Combining Hilbert Feature Sequence and Lie Group Metric Space for Few-Shot Remote Sensing Scene Classification

Few-shot learning (FSL) is a method that does not require a large number of labeled samples and has the ability to identify unseen samples. Recently, many excellent FSL methods have been developed for remote sensing scene classification (RSSC). However, for complex remote sensing scenes, the following problems have not been well addressed: 1) the order of local features and the spatial correlation between features have not been taken into consideration and 2) the current metric methods are mainly based on Euclidean space (ES), and discriminative ability is limited. Hence, we propose a framework for RSSC with FSL by combining Hilbert feature sequence and Lie group metric space (HFS-LGMS). Specifically, we adopt a lightweight four-layer convolutional neural network (CNN) as a feature extractor. For the last feature map, we regard each pixel as a multidimensional local feature. Then we organize all the features into a feature sequence along the Hilbert curve. To represent the correlation among features, we introduce the autoregressive moving average model (AMAM) to model the observed features and their spatial states. Since the parameters of the model are matrices, which are directly processed as vectors will affect performance. Therefore, we transform the matrix parameter space into the Lie group manifold space (LGMS) and introduce the Lie group intrinsic mean (LGIM) to represent the prototype. The distance between the Lie groups is measured by the geodesic distance. The similarity is measured on Lie group space. Finally, the effectiveness of HFS-LGMS is demonstrated on three public datasets.