranger- and self-matching conditions 32.
Fig. 1b depicts the processing pipeline. The whole-brain functional network nodes were defined using the Human Brainnetome Atlas 33, which consists of 210 cortical and 36 subcortical regions of interest (ROIs). This fine-grained atlas reliably integrates information from anatomical and functional connections and has been used in many neuroimaging studies to predict individual differences 34. For each participant, time series within each node were computed by averaging the blood oxygenation level-dependent (BOLD) signal over all voxels in the ROIs. We then calculated the Pearson correlation for each pair of the 246 resulting time series to obtain a 246 × 246 symmetric FC matrix for each participant. Each element in the matrix characterizes the FC strength between two nodes.
However, when combining neuroimaging and behavioral data in machine learning algorithms, an inescapable challenge is the potential curse of dimensionality caused by few samples but high dimensionality 35. The numerous unique features in the FC matrix entail a feature-selection step before model building 25, 36. To identify potential predictive features, we performed a Pearson correlation between each feature (i.e., edge) and the SPE score (based on the training set only; see Methods for details). A commonly used threshold (p < 0.01) was then applied to remove noisy edges and retain those that were significantly correlated 25. As a result, the number of selected features varied from 317 to 383 in multiple iterations, representing less than 2% of the brain’s 30,381 total edges as defined by the atlas.
Predictability of SPE. The selected features were subsequently fed into a linear SVR model. Through rigorous LOOCV, we obtained the predicted SPE value for each participant. Notably, as suggested by previous studies 37, we also employed an inner loop of 5-fold cross-validation to tune the hyperparameters of the linear SVR and avoid data leakage. Overall, in the unseen data (i.e., not used to train the model), the true value of the SPE was significantly correlated with the predicted value (r = 0.41, p < 0.001; Fig. 1c), indicating that our linear SVR model successfully predicted the SPE of individuals.
Notably, a common pitfall in machine learning is that each cross-validation fold does not satisfy independence, and the best practice for assessing the significance of model performance is permutation testing 35. Therefore, we randomly shuffled the phenotype (i.e., SPE score) and reran the prediction pipeline 1000 times to obtain a null distribution of the model performance. The p-value was calculated as (1 + the number of r-values in the null distribution that are greater than or equal to the r-values resulting from the unshuffled data)/1001. The permutation test results confirmed the significance of the predictive model (permutation p < 0.001).
Model robustness and specificity. Previous studies have suggested that the predictive power of models may be affected by confounding factors 35. In the worst case, the model may predict not the desired phenotype but confounders such as demographic variables or head movement. To verify the robustness of the identified network to these factors, we performed several control analyses. First, instead of using Pearson’s correlation, we selected the most relevant features based on partial correlation coefficients that controlled for age, gender, or head movement (defined as mean framewise displacement). The resulting networks still significantly predicted the participants’ SPE scores (rs > 0.25, permutation ps < 0.001). Second, before feature selection, we removed any edges associated with age or head movement or that differed between genders (p < 0.01). The streamlined networks still significantly predicted the SPE (rs > 0.31, permutation ps < 0.001). Third, we reconstructed a model using only these covariates as features and compared its performance with that of the main model. The results revealed that the covariate-only model could not predict participants’ SPE scores (r = -0.16, permutation p = 0.99), and Steiger’s Z test showed that its performance was significantly worse than that of the main model (z = 7.78, p < 0.001).
Another consideration for robustness is the choice of the algorithm. Although SVR is one of the most widely used algorithms 38, we replaced it with several other common linear models to further boost robustness. Note that feature selection and cross-validation (CV) strategies were the same. The results revealed that the predictions of the least absolute shrinkage and selection operator (LASSO) and ridge regression remained significant after replacing the linear SVR (r = 0.21 and 0.23, respectively, permutation ps < 0.001), whereas ordinary least squares (OLS) regression failed to predict individuals’ SPE scores (r = 0.08, permutation p = 0.07). The unsatisfactory performance of OLS can be attributed to overfitting caused by a lack of regularization 39.
Finally, to examine the specificity of the prediction model, we used the identified consensus network to predict participants’ self-construal 40, which is associated with SPE 41. The results demonstrated that although the consensus network could successfully predict SPE scores, it could not significantly predict participants’ independent self (r = -0.16, permutation p > 0.99) or interdependent self (r = 0.04, permutation p = 0.14). These results demonstrate that the consensus network is specific to the SPE, which is a behavior-level self-bias and cannot be generalized to higher-level self-reflections such as self-construals. Interestingly, a previous study demonstrated that self-interdependency has a stronger impact on individuals’ self-prioritization than self-independence 41. This is consistent with our results, showing that the interdependent self predicts slightly better than the independent self (z = 2.70, p < 0.01).
