Centrality-based nearest-neighbor projected-distance regression (C-NPDR) feature selection for correlation predictors with application to resting-state fMRI of major depressive disorder

doi:10.21203/rs.3.rs-4193488/v1

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Centrality-based nearest-neighbor projected-distance regression (C-NPDR) feature selection for correlation predictors with application to resting-state fMRI of major depressive disorder

https://doi.org/10.21203/rs.3.rs-4193488/v1

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Background.

Nearest-neighbor projected-distance regression (NPDR) is a metric-based machine learning feature selection algorithm that uses distances between samples and projected differences between variables to identify variables or features that may interact to affect the prediction of complex outcomes. Typical bioinformatics data consist of separate variables of interest like genes or proteins. In contrast, resting-state functional MRI (rs-fMRI) data is composed of time-series for brain Regions of Interest (ROIs) for each subject, and these within-brain time-series are typically transformed into correlations between pairs of ROIs. These pairs of variables of interest can then be used as input for feature selection or other machine learning. Straightforward feature selection would return the most significant pairs of ROIs; however, it would also be beneficial to know the importance of individual ROIs.

Results.

We extend NPDR to compute the importance of individual ROIs from correlation-based features. We present correlation-difference and centrality-based versions of NPDR. The centrality-based NPDR can be coupled with any centrality method and can be coupled with importance scores other than NPDR, such as random forest importance. We develop a new simulation method using random network theory to generate artificial correlation data predictors with variation in correlation that affects class prediction.

Conclusions.

We compare feature selection methods based on detecting functional simulated ROIs, and we apply the new centrality NPDR approach to a resting-state fMRI study of major depressive disorder (MDD) and healthy controls. We determine that the areas of the brain that are the most interactive in MDD patients include the middle temporal gyrus, the inferior temporal gyrus, and the dorsal entorhinal cortex. The resulting feature selection and simulation approaches can be applied to other domains that use correlation-based features.

Resting-state fMRI

statistical interactions

machine learning feature selection

Resting-state functional MRI (rs-fMRI) measures the blood-oxygen-level-dependent (BOLD) signal in regions of interest (ROIs) throughout the entire brain of a subject while at rest (i.e., not during a cognitive task) [1, 2, 3, 4]. The BOLD signal for each ROI is a time-series whose low frequency fluctuations show correlation between other ROIs. These correlations can be used to represent the functional connectivity (FC) between ROIs in a weighted brain network [5, 6, 7, 8, 9]. Differential changes, or rewiring, of correlation FC between subjects with mood disorders and healthy controls may reveal neural mechanisms of disease. Feature selection and machine learning methods that use FC measures as predictors have potential as fMRI-based biomarkers and disease classification [23].

Machine learning classification and feature selection have been used widely for rs-fMRI data to detect and better understand the mechanisms of mood disorders, including major depressive disorder (MDD) [24]. A wide variety of algorithms have been used, including Support Vector Machines (SVM), XGBoost, Random Forests, and deep learning. Various biomarkers and measures of FC between brain regions have been used as fMRI-based ML predictors, including correlation, mutual information, amplitude of low frequency fluctuation (ALFF) and regional homogeneity (ReHo). ML classification of MDD with rs-fMRI has been promising, but using ML for diagnosis is likely premature [24]. Feature selection, which is the focus of the current study, while not directly diagnostic, may provide valuable insights into the biological mechanisms of MDD.

Multiple approaches have been used to define the fMRI input predictors for ML. Some approaches for ROI feature engineering have been more data-driven, for example, by using independent component analysis (ICA) to define brain networks and ROIs [25]. Similarly, multi-voxel pattern analysis (MVPA) [12] uses SVM to build classifiers without assumptions about the organization of the brain. But these can be difficult to generalize between data sets and studies. We use preexisting ROIs based on brain atlases constructed by experts using anatomical and functional information. (Fig. 1A).

In this study, we use Pearson's correlation across the full time series to quantify FC between brain regions as a representation of temporal synchrony of their activity. For each atlas ROI (Fig. 1A), we average the voxel time series in the ROI (Fig. 1B) and then compute the correlation between all pairs of n ROI time series (Fig. 1D). For each subject, the upper triangle of the correlation matrices are stretched to create datasets where the n(n-1)/2 predictor variables are pairwise correlations between ROIs (Fig. 1D). Standard feature selection methods can then be used for this data to give the importance of ROI pairs. One of the goals of the current study is to disentangle the many important pairs to identify important individual ROIs.

