To achieve effective deep fusion features for improving the classification accuracy of hyperspectral remote sensing images (HRSIs), a pixel frequency spectrum feature is presented and introduced to convolutional neural networks (CNNs). Firstly, the fast Fourier transform is performed on each spectral pixel to obtain the amplitude spectrum, i.e., the pixel frequency spectrum feature. Then, the obtained pixel frequency spectrum is combined with the spectral pixel to form a mixed feature, i.e., spectral and frequency spectrum mixed feature (SFMF). Several multi-branch CNNs fed with pixel frequency spectrum, SFMF, spectral pixel, and spatial features are designed for extracting deep fusion features. A pre-learning strategy, i.e., basic single branch CNNs are used to pre-learn the weights of a multi-branch CNN, is also presented for improving the network convergence speed and avoiding the network from getting into a locally optimal solution to a certain extent. And after reducing the dimensionality of SFMF by principal component analysis (PCA), a 3-dimensionality (3-D) CNN is also designed to further extract the joint spatial-SFMF feature. The experimental results of three real HRSIs show that adding the presented frequency spectrum feature into CNNs can achieve better recognition results, which in turn proves that the presented multi-branch CNNs can obtain the deep fusion features with more discriminant information.

As a powerful nonlinear feature extractor, kernel principal component analysis (KPCA) has been widely adopted in many machine learning applications. However, KPCA is usually performed in a batch mode, leading to some potential problems when handling massive or online datasets. To overcome this drawback of KPCA, in this paper, we propose a two‐phase incremental KPCA (TP‐IKPCA) algorithm which can incorporate data into KPCA in an incremental fashion. In the first phase, an incremental algorithm is developed to explicitly express the data in the kernel space. In the second phase, we extend an incremental principal component analysis (IPCA) to estimate the kernel principal components. Extensive experimental results on both synthesized and real datasets showed that the proposed TP‐IKPCA produces similar principal components as conventional batch‐based KPCA but is computationally faster than KPCA and its several incremental variants. Therefore, our algorithm can be applied to massive or online datasets where the batch method is not available.

For reducing the parameters and computational complexity of networks while improving the classification accuracy of hyperspectral remote sensing images (HRSIs), a dynamic split pointwise convolution (DSPC) strategy is presented, and a lightweight convolutional neural network (CNN), i.e., CSM-DSPCss-Ghost, is proposed based on DSPC. A channel switching module (CSM) and a dynamic split pointwise convolution Ghost (DSPC-Ghost) module are presented by combining the presented DSPC with channel shuffling and the Ghost strategy, respectively. CSM replaces the first expansion pointwise convolution in the MobileNetV2 bottleneck module to reduce the parameter number and relieve the increasing channel correlation caused by the original channel expansion pointwise convolution. DSPC-Ghost replaces the second pointwise convolution in the MobileNetV2 bottleneck module, which can further reduce the number of parameters based on DSPC and extract the depth spectral and spatial features of HRSIs successively. Finally, the CSM-DSPCss-Ghost bottleneck module is presented by introducing a squeeze excitation module and a spatial attention module after the CSM and the depthwise convolution, respectively. The presented CSM-DSPCss-Ghost network consists of seven successive CSM-DSPCss-Ghost bottleneck modules. Experiments on four measured HRSIs show that, compared with 2D CNN, 3D CNN, MobileNetV2, ShuffleNet, GhostNet, and Xception, CSM-DSPCss-Ghost can significantly improve classification accuracy and running speed while reducing the number of parameters.

To effectively utilize the rich spectral information of hyperspectral remote sensing images (HRSIs), the fractional Fourier transform (FRFT) feature of HRSIs is proposed to reflect the time-domain and frequency-domain characteristics of a spectral pixel simultaneously, and an FRFT order selection criterion is also proposed based on maximizing separability. Firstly, FRFT is applied to the spectral pixels, and the amplitude spectrum is taken as the FRFT feature of HRSIs. The FRFT feature is mixed with the pixel spectral to form the presented spectral and fractional Fourier transform mixed feature (SF²MF), which contains time–frequency mixing information and spectral information of pixels. K-nearest neighbor, logistic regression, and random forest classifiers are used to verify the superiority of the proposed feature. A 1-dimensional convolutional neural network (1D-CNN) and a two-branch CNN network (Two-CNN_SF²MF-Spa) are designed to extract the depth SF²MF feature and the SF²MF-spatial joint feature, respectively. Moreover, to compensate for the defect that CNN cannot effectively capture the long-range features of spectral pixels, a long short-term memory (LSTM) network is introduced to be combined with CNN to form a two-branch network C-CLSTM_SF²MF for extracting deeper and more efficient fusion features. A 3D-CNN_SF²MF model is designed, which firstly performs the principal component analysis on the spa-SF²MF cube containing spatial information and then feeds it into the 3-dimensional convolutional neural network 3D-CNN_SF²MF to extract the SF²MF-spatial joint feature effectively. The experimental results of three real HRSIs show that the presented mixed feature SF²MF can effectively improve classification accuracy.