Hybrid Dynamic High-Order Functional Correlations and Divisive Normalization for Improved Classification of Schizophrenia and Bipolar Disorder

Authors: qiang  li
vince d calhoun
Venue: NeurIPS_cc_2024_Workshop_UniReps
Published: 2024-09-11 19:36:10

Abstract: Schizophrenia and bipolar disorder are devastating psychiatric disorders that can be difficult to adequately classify, considering commonalities that make it difficult to distinguish between them using conventional classification approaches based on low-order functional connectivity. Recently, high-order functional connectivity has emerged as a promising method for diagnosing psychiatric illnesses, and this research applied multiple strategies for distinguishing schizophrenia and bipolar disorder using features taken from dynamic high-order functional connectivity and divisive normalization. The approach that produced the greatest results combined dynamic high-order functional correlations and divisive normalization to examine patterns of intrinsic connection time courses collected from resting-state fMRI. Our findings indicate that resting-state fMRI-based dynamic high-order functional connectivity and feature enhancement through divisive normalization classification hold significant promise for improving the accuracy of psychiatric diagnoses. Moreover, to the best of our knowledge, this study is the first to integrate divisive normalization with functional connectivity in fMRI.

Main paper: 
 introduction: 
 The use of resting-state functional magnetic resonance imaging (rsfMRI) to identify individuals with schizophrenia (SZ) and bipolar disorder (BP) has gained substantial attention in global medicine and clinical practice [1] [2] [3] [4] [5] . rsfMRI allows us to investigate the intricate interaction of the brain's functional connections, revealing identifiable patterns of neural activity that may shed light on the specific characteristics of various mental disorders.Functional connectivity elucidates the intricate interplay and communication among different brain regions, coordinating various cognitive processes. Although both low-order and high-order (interactions beyond pairwise connections) static and dynamic functional connectivity are essential for our daily cognitive functioning, recent research suggests that high-order functional connectivity (HOFC) may have a distinct advantage in terms of increasing cognitive flexibility and optimizing task performance [6] [7] [8] [9] . Meanwhile, emerging evidence highlights the superior efficacy of high-order functional connectivity in fostering cognitive adaptability and diagnosing brain dysfunction from an information theory perspective [10] [11] [12] [13] [14] [15] [16] [17] . To enhance the feature from high-order dynamic functional correlations, we incorporate a divisive normalization strategy to further enhance sensitivity based on work showing its potential for capturing neural computation in the visual cortex and its use in the computer vision field [18] [19] [20] [21] .As we show, the classification of SZ and BP patients considering high-order functional connectivity appears to be a promising route, with the potential to improve the precision and specificity of psychiatric diagnostic procedures. This advancement, in turn, holds the potential to usher in an era of personalized and precisely targeted interventions, ultimately optimizing the care and outcomes for individuals grappling with these complex mental health challenges.Within the scope of this study, our primary objective is to discriminate between individuals with SZ and those with BP using high-order functional connectivity. To achieve this, we employ a combination of static and dynamic approaches involving high-order complex brain networks. Our findings can be summarized into two key observations. Firstly, we demonstrate that dynamic highorder functional connectivity furnishes a more information-rich foundation compared to low-order functional connectivity. Secondly, we illustrate that the integration of dynamic high-order brain networks and divisive normalization significantly enhances classification accuracy. Therefore, we suggest considering the potential of dynamic high-order functional connectivity as a metric to aid in the precise diagnosis of psychiatric disorders. 
rsfmri dataset acquisition: 
