# Spectral-Spatial Offset Graph Convolutional Networks for Hyperspectral Image Classification

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

#### 2.1. Graph Convolutional Network

#### 2.2. Hyperspectral Image Classification

## 3. Method

#### 3.1. Automatic Graph Learning (AGL)

_{i,j}denotes the similarity between any two nodes, i.e., ${v}_{i}$ and ${v}_{j}$. In our context, the adjacency matrix

**A**of the undirected graph

**G**, defines the relationships (or edges) among vertexes.

**A**of graph G can be obtained by Equation (5):

**I**denotes the identity matrix,

**U**is an orthogonal matrix comprised by the eigenvectors of the matrix

**L**, $\Lambda $ is a diagonal matrix comprised by eigenvalues of the matrix ${L}_{\mathrm{sym}}$.

_{sym}#### 3.2. Graph Classification Networks

#### 3.2.1. GCN

#### 3.2.2. OGC

**H**

_{in}is the input of OGC module,

**H**

_{out}is the output of OGC module and

**H**

_{GCN}is the output of GCN. According to the definition of GCN layer in Equation (13), we can get:

**W**and vector b are negligible as the weight matrix and bias term in linear transformation, and ${\widehat{L}}_{sym}$ is the regularization Laplace matrix of $\widehat{A}$ with $\widehat{A}=A+I$. Rather, $\widehat{A}=A+I$ is equivalent to adding a self-connection to the adjacency matrix to emphasize the information of each node itself. Therefore, ${H}_{in}-{H}_{GCN}$ can be approximated to the Laplace smoothing operation to the input. According to the row vector perspective of matrix multiplication, ${\widehat{L}}_{sym}{H}_{in}$ is equivalent to aggregate the important feature within neighbor nodes.

#### 3.2.3. Graph Pooling

## 4. Experiment

#### 4.1. Data Sets

- (1)
- Indian Pines Data Set: The scene over northwestern Indiana, USA was acquired over the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) sensor in 1992. The image consists of 145 × 145 pixels and the spatial resolution is 20 m per pixel.

- (2)
- Pavia University Data Set: The second image comprised by 610 × 340 pixels and each pixel are 1.3 m. It was acquired by the Reflective Optics System Imaging Spectrometer (ROSIS) sensor in 2002. There are 115 bands in the range of 0.43~0.86, and 103 bands without serious noise are selected for experiment. The data set includes nine land cover classes, and a total of 42,776 samples can be referred. As shown in Figure 6 below, the left image is a false color map, the middle column is a ground-truth map, and the right is the corresponding class name. Table 3 lists 9 major land-cover classes in this image, as well as the number of training and testing samples used for our experiments.

- (3)
- Salinas Data Set: The scene over Salinas Valley, California was acquired the AVIRIS sensor. The image consists of 512 × 217 pixels and the spatial resolution is 3.7 m per pixel. There are 204 bands are available after discarding the 20 water absorption bands. The data set contains 16 types of features, and 54,129 samples can be referred. Table 4 lists 16 main land-cover categories involved in this scene, as well as the number of training and testing samples used for our experiments. The false color map and ground-truth map are shown in Figure 7.

#### 4.2. Experimental Settings

#### 4.3. Classification Results

#### 4.3.1. Results on the Indian Pines Data Set

#### 4.3.2. Results on the Pavia University Data Set

#### 4.3.3. Results on the Salinas Data Set

#### 4.4. Impact of Patch Size

#### 4.5. Ablation Study

#### 4.6. Impact of the Number of Labeled Samples

#### 4.7. Running Time

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Classification map of various algorithms in the Indian Pines data set ((

