目的 为了解决基于卷积神经网络的算法对高光谱图像小样本分类精度较低、模型结构复杂和计算量大的问题，提出了一种变维卷积神经网络。方法 变维卷积神经网络对高光谱分类过程可根据内部特征图维度的变化分为空—谱信息融合、降维、混合特征提取与空—谱联合分类的过程。这种变维结构通过改变特征映射的维度，简化了网络结构并减少了计算量，并通过对空—谱信息的充分提取提高了卷积神经网络对小样本高光谱图像分类的精度。结果 实验分为变维卷积神经网络的性能分析实验与分类性能对比实验，所用的数据集为Indian Pines和Pavia University Scene数据集。通过实验可知，变维卷积神经网络对高光谱小样本可取得较高的分类精度，在Indian Pines和Pavia University Scene数据集上的总体分类精度分别为87.87%和98.18%，与其他分类算法对比有较明显的性能优势。结论 实验结果表明，合理的参数优化可有效提高变维卷积神经网络的分类精度，这种变维模型可较大程度提高对高光谱图像中小样本数据的分类性能，并可进一步推广到其他与高光谱图像相关的深度学习分类模型中。

Objective Hyperspectral image classification is a challenging task because of the large number of spectral channels, small-sized labeled training samples, and large spatial variability. Most existing hyperspectral image classification models only consider spectral feature information and neglect the important role of spatial information in classification. Spatial features have become increasingly important in hyperspectral image classification because adjacent pixels are likely to belong to the same category, and the spectral-spatial classification method has the best classification accuracy. Compared with other remote sensing image data, hyperspectral remote sensing image data comprise 2D spatial plane images and increase spectral dimensions that contain the spectral information of objects. Hence, hyperspectral remote sensing image data are able to form 3D data cubes containing rich image information and spectral information. However, the number of bands increases with an increase in the dimension of a hyperspectral image. The information correlation between bands is high, and the hidden features are rich. The problem with high-dimensional small-sized labeled samples is that the number of labeled samples in a dataset is much smaller than the dimension of the sample features. The high data dimensions of hyperspectral images lead to low classification accuracy, excessive dependence on training samples, extended iteration training time, and low efficiency. First, the scale of corresponding feature space increases rapidly with an increase in feature dimensions, thereby leading to dimension issues. Second, the presence of many irrelevant or noise features means that the learning samples are few, resulting in overfitting. Therefore, a small training error still leads to the poor generalization ability of classifiers, which directly reduces the prediction capability of classification models. Multi-spectral image processing algorithms cannot be directly applied to hyperspectral image processing, which involves high-dimensional information and features that are complex, diverse, and massive. A dimensionality-varied convolutional neural network is proposed in this work to solve the problems of low classification accuracy, complex model structure, and large computational complexity of the algorithm on the basis of a convolution neural network for small-sized labeled samples of hyperspectral images. Method The dimensionality-varied convolutional neural network is an improved model that is based on convolution neural networks. Optimizing the structure of 3D convolution and 2D convolution in a network is the key to a successful classification. In a dimensionality-varied convolutional neural network, the main component of the convolution layer is a convolution core. The convolution core of the 3D feature extraction process is a 3D filter composed of a set of learning parameters. The application of the 3D convolution core to hyperspectral image classification simplifies the network structure and improves the accuracy of feature extraction. The convolution core of the 2D feature extraction process is a 2D filter composed of a set of learning parameters. If the number of convolution kernels is sufficient, then we can extract all feature types of an image synthetically and obtain an effective and rich extraction of the convolution layer. The basic function of the pooling layer is to gradually reduce the size of the feature expression space so as to reduce the network parameters and computational load and thereby control the fitting. The dimensionality-varied convolutional neural network mainly uses a max pooling operation, which is a non-linear operation, and improves the computational speed and robustness of feature extraction. The classification accuracy is higher when the classification model has many layers and convolution kernels. However, as the complexity of the model increases, the computational complexity increases as well. The dimensionality-varied convolutional neural network can be divided into spectral-spatial information fusion, dimension reduction, mixed feature extraction, and spectral-spatial classification according to the changes in the dimensions of internal feature maps. The process can ensure that the network can extract small-sized labeled sample features in a certain depth. In the feature extraction process of the dimensionality-varied convolutional neural network, the dimension of the internal feature map is changed instead of retaining the 3D structure, thereby reducing the required computation and storage space. This dimensionality-varied structure simplifies the network structure and reduces computational complexity by changing the dimension of feature mapping. The accuracy of the convolutional neural network for hyperspectral image classification of small-sized labeled samples is improved by fully extracting the spectral-spatial information. Result The experiment is divided into performance analysis and classification performance comparison of the dimensionality-varied convolutional neural network. The datasets used are the Indian Pines and Pavia University Scene datasets. Experiment results show that the dimensionality-varied convolutional neural network can achieve high classification accuracy for hyperspectral images with small-sized labeled samples. The selection of parameters in the dimensionality-varied convolutional neural network greatly influences classification accuracy. Experiments on batch size, threshold, dropout, and kernel number show that a reasonable parameter selection has an important impact on the classification performance of the algorithm. For the Indian Pines and Pavia University Scene datasets, the optimal classification performance is achieved when the batch sizes are set to 40 and 150, the thresholds are both set to 1×10^-15, the dropout values are both set to 0.8, and the kernel numbers are set to 8 and 5, respectively. The overall classification accuracies for the Indian Pines and Pavia University Scene datasets are 87.87% and 98.18%, respectively. Compared with other classification algorithms, the proposed algorithm has evident performance advantages. The combination of the two optimization methods, namely, spectral-spatial information and dimensionality reduction for feature maps, can effectively improve the classification of hyperspectral images with small-sized labeled samples. Conclusion Experimental results show that by changing the dimensions of feature maps in feature extraction, high-precision spectral-spatial feature extraction is realized, and the complexity of the model is reduced. Compared with other classification algorithms, the dimensionality-varied convolutional neural network can effectively improve the classification of small-sized labeled samples and greatly reduce the complexity of the model. Reasonable parameter optimization can effectively improve the classification accuracy of the dimensionality-varied convolutional neural network. This dimensionality-varied model can greatly improve the classification performance of small-sized labeled samples in hyperspectral images and can be further extended to other deep learning classification models related to hyperspectral images.