 The entirety of our dataset, comprising derivative information from 471 subjects meticulously selected from the Bipolar and Schizophrenia Network for Intermediate Phenotypes (B-SNIP) consortium [22] , serves as the fundamental cornerstone of this research endeavor. The 288 subjects represented typical SC, and 183 were diagnosed with BP. The open-source data can be downloaded from https: //www.kaggle.com/competitions/psychosis-classification-with-rsfmri/data.The rigorous preprocessing pipeline applied to rsfMRI data, illustrated in Fig. 1 , encompasses the following essential steps:The rsfMRI data of each participant underwent a standardized preprocessing protocol, inclusive of critical steps such as rigid body motion correction, slice timing correction, and distortion correction. Following this, the preprocessed subject data were registered into a shared spatial template, resampled to isotropic voxels of 3mm 3 , and then underwent spatial smoothing utilizing a Gaussian kernel with a full width at half-maximum of 6mm. Utilizing a multi-spatial-scale template comprising 105 intrinsic connectivity networks (ICNs), which in itself was derived from an extensive dataset of over 100K subjects called the Neuromark_fMRI_2.1 network template [23] , which can be downloaded from https://trendscenter.org/data/. Meanwhile, subject-specific ICN time courses were extracted employing a spatially constrained independent component analysis (scICA) approach, implemented using the GIFT software toolbox (http://trendscenter.org/software/gift).These extracted time courses underwent a thorough cleaning process in accordance with established standards [23] . This meticulous and precision-driven methodology serves as the bedrock for upholding the integrity and trustworthiness of our dataset, thereby laying the foundation for subsequent precision analyses. Our dataset leverages the power of 105 intrinsic connectivity networks (ICNs), as visually depicted in Fig. 2 . These 105 ICNs are categorized into six distinct domains based on structural and functional characteristics: visual domain (VI, 12 sub-networks), cerebellar domain (CB, 13 sub-networks), temporal-parietal domain (TP, 13 sub-networks), sub-cortical domain (SC, 23 subnetworks), sensorimotor domain (SM, 13 sub-networks), and high-level cognitive domain (HC, 31 sub-networks). Moreover, these ICNs were derived through a multi-spatial-scale, scICA methodology, a technique that enhances generalizability and facilitates the comparability of results across diverse studies [24] .Before we go into HOFC, here we will quickly introduce the most common low-order functional connectivity (LOFC), which is estimated based on Pearson correlation (PC). The spatial network and corresponding time courses were constructed utilizing subjects with SZ and BP employing spatially constrained ICA, based on previously established group-level intrinsic connectivity networks. C. The construction of low-order and high-order functional connectivity (LOFC vs. HOFC) matrices (i.e., topographical profile similarity-based HOFC, tHOFC; associated HOFC, aHOFC) was presented in the left panel. Divisive normalization was subsequently applied to these functional connectivity matrices to enhance their features. They were then fed into the machine learning model to extract relevant features using t-test and t-test plus Lasso, with the goal of maximizing classification results.Letting x i (t) and x j (t) represent the rsfMRI signals for two brain regions i and j at time point t(t = 1, . . . , T ), then LOFC based on PC be denoted as, where xi and xj are the average of the rsfMRI signals at regions i and j.ρ ij = T t=1 (x i (t) -xi ) (x j (t) -xj ) T t=1 (x i (t) -xi ) 2 T t=1 (x j (t) -xj ) 2 (1)According to the proposal by Han et al. [25, 26] , the pairwise connection represented by tHOFC and aHOFC differs from that of LOFC due to variations in input signals. Nonetheless, both tHOFC and aHOFC characterize the interaction between two brain regions, establishing high-order functional connectivity. The LOFC are derived from the rsfMRI time series. However, these time series serve as local LOFC profiles for tHOFC. Notably, a noticeable variation between LOFC and tHOFC/aHOFC may exist for the same two brain regions, attributed to differences in input signals [25] [26] [27] .Letting ρ i represents the LOFC profile for region i, and ρ i• = ρ ik|k∈R,k̸ =i . Then the tHOFC can be denoted as,EQUATION2.4.2 Associated High-Order Functional Connectivity (aHOFC)Similar to the calculation of tHOFC, aHOFC will be calculated as follows:EQUATIONIn Fig. 3 , we present LOFC, tHOFC, and aHOFC. It is evident that HOFC significantly improves connectivity information compared to LOFC, while also preserving the original topological structure information.The dHOFC is calculated based on dynamic, time-varying LOFC profiles. First, we estimate dLOFC based on Pearson