Overall, we demonstrated that the identified networks were SPE-specific and that the trained model was robust. The predictions were not confounded by covariates such as head movements and could be achieved with different algorithms.
Contributing networks to prediction. As described above, each iteration of LOOCV may select slightly different features; therefore, we first selected those edges that appeared in all iterations to construct a consensus network (Fig. 1d) for interpretation 25. Consistent with previous prediction studies 23, 36, the highest-degree nodes (i.e., nodes with the most connections) in the consensus network were widely distributed across the brain, including the frontal, occipital, parietal, and temporal lobes, as well as the subcortical regions (see Table S1). In particular, most of these nodes were located in the right hemisphere. To better characterize the neural substrates of self-prioritization prediction, we took full advantage of the weights assigned to each feature in the SVR model. As recommended by Haufe, et al. 42, we first transformed the raw coefficients into interpretable activation patterns (see Methods for details). Subsequently, we summarized the connectivity patterns using these two methods.
First, we grouped the 246 nodes into 24 macroscale brain regions anatomically defined by the Brainnetome Atlas 33. The contribution of connectivity in each pair of macroscale regions was characterized as the sum of the activation patterns of all edges within it 43. As shown in Fig. 2, the FCs between the thalamus and the parahippocampal gyrus (PhG), lateral occipital cortex and superior temporal gyrus (STG), thalamus and insular gyrus, superior frontal gyrus (SFG) and inferior frontal gyrus (IFG) were the primary predictors of stronger self-prioritization. Meanwhile, the FCs between the PhG and middle temporal gyrus, PhG and middle frontal gyrus, and within the IFG predicted weaker self-prioritization.
Second, we regrouped the nodes into canonical networks based on the Yeo 17-network parcellation 44. The mapping relationship between nodes and networks was defined by the atlas development team 45, 46. For clarity, we merged related sub-networks in the 17 networks 47 and referred to the undefined subcortical regions as subcortical networks. For the resulting nine canonical networks, we evaluated the contribution of within- or between- network connectivity analogously to the analyses of macroscale brain regions (Fig. 3a). The results demonstrated the predictive power of connectivity between the dorsal attention network (DAN) and somatomotor network (SMN), the DMN and salience network (SN), and the DMN and DAN.
To assess the role of each canonical network individually, we performed further computational lesion analysis (see Fig. 3b). A lesion in a canonical network means that the signals of all its constituent nodes are erased, and the pipeline is then reran based on the resulting FC matrix 25. The results demonstrated that the model could still significantly predict individuals’ SPE scores without any single canonical network, which corresponds to findings in other fields, confirming that machine learning models tend to utilize whole-brain signals 48. Nevertheless, Steiger’s Z test still found several canonical networks that caused significant degradation in model performance after computational lesions, including the subcortical network (z = 5.74, p < 0.001), limbic network (z = 3.30, p < 0.001), SMN (z = 4.15, p < 0.001), DMN (z = 2.85, p < 0.01), DAN (z = 2.2, p = 0.03), and SN (z = 2.35, p = 0.02).
Longstanding controversies and disparate theories regarding the emergence of the sense of self have necessitated more neuroscientific evidence. Here, we demonstrated that individual differences in self-prioritization in behavior can be reliably decoded from whole-brain spontaneous FC, indicating readiness for self-related processes in the brain at rest, supporting the hypothesis about the embedding of self-processing within the brain’s spontaneous brain activities.
A closer look at the consensus predictive network revealed that the FCs of several nodes within the DMN, SN, and DAN over the frontal and temporal lobes, such as the SFG, IFG, and STG, contributed significantly to the model. The involvement of these regions in self-related cognition has been repeatedly reported 6, 30, 31, and our results confirmed their roles in self-processing. In addition to these high-level cortices, the current findings highlight the role of several subcortical structures, especially the FCs between the thalamus, insula, and amygdala. Although numerous studies have confirmed the role of the insula and amygdala in the self 5, 8, relatively little has been discussed regarding the thalamus. The thalamus has traditionally been described as a machine-like relay station for cortical information. However, contemporary perspectives suggest that it may continue to play an essential role in subsequent sensory and motor cortical processing through transthalamic corticocortical pathways 49. In addition, alterations in thalamocortical rs-FC have been linked to major depression and schizophrenia 50, 51. Shine 52 argued that the thalamus might be responsible for integrating and regulating the macrosystems of the brain. These views provide the basis for evidence that the thalamus, insula, and amygdala constitute neural substrates of the interoceptive self 5, 53. Moreover, previous studies have demonstrated that the thalamus is involved in self-related processing 20, 21. Our results add to these previous studies by demonstrating that the thalamus may also be involved in the self’s readiness to regulate cognitive processing.
