Semi-Supervised Tensorial Locally Linear Embedding for Feature Extraction Using PolSAR Data

Recently, the semi-supervised feature extraction, which uses both a few labeled samples and a large quantity of unlabeled samples to improve discrimination of extracted features, has attracted attention in PolSAR data processing. However, most of the feature extraction methods are based on matrix operations and need to re-arrange the multiple features into vectors. Such a vectorization way may break the spatial structure and correlation among the neighboring pixels, which leads to the degradation of classification performance. To address this issue and incorporate the superiority of semi-supervised learning, a novel semi-supervised tensorial locally linear embedding (STLLE) method is proposed for PolSAR data. Each pixel and its spatial neighbors in a local window are represented as a third-order tensor, whose first two orders represent the neighborhood pixels, and the third order denotes the multiple features. The feature extraction is converted to find an optimal projection that can transform the high-dimensional features to low-dimensional ones. This can be solved by designing an objective function, in which the tensorial discriminant item includes the between-class and within-class scatter matrices on each mode of the labeled tensors. A regularizer is based on tensorial locally linear embedding graph using labeled and unlabeled tensor samples. Moreover, the pairwise class constraints are also introduced. Finally, we can use all the extracted features with a classifier such as K-Nearest Neighbor. Experimental results on three real PolSAR datasets demonstrate that STLLE significantly improves classification accuracies compared with state-of-the-art methods, which clearly verifies that the extracted features preserve the data structures well and are more discriminative.