correlation for time-varying time series as follows:EQUATIONwhere τ = 1, . . . , T -ω + 1; i, l ∈ R, i ̸ = l, τ indicates time, ω refers to window length, and xτ i refers to the average value of the segment of the rsfMRI signal starting from τ . and then, dHOFC is constructed based on dLOFC profiles,EQUATIONAccording to the criteria given above, dHOFC provides more connectomic information compared to LOFC, tHOFC,and aHOFC. The HOFC algorithms were implemented using the BrainNetClass toolbox (https://github.com/zzstefan/BrainNetClass).Divisive normalization is a phenomenological model that captures the nonlinear response properties observed widely across sensory cortical areas [18] . Here, divisive normalization was employed to enhance features in functional connectivity matrices, utilizing a standard neural computational way in the human primary visual cortex, which has since been widely applied in image processing and deep learning [18] [19] [20] [21] . Here, we adapted and applied it to functional connectivity matrices, and it can be mathematically represented as follows:(sign(dρ il,jk ) • κ • |dρ il,jk | γ b + |dρ il,jk | γ ) -1 2 (6)There are several hyperparameters (i.e., κ, γ, b), and after tuning parameters, we selected γ = 2, b = 0.0625, and κ = 0.5. Here dρ il,jk refers to dHOFC matrix. Figure 3 : Functional connectivity matrices were constructed from SZ and BP subjects. The first row shows LOFC, tHOFC, and aHOFC, while the second row displays each after applying divisive normalization for the SZ subjects. The third row shows LOFC, tHOFC, and aHOFC, while the fourth row displays each after applying divisive normalization for the BP subjects. The community patterns present in the functional connectivity matrices were labeled accordingly.The t-test and Least absolute shrinkage and selection operator (Lasso) were used for feature extraction. Assuming X is the functional connectivity matrix of features (with shape n × p, where n is number of samples, and p is the number of features), y is the vector of class labels. For each feature j, the t-test will be,EQUATION)where Xj1 and Xj2 are the means of feature j in the two classes. s j is the standard deviation of feature j, and n j is the number of samples in class j.Compute the corresponding p-value p j for each t j , which indicates the probability of obtaining the observed t-statistic under the null hypothesis (that the feature is not associated with the class labels).Features with p-values sufficiently low (typically below a threshold, e.g., 0.05) are then selected as statistically significant features. The Lasso is a regularization technique that performs both feature selection and regularization to improve the prediction accuracy [28] .Let PL represent the total number of SZ functional connectivity matrices, NL represent the total number of BP functional connectivity matrices, TP represent the true positives (number of SZ functional connectivity matrices correctly identified as SZ), FP represent the false positives (number of BP functional connectivity matrices incorrectly identified as SZ), TN represent the true negatives (number of BP functional connectivity matrices correctly identified as BP), and FN represent the false negatives (number of SZ functional connectivity matrices incorrectly identified as BP).• F1-scoreEQUATIONThe receiver operating characteristic (ROC) curve is a probability curve created by plotting the true positive (TP) rate against the false positive (FP) rate at various threshold settings. The area under the ROC curve (AUC) represents the performance measure of a classifier. A higher AUC indicates that the classifier is better at distinguishing between SZ and BP. 
results: 
 To examine the differences between SZ and BP is complicated because the two disorders share many features. Classifying SZ and BP using machine learning relies heavily on the extracted features. In this study, we extracted features from both low-order and high-order functional connectivity metrics. Divisive normalization was employed to enhance these features, followed by feature selection using t-test and Lasso to maximize classification accuracy. First and foremost, we observed that high-order functional connectivity presents distinct connectivity patterns compared to low-order functional connectivity in SZ and BP, as illustrated in Fig. 3 . The strongest connection pattern between HC and SC exists in BP compared to SZ, and these differences could have implications for understanding the underlying mechanisms of BP and its impact on high-level cognitive functions. Moreover, they may serve as a biomarker