# A Novel Relational-Based Transductive Transfer Learning Method for PolSAR Images via Time-Series Clustering

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Introduction of Time-Series Clustering Theory into the Field of PolSAR Images

- (1)
- Source domain: an image with plenty of labeled samples.
- (2)
- Source domain samples: labeled samples in the source domain image.
- (3)
- Target domain: other images in the time-series images, except for the source domain image.
- (4)
- Target domain samples: samples in the target domain images with the sample geographical location as the source domain samples, but without an object label.
- (5)
- Time-series samples: sample sequences consisting of samples from the same geographic location of all the sequential images, including source domain samples and target domain samples.
- (6)
- Time-series samples of a certain class of objects: taking the water time-series sample as an example, it is defined as a time-series sample, for which the label in the source domain image is “water”.

**.**:

#### 2.2. A Three-Phase Time-Series Clustering Algorithm for PolSAR Images

#### 2.2.1. Initial Clustering

#### 2.2.2. Optimization Clustering

- (1)
- The R-Wishart distance between similar objects in the same image is smaller than that between different objects.
- (2)
- Due to the influence of different imaging conditions, the R-Wishart distances between the same class of objects in different temporal images are different. For example, for the time-series samples ${S}_{i}$ and ${S}_{j}$, their R-Wishart distances to the cluster center ${\omega}_{m}$ in the first and second temporal images are as follows:$$\begin{array}{c}d\left({C}_{i}^{1},\text{}{C}_{m}^{1}\right)\ne d\left({C}_{i}^{2},\text{}{C}_{m}^{2}\right)\\ d\left({C}_{j}^{1},\text{}{C}_{m}^{1}\right)\ne d\left({C}_{j}^{2},\text{}{C}_{m}^{2}\right)\end{array}$$
- (3)
- Since the influence of imaging conditions on the same class of objects is similar in a single image, the change degree of the R-Wishart distance between the same class of objects in different images will be close, as shown below:$$\left[d\text{}\left({C}_{i}^{1},\text{}{C}_{m}^{1}\right)-d\text{}\left({C}_{i}^{2},\text{}{C}_{m}^{2}\right)\right]\cong \left[d\text{}\left({C}_{j}^{1},\text{}{C}_{m}^{1}\right)-d\text{}\left({C}_{j}^{2},\text{}{C}_{m}^{2}\right)\right]$$

#### 2.2.3. Cluster Merging

**.**, the ideal result is to output four time-series cluster centers, each of which corresponds to one type of time-series sample. However, in reality, the number of types of time-series samples is unknown. If the number of cluster centers is too small, it will lead to the merging of different types of time-series cluster centers. If the number of cluster centers is too large, it may lead to the total number of unchanged samples in the final output cluster being too small. In addition, the total number of types of time-series samples in different data and different ground objects is unique, so it is impossible to obtain reliable results by setting an empirical number of clusters.

^{th}merging in the graph increases obviously, which indicates that all the same types of clusters have been merged at this time, so the 18

^{th}merging is the best merging termination position.

#### 2.3. Transductive Label Transfer-Based on Time-Series Clustering

## 3. Experiments

#### 3.1. Evaluation Methods and Experimental Setting

#### 3.1.1. Evaluation Methods

- Evaluation of the three-phase time-series clustering algorithm

- Evaluation of label transfer precision

#### 3.1.2. Experimental Setting

#### 3.2. Experiment One

#### 3.2.1. Experimental Data

#### 3.2.2. Results

#### 3.3. Experiment Two

#### 3.3.1. Experimental Data

#### 3.3.2. Results

#### 3.4. Experiment Three

#### 3.4.1. Experimental Data

#### 3.4.2. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Examples of different types of water time-series samples. Image 2 is the source domain, while the other images are target domains.

**Figure 3.**The curve of DVI change with merging times. The green line is the DVI, the blue line is the min distance between classes, and the red line is the max intra-class distance.

**Figure 4.**Pauli RGB images of the first group of time-series images, with red ${\left|{S}_{HH}-{S}_{VV}\right|}^{2}$, green $4{\left|{S}_{HV}\right|}^{2}$, and blue ${\left|{S}_{HH}+{S}_{VV}\right|}^{2}$. The image of 20170824 is the source domain and the other images are the target domain.

