# SCAFG: Classifying Single Cell Types Based on an Adaptive Threshold Fusion Graph Convolution Network

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Real Datasets

#### 2.2. Data Normalization

#### 2.3. Cosine Similarity

#### 2.4. Threshold Segmentation

#### 2.5. Similarity Distance Between Matrices

Algorithm 1 Construction of the Similarity Distance Matrix H |

Require: Incidence matrix: $S=\left\{{S}_{n},n=1,2,3,...,9\right\}$; |

For each ${S}_{n}$ in S, they have the same dimension $O({S}_{n}^{0},{S}_{n}^{1}),\hspace{0.17em}{S}_{n}^{0}={S}_{n}^{1}$; |

Ensure: |

1: for $x=0;x<8;x++$ do |

2: for $y=x+1;y<9;y++$ do |

3: $N=0;$ |

4: Calculate $H(x,y)$: |

5: for $i=0;i<{S}_{x}^{0}-1;i++$ do |

6: for $j=i+1;j<{S}_{x}^{1};j++$ do |

7: if ${S}_{x}^{ij}=={S}_{y}^{ij}$ then |

8: $N\Leftarrow N+1$ |

9: end if |

10: end for |

11: end for |

12: return $H(x,y)=H(y,x)\Leftarrow N$; |

13: end for |

14: end for |

15. return H |

#### 2.6. Fusion

Algorithm 2 Incidence Matrix Fusion to Form the Consensus Matrix Q |

Require: Similarity Distance Matrix $H,t,r,c,Max=0$; |

Ensure: |

1: for $x=0;x<8;x++$do |

2: for $y=x+1;y<9;y++$ do |

3: if $H(x,y)>=Max$ then |

4: $Max=H(x,y)$ |

5: $r=x$ |

6: $c=y$ |

7: end if |

8: end for |

9: end for |

10: return $r,c$ |

11: Select the incidence matrix ${S}_{r+1},{S}_{c+1}$ |

12: for $i=0;i<{S}_{r+1}^{0}-1;i++$ do |

13: for $j=i+1;j<{S}_{r+1}^{1};j++$ do |

14: if ${S}_{r+1}^{ij}=={S}_{c+1}^{ij}$ then |

15: $Q(x,y)={S}_{r+1}^{ij}$ |

16: else |

17: $t=\mathit{MAX}(c+1,r+1)$ |

18: $Q(x,y)={S}_{t}^{ij}$ |

19: end if |

20: $Q(y,x)=Q(x,y)$ |

21: end for |

22: end for |

23: return Q |

#### 2.7. Construction of the GCN

## 3. Results and Discussion

#### 3.1. Results

#### 3.2. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Overview of the SCAFG. (

**a**) Data preprocessing, including normalization and similarity transformation of the gene expression matrix. (

**b**) Dividing the similarity matrix into nine incidence matrices through threshold segmentation, then converting the similarities between the incidence matrices into a similarity distance matrix. (

**c**) Finding the row and column index of the largest element value in the similarity distance matrix. (

**d**) Fusing the incidence matrix and saving the consensus matrix as a graph. (

**e**) The graph is the input of the GCN, and the output is a probability matrix. The column index corresponding to the maximum probability value of each row in the probability matrix is the category to which the cell belongs.

**Figure 3.**The classification accuracy of the Chung dataset with different numbers of matrices being fused.

**Figure 4.**The box plot of the Chung dataset, recording the highest accuracy for each of the 10 experiments.

**Figure 5.**Box plots for four datasets—comparison of the classification accuracies with fusion of different matrices: (

**a**) Chu, (

**b**) Patel, (

**c**) Xin, and (

**d**) Ning.

Datasets | Number of Cells | Class | Number of Genes | Data Sources | References |
---|---|---|---|---|---|

Chung | 563 | 13 | 57915 | GSE75688 | Chung et al. [26]. |

Chu | 1018 | 7 | 19097 | GSE75748 | Chu et al. [27] |

Patel | 430 | 6 | 5948 | GSE57872 | Patel et al. [28]. |

Xin | 1600 | 8 | 39851 | GSE81608 | Xin et al. [29]. |

Ning | 460 | 4 | 19084 | GSE64016 | Ning et al. [30]. |

Dataset | Iteration | Label Propagation | Label Spreading | Self-Training | GCN | SCAFG |
---|---|---|---|---|---|---|

25 | 36.6 | 47.5 | 36.6 | 32.3 | 46.4 | |

Chung | 50 | 44.6 | 56.1 | 49.8 | 44.6 | 64.2 |

75 | 47.7 | 59.2 | 54.2 | 58.8 | 82.2 | |

25 | 44.1 | 53.2 | 58.8 | 64.2 | 70.1 | |

Chu | 50 | 58.3 | 55.6 | 69.5 | 86.7 | 92.3 |

75 | 61.5 | 56.9 | 73.2 | 89.2 | 96.4 | |

25 | 50.6 | 46.2 | 49.7 | 65.1 | 76.7 | |

Patel | 50 | 67.1 | 58.3 | 59.4 | 73.8 | 89.9 |

75 | 70.6 | 64.8 | 65.2 | 77.6 | 96.3 | |

25 | 70.2 | 64.6 | 60.1 | 80.9 | 87.4 | |

Xin | 50 | 76.2 | 74.5 | 68.5 | 82.2 | 88.1 |

75 | 80.1 | 74.8 | 74.2 | 83.6 | 91.2 | |

25 | 51.2 | 56.7 | 46.8 | 82.6 | 91.1 | |

Ning | 50 | 58.4 | 69.2 | 63.1 | 85.4 | 93.3 |

75 | 62.4 | 74.6 | 69.2 | 89.8 | 97.6 |

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**MDPI and ACS Style**

Peng, H.; Li, Y.; Zhang, W. SCAFG: Classifying Single Cell Types Based on an Adaptive Threshold Fusion Graph Convolution Network. *Mathematics* **2022**, *10*, 3407.
https://doi.org/10.3390/math10183407

**AMA Style**

Peng H, Li Y, Zhang W. SCAFG: Classifying Single Cell Types Based on an Adaptive Threshold Fusion Graph Convolution Network. *Mathematics*. 2022; 10(18):3407.
https://doi.org/10.3390/math10183407

**Chicago/Turabian Style**

Peng, Haonan, Yuanyuan Li, and Wei Zhang. 2022. "SCAFG: Classifying Single Cell Types Based on an Adaptive Threshold Fusion Graph Convolution Network" *Mathematics* 10, no. 18: 3407.
https://doi.org/10.3390/math10183407