to differentiate between SZ and BP. Secondly, we found that dynamic high-order functional connectivity indeed gives us better classification results (86.27%) compared to baseline (64.41%) and even deep learning results (70.50%), as shown in Tab.1. As we mentioned before, one of the major reasons is that dynamic high-order functional connectivity capture additional information relative to other approaches. This, typically ignored, higher order information may be important for us to better understand complex brain functions. Thirdly, we observed that divisive normalization significantly improved classification accuracy compared to not employing divisive normalization (96.61% vs. 86.27%). These results demonstrate that divisive normalization is essential for feature enhancement and significantly improves classification performance. To our knowledge, this study is the first to integrate divisive normalization with functional connectivity for this purpose. In this study, we observed that high-order functional connectivity generally provides improved classification accuracy compared to low-order functional connectivity. This improvement is primarily due to the additional connection information high-order connectivity offers. Additionally, high-order connectivity better captures the complex, non-pairwise nature of brain information interactions. We investigated various high-order functional connectivity approaches to estimate relationships that extend beyond pairwise correlations. Furthermore, we integrated a divisive normalization model to enhance connection features, which significantly improved classification accuracy. In summary, combining dynamic high-order functional connectivity with divisive normalization proves to be an effective approach for enhancing classification accuracy and holds substantial potential for application in brain disorder diagnosis. 
future work: 
 Integrating dynamic high-order functional connectivity and divisive normalization with deep learning models: Future research will focus on combining dynamic high-order functional connectivity and divisive normalization techniques within deep learning frameworks. By leveraging large-scale brain imaging datasets, we aim to develop more sophisticated models that capture intricate patterns of brain connectivity. This approach seeks to enhance the predictive power and generalization of classification algorithms, potentially leading to more accurate diagnoses and a deeper understanding of brain disorders. Implementing these advanced techniques will involve exploring various deep learning architectures, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs), to effectively process and analyze high-dimensional functional connectivity data [30, 31] . Additionally, we will investigate the integration of temporal dynamics and high-order interactions to capture evolving brain network patterns over time.Exploring beyond pairwise interactions with advanced topological data analysis: Moving beyond traditional pairwise interactions, future work will investigate advanced topological data analysis techniques to capture more complex relationships within brain connectivity [32] [33] [34] . We will explore the use of hypergraphs [34] , which can represent higher-order interactions among multiple brain regions, and persistent diagrams [33] , which offer insights into the topological features of connectivity patterns across different scales. These methods will enable us to capture and analyze intricate connectivity structures and dynamics that are not easily represented by pairwise correlations alone. By applying these advanced techniques, we aim to gain a deeper understanding of brain network organization and its implications for neurological and psychiatric disorders.Identifying potential biomarkers and key network connections in brain disorders: Our future research will focus on identifying potential biomarkers for specific brain disorders by examining which networks or connections between networks are most crucial. This involves analyzing the relationships between different brain regions and their roles in various psychiatric conditions. By leveraging dynamic high-order functional connectivity and divisive normalization, we aim to pinpoint specific networks and their interactions that may serve as reliable biomarkers. Understanding these critical connections will provide insights into the underlying mechanisms of brain disorders and contribute to the development of personalized treatment strategies.Proceedings of the II edition of the Workshop on Unifying Representations in Neural Models (NeurIPS 2024). 
 
