# Explainable Two-Layer Mode Machine Learning Method for Hyperspectral Image Classification
## 1 Introduction  
Hyperspectral images (HSIs) are obtained through an imaging spectrometer with hundreds of continuous spectral bands, and they integrate spectral and image information. They have multi-band and high spectral resolution characteristics [1]. Hyperspectral technology has become an effective tool for remote sensing applications, recognizing and learning multidimensional information from hyperspectral images to achieve corresponding research goals [2]. HSI classification has been used in agriculture for crop identification and health monitoring [3], environmental protection for land cover mapping [4], and water quality assessment [5]. In practical applications, the multi-band characteristics of hyperspectral remote sensing data enable a more comprehensive description of the reflection characteristics of ground objects and have a strong ability to identify ground object attributes [6]. However, the large amount of redundant information in the data can lead to high computational complexity, which is not conducive to subsequent image analysis and weakens the classifier's generalization ability [7]. The curse of dimensionality and the Hughes phenomenon affect classification performance [8]. In recent years, HSI classification research has made significant progress [9]. Traditional machine learning methods, such as support vector machine (SVM) [10] and random forest [11], effectively handle high-dimensional spectral data by leveraging the unique spectral signatures of materials. However, these methods often struggle with capturingcomplex spatial-spectral relationships in HSI data, which led to the exploration of more advanced techniques. With the advent of deep learning, convolutional neural networks (CNNs) emerged as a powerful tool for HSI classification. CNNs can automatically extract features from spectral and spatial dimensions of HSI data, significantly improving classification accuracy [12]. For example, 3D-CNNs have been particularly effective in capturing spatial-spectral information by applying convolutional operations across both dimensions. Also, hybrid models that combine CNNs with other architectures, such as recurrent neural networks (RNNs) or graph neural networks (GNNs) [9], have been developed to enhance performance. Due to their ability to handle non-Euclidean data and capture complex relationships between pixels, GNNs perform well. The decision-making process of deep learning models remains a black box, making it challenging to understand how and why certain classifications are made [13]. Explainable artificial intelligence (EXI) methods [14,15] address this issue by providing interpretability to complex models. Developing EXI methods based on integrating deep learning and mathematical models can help analyze the model's decision-making basis and further optimize its performance. The HSI classification methods are divided into two categories: one is the end-to-end learning approach, for example, using deep learning algorithms [16, 17, 18, 19, 20, 21] to directly train models from input data to classification results; another type has the characteristics of two-layer mode [22, 23, 24, 25, 26, 27], which completes the data representation through front-end learning and then uses classifiers to determine the classification model in back-end learning. A new two-layer mode machine learning method for HSI classification is proposed in this paper, which is shown in Figure 1.The classification method contains two layers: the front-end learning layer and the back-end learning layer. The former layer achieves HSI re-expression, which combines superpixel segmentation technology and a regularized subspace clustering method for band selection. The latter layer uses SVM or K-nearest neighbor (KNN) classification algorithms to classify the re-expressed HSI data. Finally, the evaluation metrics from the back-end learning help adjust the number of bands in the front-end learning layer. To sum up, our main contributions are as follows.