# Fusing Multiview Functional Brain Networks by Joint Embedding for Brain Disease Identification

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## Abstract

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**Background**: Functional brain networks (FBNs) derived from resting-state functional MRI (rs-fMRI) have shown great potential in identifying brain disorders, such as autistic spectrum disorder (ASD). Therefore, many FBN estimation methods have been proposed in recent years. Most existing methods only model the functional connections between brain regions of interest (ROIs) from a single view (e.g., by estimating FBNs through a specific strategy), failing to capture the complex interactions among ROIs in the brain.

**Methods**: To address this problem, we propose fusion of multiview FBNs through joint embedding, which can make full use of the common information of multiview FBNs estimated by different strategies. More specifically, we first stack the adjacency matrices of FBNs estimated by different methods into a tensor and use tensor factorization to learn the joint embedding (i.e., a common factor of all FBNs) for each ROI. Then, we use Pearson’s correlation to calculate the connections between each embedded ROI in order to reconstruct a new FBN.

**Results**: Experimental results obtained on the public ABIDE dataset with rs-fMRI data reveal that our method is superior to several state-of-the-art methods in automated ASD diagnosis. Moreover, by exploring FBN “features” that contributed most to ASD identification, we discovered potential biomarkers for ASD diagnosis. The proposed framework achieves an accuracy of $74.46\%$, which is generally better than the compared individual FBN methods. In addition, our method achieves the best performance compared to other multinetwork methods, i.e., an accuracy improvement of at least $2.72\%$.

**Conclusions**: We present a multiview FBN fusion strategy through joint embedding for fMRI-based ASD identification. The proposed fusion method has an elegant theoretical explanation from the perspective of eigenvector centrality.

## 1. Introduction

## 2. Related Work

#### 2.1. Pearson’s Correlation

#### 2.2. Sparse Representation

#### 2.3. Mutual Information

#### 2.4. Correlation’s Correlation

## 3. Materials and Methods

#### 3.1. Data Preparation

#### 3.2. Proposed Method

#### 3.2.1. Motivation

#### 3.2.2. General Framework

#### 3.2.3. Proposed Joint Embedding

#### 3.2.4. Theoretical Explanation

#### 3.2.5. Optimization

- (a)
**Update**P:

- (b)
**Update**${\mathit{R}}^{\left(k\right)}$:

Algorithm 1: Algorithm of MJE |

Input: ${\mathbf{A}}_{n}$× n × m: adjacency tensor; $\alpha $: regularization parameter; r: rank of the latentrepresentation; ${t}_{max}$: the maximum number of iterations, $\u03f5$ THIS Initialize: P with the rlargest eigenvectors of the Eigen decomposition of ${\sum}_{k}({\mathit{A}}^{\left(k\right)}+{{\mathit{A}}^{\left(k\right)}}^{T})$; ${\mathit{R}}^{\left(k\right)}$ is initialized byany random matrices While not converged or $t<{t}_{max}$ doUpdate P according to Equation (11); Update ${\mathit{R}}^{\left(k\right)}$ according to Equation (14); t = t + 1; check the convergence conditions: $\frac{{\sum}_{k=1}^{m}{\u2225{\mathit{A}}^{\left(k\right)}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}-\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}P{\mathit{R}}^{\left(k\right)}{P}^{T}\u2225}_{F}^{2}}{{\u2225\chi \u2225}_{F}^{2}}\to \u03f5$ or $t>{t}_{max}$ endReconstruct the FBN with PC for the potential representation of each ROI by $W=P{P}^{T}$ Output: Restructuring the FBN: W |

#### 3.2.6. Classification

## 4. Experiments

#### 4.1. Experimental Setting

#### 4.2. Comparison Methods

- •
**MNER**[26]: This method uses the sparse regression model with group constraints to generate multiple sparse FBNs with different sparsity levels, followed by multiview FBN fusion via a multiview learning method.- •
**LORTA**[46]: This method assumes that FBNs have similar but not necessarily the same topology across subjects. It is implemented in a two-step learning framework. First, the FBNs are estimated according to conventional methods. Then, the estimated FCNs of all subjects are stacked into a tensor and refined by low-rank tensor approximation.- •
**BMGF**[27]: This method aims to fuse a fully connected FBN and a 1-nearest neighbor (1NN) FCN, taking into account the effects of intersubject variability and cross-subject heterogeneity.- •
**GraphCGC-Net**[51]: This method is a unified three-stage graph learning framework for brain disease diagnosis. First, it constructs a coarsened graph to obtain a critical graph structure using supervised multigraph clustering. A graph GAN is then used to generate the realistic brain networks based on the coarsened graph. It further finetunes the pretrained GCN by combining the generated and original graphs into a mixed training dataset.- •
**MVS-GCN**[30]: This method is a prior brain structure learning-guided multiview graph convolution network framework. It first constructs multiview coarsened brain network structures that are consistent for all the subjects and then implements multitask graph embedding learning to capture the intrinsic correlations among different views.- •
**MFC-PL**[52]: This method trains DNN models through unsupervised and supervised training steps to learn abstract feature representations of low-order and high-order FC patterns. Then, the learned multilevel abstract FC features are combined, and an ensemble classifier is trained on the fused features for brain disease classification.- •
**BrainGC-Net**[53]: This method improves the classification performance of the graph through three mechanisms. First, a priori subnetwork structure regularization is proposed to guide the pooling process and ensure accurate subnetwork identification. Then, a graph GAN model that focuses on both embedding and graph space is proposed based on the structure of $\alpha $-GAN. In addition, a domain-consistent GCN model is proposed to alleviate the gap that exists between the real graph and the domain of the generated graph.