When organizing the brain into large-scale functional systems, the contributing FCs are widely distributed among the brain’s canonical networks. This was echoed by computational lesion analysis, which showed that six of the nine networks contributed significantly to the model’s predictive performance. This widespread pattern of results has two implications. First, although the triad of DMN-SN-DAN has been addressed by previous theoretical models that account for the neural basis of the self 1, 8, the contributions of the limbic network, SMN, and subcortical network have been less frequently discussed. In our computational lesion analysis, the impact of the SMN and subcortical network on model performance was much greater than that of the DMN, SN, and DAN, indicating that they also play significant roles in the self-prioritization process. Second, on a broader level, our results provide evidence supporting the embedding of self-processing within the brain’s spontaneous brain activities. Although previous studies have examined the association between resting-state activities and higher-level self-processing 15, 16, 17, 18, 19, our behavioral task could more readily reflect the self’s regulation of low-level processes (i.e., attention), thus providing more direct support to the fundamental self hypothesis.
To synthesize previous theoretical and empirical works, as well as the current findings, we propose a fundamental self-network model (see Fig. 4) that describes the neural mechanism that gives rise to the self and regulates other cognitive functions. Specifically, we argue that social information in stimuli affects the processing of core self circuits: self-related stimuli naturally activate the DMN-SN connection, whereas others-related stimuli trigger DAN inhibition of DMN and SN activity. The cerebral cortex generates observable self-biased behaviors through the SMN. Importantly, subcortical structures, especially the thalamus, may not only be responsible for relaying stimuli to SMNs but may also be involved in all subsequent processing.
The fundamental self-network model can be used to interpret previous findings. On the one hand, according to this model, individuals with greater self-specificity in the brain’s spontaneous activity may have stronger connectivity between the DMN and SN. The DMN is often linked to self-related processing owing to the anatomical overlap of brain regions 13, 14, 28. Similarly, representative regions of the SN, such as the insula and anterior cingulate, are consistently involved in self-related processing 5, 53. The broad involvement of the SN can be attributed to the fact that the self is a salient stimulus 29, 54. However, although DMN-SN interaction has been linked to many brain functions 55, 56, it has only recently been used to characterize the self 8. In line with their hypothesis and our model, Yankouskaya and Sui 57 observed stronger activity in DMN-SN connectivity during self-processing than during other-processing.
On the other hand, our model indicates that individuals with stronger FC between the DAN and DMN or SN possess a weaker self-prioritization tendency. Consistently, Sui et al. 31 found that the dorsolateral prefrontal cortex, a key node of the DAN, showed enhanced activation in other-reference processing compared to self-related processing. Later, Sui et al. 58 observed a hyperself-bias effect on the attentional control network in a patient with lesions. They then proposed a self-attention network to explain the role of attention in social processing 6. Based on evidence from multiple domains, they concluded that self-related stimuli are naturally salient and attention-attracting; therefore, individuals need to mobilize a top-down attentional system to suppress spontaneous self-bias when switching to other-related stimuli. This echoes our model that weaker self-bias may also stem from the stronger inhibitory capacity of the attention network.
In summary, this study takes the first step in using a data-driven machine-learning approach to predict individuals’ self-prioritization, supporting the hypothesis that self-specific information is embedded within the spontaneous activity of the brain 1. Although it contributes to our knowledge of the neural substrate of the self, the present study has several limitations that need to be acknowledged. First, although our sample size was relatively large in neuroscience research, the prediction stability of machine learning improves significantly as sample size increases 59. Given the high cross-site similarity of rs-fMRI, the predictive power of the identified networks can be validated using more diverse samples. Second, we used a perceptual matching task to measure self-bias because it excluded the effect caused by differences in stimulus familiarity 60. One promising direction is to have participants complete various self/other processing trait-like tasks and then refine the core self-representing brain regions by constructing multiple predictive models. Another trend in machine learning-based neuroimaging research is the use of multi-modal features for prediction, such as task-fMRI 25, dynamic FC 43, and structural connectivity 61. Future studies could incorporate multi-modal data into the model to determine whether better biomarkers can be identified.