**a**) Gound-truth map; (

**b**) KNN; (

**c**) SVM; (

**d**) 2D-CNN; (

**e**) CNN-PPF; (

**f**) GCN; (

**g**) miniGCN; (

**h**) MDGCN; (

**i**) FuNet-C; (

**j**) SSOGCN).

**Figure 9.**Classification map of various algorithms in the Pavia University data set ((

**a**) Gound-truth map; (

**b**) KNN; (

**c**) SVM; (

**d**) 2D-CNN; (

**e**) CNN-PPF; (

**f**) GCN; (

**g**) miniGCN; (

**h**) MDGCN; (

**i**) FuNet-C; (

**j**) SSOGCN).

**Figure 10.**Classification map of various algorithms in the Salinas data set ((

**a**) Gound-truth map; (

**b**) KNN; (

**c**) SVM; (

**d**) 2D-CNN; (

**e**) CNN-PPF; (

**f**) miniGCN; (

**g**) MDGCN; (

**h**) FuNet-C; (

**i**) SSOGCN).

**Figure 12.**Sensitivity analysis of training set size. (

**a**) Indian Pines data set. (

**b**) Pavia University data set. (

**c**) Salinas data set.

Layer | Module | Input Tensor Size | Output Tensor Size |
---|---|---|---|

1 | GCN | 32 × D × 49 | 32 × 32 × 49 |

POOL | 32 × 32 × 49 | 32 × 32 × 16 | |

2 | OGC | 32 × 32 × 16 | 32 × 32 × 16 |

POOL | 32 × 32 × 16 | 32 × 32 × 4 | |

3 | OGC | 32 × 32 × 4 | 32 × 32 × 4 |

POOL | 32 × 32 × 4 | 32 × 32 × 1 | |

4 | FC | 32 × 32 | 32 × C |

Class | Class Name | Train | Test |
---|---|---|---|

1 | Alfalfa | 15 | 31 |

2 | Corn-notill | 50 | 1378 |

3 | Corn-mintill | 50 | 780 |

4 | Corn | 50 | 187 |

5 | Grass-pasture | 50 | 433 |

6 | Grass-trees | 50 | 680 |

7 | Grass-pasture-mowed | 15 | 13 |

8 | Hay-windrowed | 50 | 428 |

9 | Oats | 15 | 5 |

10 | Soybean-notill | 50 | 922 |

11 | Soybean-mintill | 50 | 2405 |

12 | Soybean-clean | 50 | 543 |

13 | Wheat | 50 | 155 |

14 | Woods | 50 | 1215 |

15 | Buildings-Grass-Trees-Drives | 50 | 336 |

16 | Stone-Steel-Towers | 50 | 43 |

Total | 695 | 9554 |

Class | Class Name | Train | Test |
---|---|---|---|

1 | Asphalt | 50 | 6581 |

2 | Meadows | 50 | 18,599 |

3 | Gravel | 50 | 2049 |

4 | Trees | 50 | 3014 |

5 | Painted metal sheets | 50 | 1295 |

6 | Bare Soil | 50 | 4979 |

7 | Bitumen | 50 | 1280 |

8 | Self-Blocking Bricks | 50 | 3632 |

9 | Shadows | 50 | 897 |

Total | 450 | 42,326 |

Class | Class Name | Train | Test |
---|---|---|---|

1 | Brocoli_green_weeds_1 | 50 | 1959 |

2 | Brocoli_green_weeds_2 | 50 | 3676 |

3 | Fallow | 50 | 1926 |

4 | Fallow_rough_plow | 50 | 1344 |

5 | Fallow_smooth | 50 | 2628 |

6 | Stubble | 50 | 3909 |

7 | Celery | 50 | 3529 |

8 | Grapes_untrained | 50 | 11,221 |

9 | Soil_vinyard_develop | 50 | 6153 |

10 | Corn_senesced_green_weeds | 50 | 3228 |

11 | Lettuce_romaine_4wk | 50 | 1018 |

12 | Lettuce_romaine_5wk | 50 | 1877 |

13 | Lettuce_romaine_6wk | 50 | 866 |

14 | Lettuce_romaine_7wk | 50 | 1020 |

15 | Vinyard_untrained | 50 | 7218 |

16 | Vinyard_vertical_trellis | 50 | 1757 |

Total | 800 | 53,329 |

Class | KNN | SVM | 2D-CNN | CNN-PPF | GCN | miniGCN | MDGCN | FuNet-C | SSOGCN |
---|---|---|---|---|---|---|---|---|---|