#### 4.3. Results

#### 4.3.1. Initial FBN Parameter Selection

#### 4.3.2. Results of ASD Identification

## 5. Discussion

#### 5.1. Sensitivity to Parameters

#### 5.2. Influence of Proposed Fusion Strategy

#### 5.3. Influence of Number of FBNs

#### 5.4. Identified Discriminative Features

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the proposed multiview functional brain network fusion method, including six major parts: (1) rs-fMRI preprocessing; (2) estimation of initial functional brain networks (FBNs) based on four strategies, i.e., Pearson’s correlation (PC), sparse representation (SR), mutual information (MI), and correlation’s correlation (CC); (3) selection of the initial FBNs under the optimal parameter; (4) factorization of the tensor stacked by the selected FBNs to obtain the common matrix (P) of different FBNs; (5) construction of a new FBN based on P for each subject; and (6) disease diagnosis.

**Figure 2.**The cross-validation mechanism used in our experiments includes the internal LOO method to determine the best parameters and the external LOO method to obtain classification results.

**Figure 3.**Frequencies of the optimal p values selected in an inner loop for the four different methods based on a t-test with $p=\{0.01,0.05,0.001,0.005$}. The horizontal axis indicates the multiple thresholds for the different methods, and the vertical coordinates indicate the frequencies of occurrence of the different thresholds.

**Figure 4.**Classification results (ACC and AUC) of our proposed method according to different parameters based on a t-test with a p-value of $0.001$. (

**a**) Influence of the regularization parameter ($\alpha $) on the model classification results; (

**b**) effect of the embedding space dimension (r) on the model classification results.

**Figure 5.**The most discriminative features detected by the proposed method in ASD vs. NC classification based on an AAL template. This figure was created using circularGraphtool (http://www.mathworks.com/matlabcentral/fileexchange/48576-circulargraph (accessed on 10 October 2022)).

**Table 1.**Demographic and clinical information of subjects at the NYU site from the ABIDE dataset [38]. Values are reported as mean ± standard deviation. M/F: male/female; MMSE: Mini-Mental Examination; GCDR: Global Clinical Dementia Rating; FIQ: Full-Scale Intelligence Quotient; VIQ: Verbal Intelligence Quotient; PIQ: Performance Intelligence Quotient.

Dataset | Class | Gender (M/F) | Age (Years) | FIQ | VIQ | PIQ |
---|---|---|---|---|---|---|

ABIDE | ASD | $68/11$ | $18.58\pm 11.45$ | $107.92\pm 3.15$ | $105.81\pm 1.23$ | $108.81\pm 2.10$ |

NC | $79/26$ | $19.13\pm 11.85$ | $113.15\pm 2.45$ | $113.13\pm 1.15$ | $115.07\pm 2.08$ |

**Table 2.**Interclass FBN distance between ASD patients and normal controls based on different methods. Aver: averaging fusion; Min: minimization fusion; Max: maximization fusion.

Method | PC | SR | MI | CC | Aver | Min | Max | Ours |
---|---|---|---|---|---|---|---|---|

Interclass FBN Distance | 9.20 | 2.52 | 6.41 | 12.26 | 5.88 | 6.87 | 6.02 | 13.24 |

**Table 3.**Classification results (mean ± standard deviation) of six methods in the task of ASD vs. NC classification, with best results shown in bold.