Participants. A total of 380 healthy young participants were recruited from Tsinghua University and the surrounding community. After excluding subjects with missing SPE scores or demographic data (n = 20) or excessive head motion during scanning (n = 12, defined as >0.2 mm mean framewise displacement), the final sample used for analysis included 348 individuals (182 women; mean age, 22.5 years; age range, 18-34 years). All the participants provided informed consent. This study was conducted under an ethical protocol approved by the Ethics Committee of the Center for Biomedical Imaging Research at Tsinghua University.
Behavioral assessment. We used a well-established perceptual matching paradigm to quantify the magnitude of an individual’s self-prioritization 9. There were two phases in this task. In the learning phase, participants were instructed to associate two geometric shapes (i.e., square and circle) with two personalized labels (i.e., “you” and “stranger”). For example, participants may be told that a square represents themselves and a circle represents a stranger. The matching pattern was counterbalanced across participants, who were asked to judge whether an upcoming series of random shape-label pairs corresponded to it.
After the associations were created, participants started the matching phase immediately. Each trial started with a central fixation cross (0.8° × 0.8° visual angle) for 500 ms. Then, a shape (3.8° × 3.8°) and a label (2.4° × 1.6°) were presented above and below the fixation cross for 100 ms. A subsequent blank frame occupied the screen until a response was made or 1100 ms elapsed, during which the participants were expected to judge whether the shape-label pairing was correct as quickly and accurately as possible. Feedback (correct or incorrect) was provided on the screen for 500 ms at the end of each trial. Each participant completed 96 trials following 12 practice trials, with a total of 24 trials for each condition (self-matching, self-mismatching, stranger-matching, and stranger-mismatching). All stimuli were rendered on a gray background on a 17-inch monitor (1024 × 768 at 60 Hz). The experiment was run on a PC using E-prime software (version 2.0).
Previous studies using this paradigm have generally performed group-wise analyses to compare differences between the self and other conditions 29, 31. However, machine learning techniques, entail specific individualized scores for prediction. Given that self-prioritization has been most robustly characterized by differences between the reaction time of the self and others in matching conditions 31, we defined the SPE score as the difference in mean reaction time (RT) between these two matching conditions (i.e., SPE score = RTstranger-matching – RTself-matching). This metric has also been employed in previous neuroscience research on the SPE 41.
Image acquisition. Images were acquired with a Philips Achieva 3.0T TX system at the Center of Bio-Medical Imaging Research, Tsinghua University. All participants completed a 508.3-second rs-fMRI scanning, during which they were instructed to open their eyes, to not think about anything systematically, and to not fall asleep. Functional images were acquired with a T2-weighted echo-planar imaging sequence using the following parameters: repetition time (TR) = 2300 ms, echo time (TE) = 30 ms, flip angle = 90°, 37 ascending slices, field of view (FOV) = 256 × 256, acquisition matrix = 96 × 96 ×37, voxel size = 2.5 × 2.5 × 3.45 mm. A high-resolution T1-weighted structural image was also obtained for each participant using the following parameters: TR = 8.2 ms, TE = 3.8 ms, 160 contiguous sagittal slices, flip angle = 8°, FOV = 256 × 256, acquisition matrix = 256 × 256 × 160, voxel size = 0.938 × 0.938 × 1 mm; SENSE factor: anterior-posterior (AP) = 2, right-left (RL) = 1.5. Participants completed the behavioral assessment outside the MRI scanner.
Image preprocessing and connectome construction. Imaging data were preprocessed using the DPABI software package (version 6.0) 62, which is based on Statistical Parametric Mapping (SPM12, https://www.fil.ion.ucl.ac.uk/spm/) and has been widely used. The preprocessing procedure included the following steps: (1) the first 10 functional volumes were removed to ensure signal stability; (2) the remaining 211 volumes were slice timing corrected and realigned to the first image; (3) the T1-weighted structural images were co-registered to the mean functional image and then segmented into gray matter, white matter, and cerebrospinal fluid; (4) the nuisance signals were regressed out, including the Friston 24 head-motion parameters 63, five principal components of white matter and cerebrospinal fluid signals, global signals, and linear signal trends; (5) derived images were normalized to the Montreal Neurological Institute space using the Diffeomorphic Anatomical Registration Through Exponentiated Lie algebra (DARTEL) algorithm and resampled to 3-mm cubic voxels; (6) the normalized images were spatially smoothed with a 4-mm Gaussian kernel and temporally smoothed using the frequency bandwidth of 0.01-0.1 Hz; (7) to further eliminate effects of head movement, as suggested by Power et al. 64, we applied a common threshold to scrub the volumes with framewise diffusion greater than 0.5 mm 26, 65. Notably, in line with many neuroimaging prediction works 61, 66, we employed a contentious step, global signal regression, in this study. The primary consideration behind this procedure is that global signal regression not only efficiently removes artifacts caused by head movement and physiological factors but also robustly improves behavioral prediction performance 67.
