# Classification of PolSAR Images Using Multilayer Autoencoders and a Self-Paced Learning Approach

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

- ${v}_{i}$ is monotonically decreasing with respect to the training loss ${l}_{i}=L({y}_{i},g({\mathit{x}}_{i},\mathit{w}))$, and it holds that $\underset{{l}_{i}->0}{\mathrm{lim}}{v}_{i}=1$, $\underset{{l}_{i}->\infty}{\mathrm{lim}}{v}_{i}=0$.
- ${v}_{i}$ is monotonically increasing with respect to the pace parameter $\lambda $, and it holds that $\underset{\lambda ->0}{\mathrm{lim}}{v}_{i}=0$, $\underset{\lambda ->\infty}{\mathrm{lim}}{v}_{i}=1$.

- Step 1: Initialize the weights of all samples $\mathit{v}$ and parameter $\lambda $.
- Step 2: Fix $\mathit{v}$, and update $\mathit{w}$ by Equation (2).
- Step 3: Fix $\mathit{w}$, calculate the training loss $L({y}_{i},g({\mathit{x}}_{i},\mathit{w}))$, and update $\mathit{v}$ by Equation (4).
- Step 4: If $\mathit{v}$ and $\mathit{w}$ have converged, then go to step 5; otherwise, repeat step 2 and step 3.
- Step 5: Update $\lambda $, $\lambda =\kappa \lambda ,\text{}\kappa 1$.
- Step 6: Repeat step 2 to step 5 until the mean of $\mathit{v}$ is equal to or approximately 1. Finally, obtain the solution of $\mathit{w}$.

## 3. Proposed Method

#### 3.1. Multilayer Autoencoders Network

**T**of the PolSAR data, and the row vector is used as the input vector of the network. In the PolSAR data, each pixel is represented as a $2\times 2$ scattering matrix

**S**:

**T**is obtained by

**S**, which is defined in Equation (6), as follows:

**T**:

#### 3.2. Optimization of Multilayer Autoencoders Network Based on SPL

#### 3.2.1. Unsupervised Pre-Training the Parameters of Each Autoencoder Layer

**W**and

**b**.

**W**,

**b**and ${v}_{i}$) in the objective function in Equation (13), and it is difficult to optimize these variables at the same time. We can obtain the solution according to the following steps:

- Step 1: initialize the parameters: ${\mathbf{W}}^{(k,1)}$, ${\mathit{b}}^{(k,1)}$, ${\mathbf{W}}^{(k,2)}$, ${\mathit{b}}^{(k,2)}$ and $\lambda $.
- Step 2: apply the mini-batch gradient descent algorithm based on SPL to optimize the parameters.
- Step 2.1: select a mini-batch sample to optimize the parameters.
- Step 2.2: calculate the output vector and loss function for each input vector through forward propagation, and then, calculate the weight parameter ${v}_{i}$ by Equation (4).
- Step 2.3: fix the weight parameter ${v}_{i}$, and use back propagation to train the parameters ${\mathbf{W}}^{(k,1)}$, ${\mathit{b}}^{(k,1)}$, ${\mathbf{W}}^{(k,2)}$, ${\mathit{b}}^{(k,2)}$.
- Step 2.4: Update $\lambda $, $\lambda =\kappa \lambda ,\text{}\kappa 1$. In general, we need the range of training loss values in advance to determine the initial value of $\lambda $ and the step size $\kappa $. In our experiment, the initial value of $\lambda $ is set to the first quartile of the sample training losses, and $\kappa =1.1$.
- Step 2.5: repeat step 2.2 to step 2.4 until the value of $\mathit{v}$ is approximately 1 (all the samples of the current iteration have been completely learned). Here, $\mathit{v}$ is defined as $\mathit{v}=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}{v}_{i}}$.
- Step 2.6: a new mini-batch sample is selected to optimize the parameter until all the samples are learned.
- Step 3: repeat step 2 until the number of epochs achieve a predefined threshold, and then, obtain the parameters ${\mathbf{W}}^{(k,1)}$ and ${\mathit{b}}^{(k,1)}$.

#### 3.2.2. Supervised Fine-Tuning Those Parameters with Softmax Regression

## 4. Experiments

#### 4.1. Network Architecture Analysis

#### 4.2. Flevoland Dataset from AIRSAR

#### 4.2.1. Convergence Analysis of Our Algorithm

#### 4.2.2. Classification Results

#### 4.3. Flevoland Dataset from RADARSAT-2

#### 4.4. Yellow River Delta Dataset from ALOS-2

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Two-layer autoencoder with softmax regression neural network; (

**b**) 1

^{st}autoencoder network.