A common way to identify important ROIs is to perform a seed-based analysis, where the global correlation between a given seed region and all other brain regions is computed [26], and then this centrality quantity can be tested for all ROIs for association with an outcome like MDD. In the current study, we use centrality in a different way with our nearest-neighbor projected distance regression (NPDR) approach [15]. We apply NPDR to correlation-based predictors (Fig. 1D) and then use network theory to determine the cumulative effect of the differential correlations for each ROI. In addition to this centrality-NPDR (c-NPDR), we also use a correlation-based projected difference to directly compute the importance of ROIs. We also apply this centrality approach with random forest (c-rf). We compare the rs-fMRI feature selection methods using a new simulation tool, and we apply the methods to a previous rs-fMRI study of MDD.

We describe a new centrality-based algorithm and projected correlation distance algorithm for ranking the importance of ROIs for predicting a class variable. Both of these methods are based on nearest-neighbor projected-distance regression (NPDR), a machine learning algorithm that is able to detect statistical interactions using nearest neighbors in a high-dimensional space [15]. NPDR minimizes a contrastive loss function for pairs of samples $(i,j)$. The contrastive loss ${\delta }_{ij}\left(y\right)$ is an indicator of whether samples $(i,j)$ are in the same class or a different class based on class variable y. The contrastive loss can be penalized by LASSO or Ridge, or it can be unpenalized and P-values can be computed. Rather than using the predictor/attribute values directly in the regression, NPDR uses the difference ${\stackrel{⃑}{d}}_{ij}\left(X\right)$ (or projected distance onto the attributes X) between subjects $(i,j)$. The vector denotes the projected distance for all attributes in the set X. In the current application, the attributes are Pearson correlations between pairs of ROIs. For centrality NPDR (c-NPDR), the projected distance or diff, ${d}_{ij}\left(p\right)$, is the absolute difference between subjects $(i,j)$ for one correlation attribute p (correlation between a pair of ROIs):

$${d}_{ij}\left(p\right)=\left|{A}_{p}^{\left(i\right)}-{A}_{p}^{\left(j\right)}\right|$$

where ${A}_{p}^{\left(i\right)}$is the correlation for subject i between a pair of ROIs, represented by p. Thus, if there are n ROIs, the NPDR design matrix consists of n(n-1)/2 attribute columns; one for each pair of ROIs.

The NPDR-selected ROI pairs can then be used in any number of centrality algorithms to rank the importance of individual ROIs. For comparison, we use the following centralities: degree, betweenness, eigenvector and integrated value of influence (IVI) [30].

The other NPDR-based method (correlation-diff-NPDR) for ranking the importance of ROIs from ROI-pair correlation data uses a more complex projected distance, ${d}_{ij}^{CD}$, but directly gives importance of individual ROIs without centrality calculations [27]. The correlation-diff (CD) or correlation projected distance for ROI r is given by

$${d}_{ij}^{CD}\left(r\right)={\sum }_{k\ne r}\left|{A}_{rk}^{\left(i\right)}-{A}_{rk}^{\left(j\right)}\right|$$

where ${A}_{rk}^{\left(i\right)}$ is the correlation between ROIs r and k for subject i. Thus, the correlation-diff for ROI r is the absolute sum of differences between r and all other ROIs. If there are n ROIs, the NPDR design matrix for Eq. (2) will have n columns as opposed to n(n-1)/2 for Eq. (1). Thus, NPDR with Eq. (2) yields importance scores for ROIs, while NPDR with Eq. (1) yields the importance of ROI pairs. In both cases (Eqs. 1 and 2), NPDR importance can be computed in terms of individual P-values or in a multivariate model with LASSO or Ridge.

In order to threshold the results of correlation-diff-NPDR and cNPDR, we use regularization and p-values. We use the LASSO penalty, also known as the L1 penalty, which is a regularization technique used in regression models to prevent overfitting and to enhance the model's prediction accuracy and interpretability. For non-penalized methods, we use a p-value adjusted cutoff, where ROI pairs that had an adjusted p-value > 0.05 are removed from the network. To threshold the random forest results, we use a cutoff of the top 100 pairs of ROIs (Fig. 2).