1 | 15.54 | 16.89 | 12.03 | 16.22 | 18.92 | 17.57 | 93.54 | 29.59 | 20.95 |

2 | 45.79 | 68.94 | 70.6 | 67.49 | 75.47 | 68.07 | 65.82 | 78.81 | 87.52 |

3 | 54.87 | 57.56 | 68.25 | 55.38 | 62.05 | 53.97 | 83.33 | 84.49 | 93.46 |

4 | 63.64 | 79.68 | 99.52 | 78.07 | 86.63 | 66.84 | 96.25 | 96.26 | 100.0 |

5 | 84.30 | 89.15 | 94.48 | 89.61 | 88.68 | 77.37 | 79.44 | 97.92 | 98.38 |

6 | 87.65 | 91.32 | 100.0 | 92.50 | 94.85 | 93.38 | 92.05 | 99.12 | 98.68 |

7 | 92.31 | 92.31 | 100.0 | 100.0 | 100.0 | 100.0 | 23.07 | 100.0 | 100.0 |

8 | 89.72 | 95.09 | 97.1 | 96.73 | 97.20 | 98.36 | 100.0 | 100.0 | 100.0 |

9 | 80.00 | 100.0 | 100.0 | 100.0 | 100.0 | 80.00 | 0.00 | 100.0 | 100.0 |

10 | 67.68 | 77.66 | 75.58 | 74.51 | 80.48 | 69.52 | 73.53 | 85.25 | 92.41 |

11 | 49.94 | 59.09 | 70.8 | 63.58 | 59.58 | 63.04 | 88.77 | 78.50 | 90.19 |

12 | 44.94 | 62.80 | 65.72 | 78.08 | 79.56 | 64.64 | 67.77 | 79.74 | 95.76 |

13 | 96.13 | 98.06 | 100.0 | 100.0 | 98.71 | 98.06 | 100.0 | 100.0 | 99.35 |

14 | 74.65 | 80.00 | 89.15 | 84.44 | 80.41 | 86.17 | 92.02 | 96.30 | 97.12 |

15 | 52.98 | 71.43 | 84.27 | 76.19 | 80.06 | 69.64 | 96.43 | 89.29 | 99.11 |

16 | 93.02 | 93.02 | 100.00 | 97.67 | 95.35 | 90.70 | 83.72 | 100.0 | 100.0 |

OA(%) | 61.06 | 71.20 | 78.93 | 73.42 | 74.7 | 71.33 | 80.53 | 85.54 | 92.51 |

AA(%) | 68.32 | 77.06 | 83.32 | 79.41 | 81.12 | 74.83 | 77.23 | 87.83 | 92.06 |

KA(%) | 56.29 | 67.60 | 76.10 | 69.91 | 71.47 | 67.42 | 81.11 | 83.52 | 91.45 |

Class | KNN | SVM | 2D-CNN | CNN-PPF | GCN | miniGCN | MDGCN | FuNet-C | SSOGCN |
---|---|---|---|---|---|---|---|---|---|

1 | 67.45 | 63.07 | 76.10 | 57.73 | 64.03 | 78.62 | 62.80 | 85.34 | 95.00 |

2 | 70.88 | 82.59 | 83.52 | 83.56 | 83.42 | 86.77 | 88.67 | 95.33 | 99.09 |

3 | 67.01 | 81.80 | 75.40 | 82.97 | 78.09 | 70.82 | 93.76 | 91.65 | 84.58 |

4 | 88.12 | 90.44 | 97.51 | 89.28 | 89.25 | 88.49 | 81.89 | 96.95 | 95.92 |

5 | 98.92 | 99.61 | 99.46 | 99.00 | 98.61 | 98.53 | 97.17 | 99.92 | 99.77 |

6 | 69.05 | 82.43 | 78.53 | 54.35 | 86.10 | 81.74 | 99.22 | 90.76 | 97.23 |

7 | 87.97 | 92.11 | 94.77 | 93.52 | 90.47 | 90.16 | 85.19 | 97.89 | 98.28 |

8 | 71.97 | 78.85 | 84.55 | 62.89 | 79.87 | 83.07 | 79.79 | 88.79 | 96.26 |

9 | 100.0 | 99.89 | 100.0 | 100.0 | 100.0 | 100.0 | 53.33 | 100.0 | 99.89 |

OA(%) | 73.26 | 80.44 | 83.65 | 75.35 | 81.14 | 84.69 | 84.24 | 92.93 | 97.08 |

AA(%) | 80.15 | 85.64 | 87.76 | 80.36 | 85.54 | 86.47 | 82.37 | 94.07 | 96.22 |

KA(%) | 65.96 | 74.96 | 78.79 | 67.64 | 75.84 | 79.99 | 79.57 | 90.66 | 96.11 |

Class | KNN | SVM | 2D-CNN | CNN-PPF | miniGCN | MDGCN | FuNet-C | SSOGCN |
---|---|---|---|---|---|---|---|---|