 Appendix:  


Decision: In light of the reviewers' feedback and relevancy of the submission, we are pleased to accept this paper for presentation at UniReps 2024. We kindly ask the authors to incorporate the reviewers' suggestions and feedback in the final camera-ready version of the manuscript.

Reviews: review: title: title: Review of "Hybrid Dynamic High-Order Functional Correlations and Divisive Normalization for Improved Classification of Schizophrenia and Bipolar Disorder"
main_review: main_review: The paper makes a valuable contribution to the field of psychiatric disorder classification by introducing hybrid methods that combine dynamic high-order functional correlations (dHOFC) with divisive normalization. The methodological rigor is commendable, and the mathematical formulations provided are generally well-grounded in the literature. The results are promising, as the proposed method shows notable improvements over existing approaches.
* Strengths:
    * The inclusion of both dynamic and high-order functional connectivity is innovative and addresses limitations in previous low-order functional connectivity approaches.
    * Divisive normalization enhances the feature representation and demonstrates superior performance in classification tasks, as shown by a significant increase in AUC (up to 96.61%).
    * The dataset used is well-established (B-SNIP), ensuring the robustness of the findings.
* Weaknesses:
    * The paper could benefit from a more thorough description of the parameter tuning process for divisive normalization and its impact on the final results.
    * Although the results are promising, the comparison with deep learning-based methods could be expanded. It would be beneficial to see more direct comparisons with contemporary neural network approaches in psychiatric disorder classification.
Clarity
The paper is clearly structured, and the flow of the narrative is logical. However, some sections could be explained in more detail to improve accessibility for a broader audience.
* Strengths:
    * The figures, especially those presenting the functional connectivity matrices before and after divisive normalization, are clear and helpful for visualizing the improvements introduced by the method.
    * The mathematical derivations are precise and well-referenced, enhancing the technical robustness of the work.
* Weaknesses:
    * The introduction to divisive normalization and its application in functional connectivity is somewhat brief. A more intuitive explanation for readers unfamiliar with this technique would improve the paper's accessibility.
    * Some notation, particularly in the equations for dynamic high-order functional connectivity (Eq. 5), could be better clarified, as the indices and symbols may confuse non-experts.
Originality
The paper offers a novel combination of dynamic high-order functional connectivity and divisive normalization, which has not been extensively explored in the classification of psychiatric disorders. This approach introduces new perspectives on leveraging complex brain network information for diagnosis.
* Strengths:
    * The fusion of dHOFC and DN is a unique contribution and shows potential for broader applications beyond schizophrenia and bipolar disorder classification.
    * The integration of divisive normalization into fMRI data processing is a fresh application of a technique primarily used in image processing, showcasing the cross-disciplinary potential of the method.
* Weaknesses:
    * While novel, the paper could include more discussions about how this approach might generalize to other psychiatric disorders or neurodegenerative diseases. Furthermore, the theoretical justification for why divisive normalization works well in this context could be expanded.
Significance
The potential impact of this research is substantial. If validated with larger datasets and applied to other disorders, this approach could significantly improve diagnostic accuracy in clinical settings.
* Strengths:
    * The improvements in classification accuracy are substantial, especially with the inclusion of divisive normalization, which boosts the AUC to 96.61%.
    * The methodology has the potential to inform the development of new diagnostic tools that use fMRI data for more precise and personalized psychiatric diagnoses.
* Weaknesses:
    * The practical significance could be enhanced by demonstrating the method’s utility in clinical trials or real-world diagnostic settings. At present, the application remains somewhat theoretical without sufficient validation in applied environments.

Pros
1. Innovative integration of dynamic high-order functional connectivity and divisive normalization.
2. Significant improvements in classification accuracy compared to baseline methods.
3. Well-designed experiments using a robust dataset (B-SNIP).
4. Clear and informative visualizations of functional connectivity matrices.

Cons
1. Insufficient explanation of parameter tuning and its impact on the results.
2. Limited comparison with contemporary deep learning methods for psychiatric disorder classification.
3. Certain notational and technical sections could benefit from more clarity and detail for a broader audience.
4. More extensive real-world validation would strengthen the paper’s impact.