Correlation-diff-NPDR directly yields a list of significant individual ROIs. However, the centrality methods need an additional step to map pair importance to individual importance. The c-NPDR and c-rf methods yield lists of important pairs of ROIs, so we apply centralities to the resulting edge lists to obtain a list of important individual ROIs (Fig. 2). The significant pairs of ROIs are graphed as a network, where the nodes are ROIs and edges are defined when the ROI pairs have a correlation that affects the outcome variable (e.g., MDD). This interaction network is a way to visualize the importance of MDD nodes based on their connections and visualize local structure. We quantify the importance of individual ROIs using common centralities, degree, eigenvector, betweenness, and IVI [30]. IVI combines multiple centrality measures.

We compare the NPDR methods to a centrality version of random forest (c-rf). We use the correlation predictor data (Fig. 1d) with random forest permutation importance with 5000 trees, filter the correlation pairs to the top 200 to create a network, and then computed ROI centralities.

Simulation Method and Real Data.

Simulation Approach. We develop a random network approach to simulate correlation-based features, a fraction of which are functional or associated with the case-control status (Fig. 3). The application we have in mind is correlation between brain ROIs in resting-state fMRI studies, where correlation is calculated from the BOLD signal time-series. We do not simulate the time series, but rather directly simulate the correlations and their differences between groups. Features or predictors are correlations between pairs of ROIs rather than ROIs themselves. We note that these simulations and feature selection methods would also apply to other types of correlation-based data in other research domains.

The user specifies the number of ROIs, the number of cases and controls, the number of functional ROIs (i.e., that are associated with the outcome), the effect size and the type of underlying random network for the brain. The user can specify their own network, for example from real data, or they can generate any network from the igraph library. Initial correlation matrices are generated for each sample based on the network, where connected ROIs have higher random correlations than unconnected ROIs.

Functional nodes are chosen from the largest connected component (i.e. group of nodes such that there is a path between any pair of nodes in the group). Edges between the functional nodes (green edges in Fig. 3) are then used to create differential correlation between cases and controls (black dots in Fig. 3 heatmaps). We use a parameter called “multiway” that controls how many edges we randomly select to generate differential correlation. For example, a multiway of 2 will use only a subset of the possible edges between functional nodes (a subset of possible edges will be green). If we set multiway to the maximum, then all possible edges between functional nodes will have differential correlation (green). We use multiway = 5 in this application.

We generate replicate simulations to compare feature selection methods based on the ability to detect the ground truth functional ROIs. We use the F1 Score to test whether the top ROI features selected by a method overlap with the top functional features.

Real Data. We compare feature selection methods on data from the Tulsa 1000 (T1000), a longitudinal study at the Laureate Institute for Brain Research following 1000 individuals, including healthy individuals and those with mood and other disorders [28]. We use rs-fMRI time series for 188 MDD subjects and 47 healthy controls (HC) from T1000 (163 female and 72 male). We use the Automated Anatomical Labelling Atlas (AAL Atlas) with 87 ROIs and the Brainnetome Atlas with 246 ROIs to define consistent and interpretable mappings for selected features [29, 10]. The Brainnetome Atlas parcellates the brain based on structural and connectivity features. It is based on neuroimaging data, particularly rs-fMRI and diffusion tensor imaging (DTI) data, which reveal both the functional and structural connectivity patterns in the brain. For each atlas, we detrended the signals and averaged the time-series for the voxels within an atlas ROI.

We simulate 50 replicate datasets each with 100 cases, 100 controls, and 100 ROIs. We select 10 functional ROIs, but their effects are detected through their correlations with each other in correlation-predictor datasets. The underlying correlation networks are based on Erdos-Renyi random networks with p = 0.1 connection probability. We used a medium effect size of 0.5 Cohen’s d.

We apply six feature selection methods to the replicate simulations (Fig. 4) and compare them based on their average ability to detect the 10 functional ROIs. Centrality-Random Forest (c-rf) with degree centrality (red, Fig. 4) has a similar mean F1 score to correlation-diff NPDR (corr-diff) using Ridge regression (green CD Ridge, Fig. 4), and they are both similar to centrality-NPDR (c-npdr) with degree centrality (left blue). The npdr-based methods corr-diff and c-npdr with degree have slightly less variation than c-rf. The F1 scores for centrality-based NPDR methods (all blue, Fig. 4) depend on the centrality method used. C-NPDR works best with degree, whereas IVI, betweenness, and eigenvector centralities are noticeably worse. The close similarity between corr-diff and c-npdr (Eq. 1) with degree suggests that the corr-diff NPDR difference metric (Eq. 2) works mathematically like degree.