After image preprocessing, we used the Human Brainnetome Atlas 33 to construct an FC matrix for each participant by computing the Pearson correlation of the mean BOLD signal time course within each ROI.
Individualized prediction. As described above, one major issue that needed to be addressed in the prediction pipeline was the potential curse of dimensionality caused by few samples but high dimensionality. Although numerous voxels in the brain were grouped into 246 ROIs, more than 30,000 unique features remained in the FC matrix. Two typical solutions are to retain only the most relevant features before feeding them into the model and to use regularization techniques in the model to mitigate the influence of non-predictive features 39. We developed a prediction framework that integrates feature selection and a regularized linear SVR model to predict individuals’ SPE scores based on whole-brain FC (see Fig. S1).
We implemented the linear SVR using the Scikit-learn library 68. SVR is a powerful supervised machine-learning algorithm that is extensively used in studies of neuroscience and psychology 38. SVR can be highly predictive and interpretive when constructed based on a linear kernel function. Linear SVR uses a regularization hyperparameter C to determine the model complexity tradeoff and thus has a significant impact on model performance. To avoid data leakage during hyperparameter determination, we employed a nested CV procedure with leave-one-out for the outer loop and 5-fold for the inner loop. As demonstrated by Vabalas, et al. 37, only a nested CV framework with completely separated training and testing data can guarantee unbiased performance estimates.
The inner 5-fold CV was applied to quickly find the best hyperparameters (i.e., C), also known as a grid search. The dataset input to the inner loop was randomly divided into five parts, four of which were regarded as the subtraining set and the remaining part as the subtest set. For the feature selection step, we first performed a Pearson correlation between each feature (i.e., edge) and the SPE score for the samples in the subtraining set. A commonly used threshold (p < 0.01) was then applied to remove noisy edges and retain those that were significantly correlated 25. These selected features were fed into the linear SVR models built with different values of C. Finally, according to the performance of these models on the subtest set, the best hyperparameter C was obtained and passed to the training set of the outer loop.
The outer loop adopted LOOCV to exploit every sample and evaluate the prediction performance more robustly 37. In each of the N iterations, a different participant was left out as the test set and the remaining N-1 as the training set. The training set then reselected features in a manner similar to the inner loop (Pearson correlation threshold p < 0.01). The retained edges were fed into the tuned linear SVR model with the best hyperparameter C determined by the inner loop. The predicted value for the test set was obtained by feeding the same features into the trained model. After N iterations, we acquired a predicted SPE score for all participants.
Quantifying edgewise feature importance. In the present study, we mainly relied on FCs between brain regions or functional systems to characterize the neural basis of the SPE, which entails precise quantification of the contribution of each edge. Traditionally, linear machine-learning algorithms rank feature importance based primarily on the raw weights assigned to features 69. However, Haufe, et al. 42 recently suggested that such an interpretation of the backward model (e.g., SVR and LASSO) may yield misleading conclusions. As a remedy for this case, they proposed the following formula to transform the weight matrix into an interpretable activation pattern matrix:
Competing interests: The authors declare no competing interests.
Author contributions: F.W. conceptualized the work and collected the data. Y.Z., F.W., and J.S. performed the analyses. Y.Z. wrote the codes and initial draft. F.W., J.S., and Y.Z. revised the manuscript. F.W. supervised the project.
Acknowledgments: F.W. acknowledges the financial support from The Research Project of Shanghai Science and Technology Commission (20dz2260300). J.S. acknowledges the financial support from the Leverhulme Trust (RPG-2019-010).
Data Availability. The Human Brainnetome Atlas is available online at https://atlas.brainnetome.org/download.html. Preprocessed image data and behavioral data were deposited in the Open Science Framework and can be retrieved from https://osf.io/hbrus/?view_only=98b2095f72e64fd382fc0d33de3f4497.
Code Availability. Analysis scripts were deposited in the Open Science Framework and can be retrieved from https://osf.io/hbrus/?view_only=98b2095f72e64fd382fc0d33de3f4497.
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There is NO Competing Interest.