Overall Evaluation
This paper presents a strong contribution to the field of psychiatric disorder classification, especially in the application of fMRI data analysis. The combination of dynamic high-order functional connectivity and divisive normalization is innovative and offers promising results. However, the paper would benefit from additional clarity in the technical explanations and further comparisons with state-of-the-art deep learning models. The real-world significance of the findings could also be more thoroughly explored.
title: title: The paper presents a promising approach to classifying schizophrenia and bipolar disorder using dynamic high-order functional connectivity and divisive normalization, which could offer improved diagnostic accuracy. However, the study would benefit from clearer explanations of parameter selection, better visualizations, addressing the imbalance in sensitivity and specificity, and more clarity on the contribution of divisive normalization versus dynamic connectivity in the performance boost.
main_review: main_review: The paper introduces a novel approach to classifying schizophrenia and bipolar disorder using dynamic high-order functional connectivity and divisive normalization. This method offers a promising alternative to traditional low-order connectivity analysis, which has limitations in distinguishing these disorders. By leveraging resting-state fMRI and brain dynamics, the study provides valuable insights and may be among the first to apply high-order functional connectivity maps to this classification problem.

1- In Figure 3, it would be beneficial to include visualizations of sample high-order functional graphs for bipolar patients to help visually identify which functional connections differ between schizophrenia and bipolar disorder subjects.

2- Given the lack of ground truth for functional maps in resting-state brain data, a clearer explanation of how the parameters in Equation 6 were selected would be helpful. The paper mentions specific values but does not discuss how they were optimized.

3- The model reports high specificity, AUC, and F1-scores but low sensitivity, indicating that while it performs well for one group, it struggles to identify the other. This imbalance could be addressed by adjusting the classification threshold, re-examining feature extraction, or applying class weighting to improve sensitivity and balance the metrics more effectively.
It would be valuable if the authors could highlight the most important connections for distinguishing bipolar from schizophrenia subjects, which would help interpret the functional connectivity patterns.

4- It is unclear whether the reported performance improvement is due to the inclusion of the divisive normalization step or the superior performance of dynamic versus static high-order functional connectivity. Clarifying this distinction would provide better insight into the method’s effectiveness.
title: title: Interesting idea, but needs a lot of refinement
main_review: main_review: ### Summary
This paper tackles the problem of classifying schizophrenia and bipolar disorder based on fMRI data. The authors show that using high-order functional connectivity features allows even simple models such as SVMs to achieve better results compared to the solutions based on the low-order functional connectivity method used so far.  

### Major strengths:
* The paper is relevant.
* The idea is interesting and fresh.

### Major weaknesses: 
* 2.4 This section seems very unclear to me. What does $ \tau $ represent in Eq. 3? What is even the difference between tHOFC and aHOFC? The paper is designed specifically to solve the domain problem, so it really should be explained better, especially for the AI community. 
* Section 2.8 I do not think the description of the metrics is necessary here. I mean especially the formulas. 
* The results are very concerning to me. Even though the ROC AUC is higher for the proposed method, sensitivity and specificity measures seem very unbalanced. For instance, 3.78% sensitivity and 95.68% specificity suggest, that the model is virtually incapable of properly recognising schizophrenia at all. Are those results reported for the best thresholds or just for standard 0.5? 
* Choosing the Kaggle best score as a baseline does not feel like a good idea. What model did it use? What was the sensitivity or F1 score? 

### Minor weaknesses:
* Line 112. I would change "... free parameters" -> "... hyperparameters"
* Eq 1. Should not it be: $p_{ij} = \frac{\sum_{t=1}^{T}\left( x_i(t) - \hat{x_i} \right)\left( x_j(t) - \hat{x_j} \right)}{\sqrt{\sum_{t=1}^{T}\left( x_i(t) - \hat{x_i} \right)^2\sum_{t=1}^{T}\left( x_j(t) - \hat{x_j} \right)^2}}$
* Eq 2. Should not it be:  $ p_{ij} = \frac{\sum_{k}\left( \rho_{ik} - \hat{\rho_i} \right)\left( \rho_{jk} - \hat{\rho_j} \right)}{\sqrt{\sum_{k=t}\left( \rho_{ik} - \hat{\rho_i} \right)^2\left( \rho_{jk} - \hat{\rho_j} \right)^2}} $
* Table 1. looks very overwhelming, and the colours do not help. 
* The whole paper sometimes feels like a sequence of random statements not connected to the rest, especially section 2.7.