We apply four feature selection methods to the real rs-fMRI study to compare the selected important ROIs for MDD (Table 1). The correlation-diff NPDR with LASSO selects the fewest features because it has a tendency to eliminate correlated features (first column, Table 1). The other correlation-diff NPDR (second column, Table 1) uses an adjusted p-value cutoff, and it results in more selected features in part due to inclusion of more correlated features. The centrality methods with degree, NPDR (column 3) and random forest (column four), use a manual threshold because degree centrality does not have a statistical threshold.

For the Brainnetome atlas (top, Table 1), NPDR correlation-diff LASSO (column 1) selects the most parsimonious list of ROIs, and the these features are included in the longer lists of NPDR methods (columns 2 and 3). The random forest method has a slightly different set of selected ROIs because it is not metric based and it tends to find more main effects than interactions compared to NPDR methods. We highlight the selected ROIs involving MTG (middle temporal gyrus) because it is the top ROI found by NPDR correlation-diff and has been associated with MDD [20], [31].

For the AAL atlas (bottom section, Table 1), the three NPDR methods have a consensus of ROIs selected by the LASSO method. These regions include the dorsal and ventral default mode networks (DMN) and the right executive control network (ECN). The random forest centrality method includes multiple blocks of correlated variables (bottom, Table 1) in regions like Anterior Salience, Auditory, and dorsal DMN. The NPDR methods have reduced correlation, and the LASSO version automatically selects a parsimonious set of ROIs. The highest NPDR degree nodes for AAL (Dorsal_DMN_ 03 and Ventral_DMN_07) are in the same Louvain graph cluster and the third highest degree node (Right_ECN_04) is in a different cluster (Fig. 5).

The middle temporal gyrus (MTG) was found by all feature selection methods to be important for MDD (Table 1). The centrality random forest method only identified the left MTG while the LASSO correlation-diff NPDR identified only the right MTG. The other NPDR methods, including the centrality based method, identified both left and right MTG. MTG is critical for semantic memory processing, visual perception, and language processing [17], and studies have found associations with MDD. For example, studies using structural and functional MRI identified significant gray matter abnormalities in the right MTG among patients with treatment-resistant depression (TRD) and treatment-responsive depression (TSD) compared to healthy controls [20]. The reduced gray matter volume in the bilateral MTG is indicative of structural changes associated with MDD. Similarly, a previous study found fractional amplitude of low-frequency fluctuation (fALFF) was higher in patients with MDD in the right and left MTG [31].

All tested methods also identified STG (superior temporal gyrus) and ITG (inferior temporal gyrus) as important for MDD. In patients with anxious depression versus healthy controls, a previous study found increased fALFF values in the left STG [32]. While not previously linked to MDD, ITG showed gray matter volume reductions in the MTG and ITG in chronic schizophrenia patients [21]. The link to another psychiatric condition could indicate a broader role for ITG in mood disorders.

The application of machine learning and feature selection algorithms to fMRI data is increasingly critical toward understanding biological mechanisms of disorders. New methods are needed that can account for interactions between variables and regions of interest. NPDR has been shown previously to be able to detect interactions, and we extended it to handle data where the predictors are correlations between pairs of ROIs. We also developed a new simulation approach to compare these methods. We found that c-NPDR with degree is similar to the correlation-diff NPDR. This suggests a mathematical connection between the correlation-diff metric and degree centrality, and it suggests ways that correlation-diff might be improved by using other centralities. We applied these NPDR methods and a random forest approach to correlation data from a real rs-fMRI dataset for MDD, and the consensus between these methods found MTG, ITG, and STG to be important MDD ROIs.

rs-fMRI

resting-state functional magnetic resonance imaging

MDD

major depressive disorder

healthy control

ROI

region of interest

Author Contribution

EK and BM wrote the main manuscript. EK implemented the centrality approach and performed data analysis. BD developed the corr-diff approach and simulation method. HL performed simulation analysis. JL and RK contributed to analysis design. All authors reviewed the manuscript. BM led the overall design.

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Table 1 is available in the Supplementary Files section.

No competing interests reported.

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Centrality-based nearest-neighbor projected-distance regression (C-NPDR) feature selection for correlation predictors with application to resting-state fMRI of major depressive disorder

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Abstract

Background.

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Background

Methods

Results

Discussion

Conclusions

Abbreviations

Declarations

Author Contribution

References

Tables

Additional Declarations

Supplementary Files

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