# A Deep Learning Model for Data-Driven Discovery of Functional Connectivity

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.1.1. Fbirn

#### 2.1.2. Preprocessing

#### 2.2. Method

#### 2.2.1. Cnn Encoder

#### 2.2.2. Self Attention

#### 2.2.3. GNN

#### 2.2.4. Training and Testing

## 3. Results

#### 3.1. Classification

#### 3.2. Functional Connectivity

#### 3.3. Region Selection

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**BrainGNN architecture using: (

**a**) Preprocessing: to preprocess the raw data with different steps (Section 2.1.2); (

**b**) 1DCNN: to create embedding for regions (Section 2.2.1); (

**c**) Self-attention: to create connectivity between regions (Section 2.2.2); (

**d**) GNN: to obtain a single feature vector for the entire graph (Section 2.2.3); and (

**e**) Linear classifier: to obtain the final classification.

**Figure 2.**KDE plot of probability density of receiver operating characteristic curve (ROC-AUC) score on Function Biomedical Informatics Research Network (FBIRN) dataset. The 190 points on the x-axis signifies the 19 fold cross validation, 10 trials per cross validation. With average and median of (∼0.8), density peaks at (∼0.8) AUC.

**Figure 3.**The ROC curves of the 19 models generated using each fold of cross validation. The graph is symmetrical and well balanced. It shows that the model did not learn one class over the other.

**Figure 4.**BrainGNN comparision with other popular methods. BrainGNN provides mean AUC as $0.79$, which is just (∼0.02) less than the best performing model (SVM). Methods like WholeMILC (UFPT) and l1 logistic regression failed to learn on the input data. The l1 logistic regression model does perform better with a very weak regularization term.

**Figure 5.**Connectivity between regions of subjects of both classes using BrainGNN and sFNC (PCC method).

**BrainGNN**: the similarity of connection between a class and difference across class is compelling. Weights of SZ class are more sparse than HC, highlighting the fact that fewer regions receive higher weights for subjects with SZ. Refer to Table 2 for results of statistical testing between weights of HC and SZ subjects.

**sFNC**: the matrices are symmetric but are less informative than those that were produced by BrainGNN. Most of the regions are assigend unit weight.

**Figure 6.**(

**a**) Histogram of regions selected after the last pooling layer of GNN. 2nd fold of the cross validation gives this figure. All the 23 regions are selected an equal number of times (16). It further signifies the important of these regions, showing that, for all subjects across both classes, these 23 regions are always selection. (

**b**) mapping the 23 regions back on the brain across the three anatomical planes. 100th time point is selected for these brain scans. X axis shows different slices of the plane.

CV Fold | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

AUC | 0.695 | 0.955 | 0.644 | 0.752 | 0.908 | 0.917 | 0.894 | 0.803 | 0.649 | 0.805 | 0.922 | 0.699 | 0.625 | 0.780 | 0.794 | 0.766 | 0.914 | 0.750 | 0.777 |

**Table 2.**Statistical testing between weight matrices of healthy controls (HC) and schizophrenia (SZ). The test shows that weights of regions differ across HC and SZ subjects. Refer to Figure 4 for mean and deviation of these folds.

Test | p Value |
---|---|

Mann-Whitney U Test | 0.0 |

Welch’s t-test | 0.0 |

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**MDPI and ACS Style**

Mahmood, U.; Fu, Z.; Calhoun, V.D.; Plis, S.
A Deep Learning Model for Data-Driven Discovery of Functional Connectivity. *Algorithms* **2021**, *14*, 75.
https://doi.org/10.3390/a14030075

**AMA Style**

Mahmood U, Fu Z, Calhoun VD, Plis S.
A Deep Learning Model for Data-Driven Discovery of Functional Connectivity. *Algorithms*. 2021; 14(3):75.
https://doi.org/10.3390/a14030075

**Chicago/Turabian Style**

Mahmood, Usman, Zening Fu, Vince D. Calhoun, and Sergey Plis.
2021. "A Deep Learning Model for Data-Driven Discovery of Functional Connectivity" *Algorithms* 14, no. 3: 75.
https://doi.org/10.3390/a14030075