Method | ACC (%) | SEN (%) | SPE (%) | BAC (%) | PPV (%) | NPV (%) | AUC (%) |
---|---|---|---|---|---|---|---|

MNER [26] | 70.65 | 58.82 | 74.29 | 66.66 | 61.98 | 74.29 | 73.32 |

LORTA [46] | 68.48 | 71.70 | 64.10 | 67.90 | 64.93 | 74.29 | 74.29 |

BMGF [27] | 66.30 | 60.76 | 70.48 | 65.62 | 60.76 | 70.48 | 70.56 |

GraphCGC-Net [51] | 71.74 | 63.83 | 78.26 | 71.05 | 75.00 | 78.26 | 77.42 |

MVS-GCN [30] | 67.93 | 58.23 | 75.24 | 66.73 | 63.89 | 70.54 | 71.14 |

MFC-PL [52] | 66.74 | 56.54 | 74.95 | 65.75 | 63.10 | 63.10 | 69.70 |

BrainGC-Net [53] | 77.43 | 59.30 | 51.20 | 58.52 | 59.17 | 64.30 | 74.83 |

Ours | 74.46 | 64.56 | 81.90 | 73.23 | 72.86 | 75.44 | 81.72 |

**Table 4.**Classification results (mean ± standard deviation) of the proposed method and four single-view methods (i.e., PC, SR, MI, and CC) based on different p-values involved in the t-test. CV: cross validation.

CV | p-Value | Method | ACC (%) | SEN (%) | SPE (%) | BAC (%) | PPV (%) | NPV (%) | AUC (%) |
---|---|---|---|---|---|---|---|---|---|

LOOCV | p = 0.01 | PC | 66.85 | 65.82 | 67.62 | 66.72 | 60.47 | 72.45 | 74.56 |

SR | 66.31 | 49.37 | 79.05 | 64.21 | 63.93 | 67.48 | 71.78 | ||

MI | 57.07 | 36.71 | 72.38 | 54.54 | 50.00 | 60.32 | 57.18 | ||

CC | 65.76 | 58.23 | 71.43 | 64.83 | 60.53 | 69.44 | 72.68 | ||

Ours | 73.91 | 65.82 | 80.00 | 72.91 | 71.23 | 75.68 | 75.68 | ||

p = 0.05 | PC | 67.39 | 59.49 | 73.33 | 66.41 | 62.67 | 70.64 | 71.79 | |

SR | 59.78 | 46.84 | 69.52 | 58.18 | 53.62 | 63.48 | 58.64 | ||

MI | 55.43 | 41.77 | 65.71 | 53.74 | 47.83 | 60.00 | 62.69 | ||

CC | 66.85 | 58.23 | 73.33 | 65.78 | 62.16 | 70.00 | 69.99 | ||

Ours | 66.30 | 60.76 | 70.48 | 65.62 | 60.76 | 70.48 | 70.56 | ||

p = 0.001 | PC | 66.30 | 65.82 | 66.67 | 66.24 | 59.77 | 72.16 | 70.17 | |

SR | 63.04 | 51.90 | 71.43 | 61.66 | 57.75 | 66.37 | 64.48 | ||

MI | 64.13 | 62.03 | 65.71 | 63.87 | 57.65 | 69.70 | 72.56 | ||

CC | 70.11 | 64.56 | 74.29 | 69.42 | 65.38 | 73.58 | 78.52 | ||

Ours | 74.46 | 64.56 | 81.90 | 73.23 | 72.86 | 75.44 | 81.72 | ||

p = 0.005 | PC | 69.02 | 68.35 | 69.52 | 68.94 | 62.79 | 74.49 | 73.25 | |

SR | 67.39 | 48.10 | 81.90 | 65.00 | 66.67 | 67.72 | 70.61 | ||

MI | 55.43 | 41.77 | 65.71 | 53.74 | 47.83 | 60.00 | 62.69 | ||

CC | 69.57 | 63.29 | 74.29 | 68.79 | 64.94 | 72.90 | 77.37 | ||

Ours | 74.46 | 68.35 | 79.05 | 73.70 | 71.05 | 76.85 | 76.85 |

Method | Number of FBNs | ||
---|---|---|---|

Two-View FBNs | Three-View FBNs | Four-View FBNs | |

Averaging Fusion | 62.74% | 63.99% | 64.77% |

Ours | 71.73% | 72.14% | 74.41% |

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## Share and Cite

**MDPI and ACS Style**

Wang, C.; Zhang, L.; Zhang, J.; Qiao, L.; Liu, M.
Fusing Multiview Functional Brain Networks by Joint Embedding for Brain Disease Identification. *J. Pers. Med.* **2023**, *13*, 251.
https://doi.org/10.3390/jpm13020251

**AMA Style**

Wang C, Zhang L, Zhang J, Qiao L, Liu M.
Fusing Multiview Functional Brain Networks by Joint Embedding for Brain Disease Identification. *Journal of Personalized Medicine*. 2023; 13(2):251.
https://doi.org/10.3390/jpm13020251

**Chicago/Turabian Style**

Wang, Chengcheng, Limei Zhang, Jinshan Zhang, Lishan Qiao, and Mingxia Liu.
2023. "Fusing Multiview Functional Brain Networks by Joint Embedding for Brain Disease Identification" *Journal of Personalized Medicine* 13, no. 2: 251.
https://doi.org/10.3390/jpm13020251