**Figure 5.**The classification results of the Flevoland dataset from AIRSAR. (

**a**) SVM, OA = 0.8708; (

**b**) SRC, OA = 0.8231; (

**c**) WC, OA = 0.8504; (

**d**) MAE, OA = 0.9304; (

**e**) SPLMAE, OA = 0.9473.

**Figure 6.**The classification results of the Flevoland dataset from RADARSAT-2. (

**a**) Pauli RGB; (

**b**) Ground truth; black area denotes unlabeled pixels; (

**c**) SVM, OA = 0.9229; (

**d**) SRC, OA = 0.8231; (

**e**) WC, OA = 0.8382; (

**f**) MAE, OA = 0.9449; (

**g**) SPLMAE, OA = 0.9482.

**Figure 9.**The classification results of the sub-image. (

**a**) Pauli RGB; (

**b**) SVM; (

**c**) SRC; (

**d**) WC; (

**e**) MAE; (

**f**) SPLMAE.

**Table 1.**The accuracies of the Flevoland dataset from AIRSAR. AA: average accuracy; OA: overall accuracy.

Class | SVM | SRC | WC | MAE | SPLMAE |
---|---|---|---|---|---|

Stembeans | 0.9719 | 0.9642 | 0.9508 | 0.9842 | 0.9801 |

Rapeseed | 0.7351 | 0.6049 | 0.7484 | 0.8487 | 0.9003 |

Bare soil | 0.9802 | 0.9211 | 0.9920 | 0.9039 | 0.8649 |

Potatoes | 0.9811 | 0.6631 | 0.8775 | 0.9858 | 0.9815 |

Beet | 0.9541 | 0.9561 | 0.9513 | 0.9679 | 0.9713 |

Wheat 2 | 0.7875 | 0.7797 | 0.8272 | 0.8582 | 0.8559 |

Peas | 0.9258 | 0.9396 | 0.9628 | 0.9664 | 0.9676 |

Wheat 3 | 0.9288 | 0.8226 | 0.8864 | 0.9732 | 0.9749 |

Lucerne | 0.9292 | 0.9513 | 0.9293 | 0.9553 | 0.9608 |

Barley | 0.9365 | 0.9322 | 0.9526 | 0.9738 | 0.9795 |

Wheat | 0.8128 | 0.7610 | 0.8622 | 0.9656 | 0.9592 |

Grasses | 0.8373 | 0.6284 | 0.7246 | 0.8203 | 0.8555 |

Forest | 0.7562 | 0.9797 | 0.8791 | 0.9601 | 0.9707 |

Water | 0.8213 | 0.8002 | 0.5175 | 0.7981 | 0.9434 |

AA | 0.8827 | 0.8360 | 0.8616 | 0.9258 | 0.9404 |

OA | 0.8708 | 0.8231 | 0.8504 | 0.9304 | 0.9473 |

Train + Test time (s) | 1.3 + 17 | 84 + 155 | 130 | 1539 + 3.4 | 1495 + 3.5 |

**Table 2.**The accuracies of Flevoland dataset from RADARSAT-2. AA: average accuracy; OA: overall accuracy.

Class | SVM | SRC | WC | MAE | SPLMAE |
---|---|---|---|---|---|

Urban | 0.8051 | 0.7579 | 0.6022 | 0.8712 | 0.8921 |

Water | 0.9693 | 0.9779 | 0.9854 | 0.9878 | 0.9870 |

Forest | 0.9207 | 0.9195 | 0.8479 | 0.9537 | 0.9468 |

Cropland | 0.9372 | 0.8759 | 0.8071 | 0.9327 | 0.9408 |

AA | 0.9080 | 0.8828 | 0.8107 | 0.9363 | 0.9417 |

OA | 0.9229 | 0.8978 | 0.8382 | 0.9449 | 0.9482 |

Train + Test time (s) | 1+ 11.7 | 26 + 436 | 87.5 | 51 + 5 | 42 + 4.7 |

Class | SVM | SRC | WC | MAE | SPLMAE |
---|---|---|---|---|---|

Pond | 0.8540 | 0.3680 | -- | 0.9230 | 0.9132 |

Alkali Soil | 0.8498 | 0.4681 | -- | 0.8350 | 0.8523 |

Coastal Shoal | 0.7192 | 0.4912 | -- | 0.7798 | 0.7758 |

Wetland | 0.5544 | 0.2311 | -- | 0.5908 | 0.6678 |

Plantation | 0.5280 | 0.4377 | -- | 0.7175 | 0.7124 |

River | 0.1444 | 0.3144 | -- | 0.3215 | 0.4489 |

AA | 0.6083 | 0.3851 | 0.6 | 0.6946 | 0.7284 |

OA | 0.7113 | 0.3963 | -- | 0.7627 | 0.7812 |

Train + Test time (s) | 5 + 305 | 39 + 2871 | -- | 5840 + 52 | 5643 + 53 |

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**MDPI and ACS Style**

Chen, W.; Gou, S.; Wang, X.; Li, X.; Jiao, L. Classification of PolSAR Images Using Multilayer Autoencoders and a Self-Paced Learning Approach. *Remote Sens.* **2018**, *10*, 110.
https://doi.org/10.3390/rs10010110

**AMA Style**

Chen W, Gou S, Wang X, Li X, Jiao L. Classification of PolSAR Images Using Multilayer Autoencoders and a Self-Paced Learning Approach. *Remote Sensing*. 2018; 10(1):110.
https://doi.org/10.3390/rs10010110

**Chicago/Turabian Style**

Chen, Wenshuai, Shuiping Gou, Xinlin Wang, Xiaofeng Li, and Licheng Jiao. 2018. "Classification of PolSAR Images Using Multilayer Autoencoders and a Self-Paced Learning Approach" *Remote Sensing* 10, no. 1: 110.
https://doi.org/10.3390/rs10010110