###### Abstract
Additionally, it can show different scattering characteristics for crops in different growing periods, which greatly improves the classification accuracy of crops [23, 24, 25]. Recently, a number of classification algorithms with PolSAR data have been presented in the literature, which can be roughly divided into three categories:  
1. [label=(0)]
2. Algorithms based on statistical models [26]. For example, [PERSON] et al. proposed a classical classifier based on the complex Wishart distribution [27];
3. Algorithms based on the scattering mechanisms of polarization [28]. The points with the same physical meaning are classified using the polarization scattering parameters obtained by the coherent and incoherent decomposition algorithms (such as Pauli decomposition [29], Freeman decomposition [30], etc.) [31, 32, 33, 34, 35];
4. The classification schemes based on machine learning [36], e.g., support vector machine (SVM) [37] and various neural networks [38]. For instance, [PERSON] et al. use the SVM to classify four crops (rice, maize, grape and cotton) in the Nile Delta, Egypt [39]. With the collection of multi-temporal PolSAR data, the various classification algorithms based on time-series information have also been developed. For example, long short-term memory (LSTM) network has been exploited to recognize and classify the multi-temporal PolSAR images [40]. [PERSON] et al. classify the summer crops in Yolo County, California using the LSTM algorithm with Landsat Enhanced Vegetation Index (EVI) time series [25]. It can be seen that the research and application of multi-temporal PolSAR data are constantly progressing. For LSTM algorithm, the performance of this network mainly depends on input features, so a large amount of decomposition algorithms have been developed to extract the polarization scattering characteristics [41, 42, 43, 44]. However, the direct use of polarization features will result in the so-called \"dimension disaster\" problem for the various classifiers. Therefore, the dimension reduction for the extracted multi-temporal features has become a significant work. Some methods, such as principle component analysis (PCA) [45] and locally linear embedded (LLE) [46], etc., are popular for feature compression to solve the \"dimension disaster\" problem. For instance, the PCA method actually provides the optimal linear solution for data compression in the sense of minimum mean square error (MMSE) [47]. The advantage of PCA lies in the fast restoration of original data by subspace projection at a cost of minimum error. However, it cannot be guaranteed that the principle components extracted by PCA provide the most relevant information for crop type discrimination. Independent Component Analysis (ICA) is the generalization of PCA, which can gain independent gains. [PERSON] et al. adopt the ICA to recognize the face images of the FERET face database [48]. Tensor decomposition is often used to extract certain elementary features from image data. [PERSON] et al. used tensor decomposition method to achieve the feature learning on satellite imagery [49]. Non-negative matrix factorization (NMF) is based on non-negative constraints, which allows learn parts from objects. [PERSON] et al. applied the reduce dimensionality method NMF as the preprocessing of remote sensing imagery classification [50]. However, they are not suitable for dimensionality reduction about PolSAR data of crops. Additionally, the LLE method can voluntarily extract the low-dimensional feature of nonlinear from high-dimensional data, but it is very sensitive to outliers [51]. In most recent years, with the development of deep learning, the convolutional neural network (CNN) has been gradually applied in remote sensing data analysis [52]. At present, some successful network structures (e.g., auto-encoder [53; 54] and sparse auto-encoder (SAE) [17; 55].) have been presented, yielding excellent performances in feature compression and image classification.