**Figure 5.**The mean and standard deviation curves of each phase. (

**a**) The DVI of each phase. (

**b**) The purity of each phase.

**Figure 7.**Pauli RGB images of the second group of time-series images, with red ${\left|{S}_{HH}-{S}_{VV}\right|}^{2}$, green $4{\left|{S}_{HV}\right|}^{2}$, and blue ${\left|{S}_{HH}+{S}_{VV}\right|}^{2}$. The image of 2011 is the source domain and the other images are the target domain.

**Figure 8.**The mean and standard deviation curves of each phase. (

**a**) The DVI of each phase. (

**b**) The purity of each phase.

**Figure 10.**Pauli RGB images of the third group of time-series images, with red ${\left|{S}_{HH}-{S}_{VV}\right|}^{2}$, green $4{\left|{S}_{HV}\right|}^{2}$, and blue ${\left|{S}_{HH}+{S}_{VV}\right|}^{2}$. The image of 2008 is the source domain and the other images are the target domain.

**Figure 11.**The mean and standard deviation curves of each phase. (

**a**) The DVI of each phase. (

**b**) The purity of each phase.

**Figure 12.**The mean and standard deviation of the label transfer precision of the different objects.

**Table 1.**Sample usage in each experiment. TCTLT: transductive label transfer; TrBagg: transfer bagging; BETL: bagging-based ensemble transfer learning.

Algorithm | Source Domain Labeled Samples | Target Domain Labeled Samples | Target Domain Unlabeled Samples |
---|---|---|---|

TCTLT | 300/class | 0/class | 300/class |

TrBagg | 300/class | 5/class | 300/class |

BETL | 300/class | 5/class | 300/class |

Number | Date | Sensor | Direction | Band (Frequency) | Polarization | Incidence Angle (Degrees) |
---|---|---|---|---|---|---|

1 | 20170824 | GF-3 | ASC | C (5.4 GHz) | Full | 35.3~37.0 |

2 | 20170529 | GF-3 | ASC | C (5.4 GHz) | Full | 35.3–37.0 |

3 | 20170430 | GF-3 | ASC | C (5.4 GHz) | Full | 35.3~37.1 |

4 | 20170212 | GF-3 | DEC | C (5.4 GHz) | Full | 35.4~37.1 |

Number | Date | Sensor | Direction | Band (Frequency) | Polarization | Incidence Angle (Degrees) |
---|---|---|---|---|---|---|

1 | 2011 | RADARSAT-2 | ASC | C (5.4 GHz) | Full | 40.2~41.6 |

2 | 2015 | RADARSAT-2 | ASC | C (5.4 GHz) | Full | 40.2~41.6 |

3 | 2016 | RADARSAT-2 | ASC | C (5.4 GHz) | Full | 45.2~46.5 |

4 | 2017 | GF-3 | ASC | C (5.4 GHz) | Full | 35.3~37.0 |

Number | Date | Sensor | Direction | Band (Frequency) | Polarization | Incidence Angle (Degrees) |
---|---|---|---|---|---|---|

1 | 2008 | RADARSAT-2 | ASC | C (5.4 GHz) | Full | 38.4~39.8 |

2 | 2009 | RADARSAT-2 | ASC | C (5.4 GHz) | Full | 38.4~39.8 |

3 | 2010 | RADARSAT-2 | ASC | C (5.4 GHz) | Full | 38.4~39.8 |

4 | 2013 | RADARSAT-2 | ASC | C (5.4 GHz) | Full | 38.4~39.8 |

5 | 2014 | RADARSAT-2 | ASC | C (5.4 GHz) | Full | 38.4~39.8 |

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**MDPI and ACS Style**

Qin, X.; Yang, J.; Li, P.; Sun, W.; Liu, W. A Novel Relational-Based Transductive Transfer Learning Method for PolSAR Images via Time-Series Clustering. *Remote Sens.* **2019**, *11*, 1358.
https://doi.org/10.3390/rs11111358

**AMA Style**

Qin X, Yang J, Li P, Sun W, Liu W. A Novel Relational-Based Transductive Transfer Learning Method for PolSAR Images via Time-Series Clustering. *Remote Sensing*. 2019; 11(11):1358.
https://doi.org/10.3390/rs11111358

**Chicago/Turabian Style**

Qin, Xingli, Jie Yang, Pingxiang Li, Weidong Sun, and Wei Liu. 2019. "A Novel Relational-Based Transductive Transfer Learning Method for PolSAR Images via Time-Series Clustering" *Remote Sensing* 11, no. 11: 1358.
https://doi.org/10.3390/rs11111358