1 | 88.42 | 97.13 | 95.61 | 85.15 | 97.60 | 100.0 | 100.0 | 100.0 |

2 | 88.25 | 97.08 | 97.03 | 99.97 | 99.89 | 100.0 | 99.97 | 100.0 |

3 | 93.82 | 91.49 | 96.0 | 94.65 | 93.87 | 63.11 | 99.22 | 99.88 |

4 | 90.48 | 99.56 | 99.55 | 99.63 | 99.03 | 97.06 | 99.55 | 99.75 |

5 | 83.87 | 92.84 | 96.88 | 97.41 | 97.45 | 99.74 | 97.34 | 97.26 |

6 | 82.02 | 99.72 | 99.39 | 99.82 | 99.97 | 100.0 | 100.0 | 100.0 |

7 | 87.79 | 99.3 | 99.12 | 99.60 | 99.63 | 100.0 | 99.43 | 100.0 |

8 | 50.84 | 57.58 | 51.38 | 92.06 | 67.13 | 85.47 | 64.46 | 83.12 |

9 | 81.75 | 97.69 | 97.40 | 99.58 | 99.38 | 100.0 | 99.93 | 99.80 |

10 | 97.40 | 85.0 | 90.68 | 89.71 | 92.13 | 98.66 | 97.15 | 97.84 |

11 | 78.09 | 92.81 | 98.13 | 93.03 | 97.35 | 48.78 | 99.71 | 99.45 |

12 | 87.16 | 98.74 | 99.89 | 99.73 | 99.89 | 100.0 | 100.0 | 99.94 |

13 | 88.34 | 99.10 | 99.65 | 99.77 | 99.54 | 100.0 | 100.0 | 100.0 |

14 | 80.29 | 90.81 | 98.63 | 93.24 | 98.14 | 99.63 | 98.92 | 100.0 |

15 | 63.52 | 52.01 | 66.42 | 23.04 | 70.16 | 81.84 | 76.20 | 91.99 |

16 | 89.53 | 93.66 | 97.10 | 98.01 | 98.41 | 93.36 | 98.69 | 99.94 |

OA(%) | 76.05 | 81.84 | 83.41 | 85.98 | 87.85 | 91.72 | 88.84 | 95.05 |

AA(%) | 83.22 | 90.28 | 92.68 | 91.52 | 94.35 | 91.70 | 95.66 | 98.06 |

KA(%) | 73.52 | 79.85 | 81.62 | 84.27 | 86.5 | 90.77 | 87.61 | 94.49 |

Data Set | Without OGC | Without AGL | Without Graph Pooling | SSOGCN |
---|---|---|---|---|

Indian Pines | 90.12 | 91.38 | 86.65 | 92.51 |

Pavia University | 94.91 | 94.04 | 93.47 | 97.08 |

Salinas | 93.74 | 93.85 | 88.60 | 95.05 |

**Table 9.**Run time comparison and parameter number comparison of depth model in the Indian Pines data set.

Methods | Time (s) | Params (K) |
---|---|---|

2D-CNN | 178.06 | 30.0 |

CNN-PPF | 61.86 | 44.82 |

GCN | 198.12 | 4.36 |

miniGCN | 776.86 | 28.70 |

MDGCN | 322.01 | 13.07 |

FuNet-C | 678.13 | 148.59 |

SSOGCN | 597.05 | 23.41 |

**Table 10.**Run time comparison and parameter number comparison of depth model in the Pavia University data set.

Methods | Time (s) | Params (K) |
---|---|---|

2D-CNN | 167.65 | 29.10 |

CNN-PPF | 149.18 | 31.50 |

GCN | 410.38 | 2.27 |

miniGCN | 2925.70 | 15.19 |

MDGCN | 447.87 | 6.81 |

FuNet-C | 2753.58 | 77.44 |

SSOGCN | 1471.03 | 12.22 |

**Table 11.**Run time comparison and parameter number comparison of depth model in the Salinas University data set.

Methods | Time (s) | Params (K) |
---|---|---|

2D-CNN | 283.94 | 30.00 |

CNN-PPF | 243.28 | 45.32 |

miniGCN | 1273.54 | 29.22 |

MDGCN | 458.48 | 13.31 |

FuNet-C | 5002.85 | 150.264 |

SSOGCN | 1183.93 | 23.96 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, M.; Luo, H.; Song, W.; Mei, H.; Su, C.
Spectral-Spatial Offset Graph Convolutional Networks for Hyperspectral Image Classification. *Remote Sens.* **2021**, *13*, 4342.
https://doi.org/10.3390/rs13214342

**AMA Style**

Zhang M, Luo H, Song W, Mei H, Su C.
Spectral-Spatial Offset Graph Convolutional Networks for Hyperspectral Image Classification. *Remote Sensing*. 2021; 13(21):4342.
https://doi.org/10.3390/rs13214342

**Chicago/Turabian Style**

Zhang, Minghua, Hongling Luo, Wei Song, Haibin Mei, and Cheng Su.
2021. "Spectral-Spatial Offset Graph Convolutional Networks for Hyperspectral Image Classification" *Remote Sensing* 13, no. 21: 4342.
https://doi.org/10.3390/rs13214342