At present, spectral clustering is an important branch of unsupervised learning, and its application in deep learning has been widely concerned. However, for high-dimensional sparse datasets, the complexity of network scale leads to parameter explosion, and static Gaussian kernel often has wrong preset data structure. To overcome these challenges, we propose a novel deep clustering model, Deep Clustering Based on Sparse Kolmogorov-Arnold Network (KAN) and Spectral Constraint. It contains a deep sparse clustering framework, in which sparse KAN and the orthogonal layer are designed to enhance the sparsity of the activation function matrix, reduce the number of parameters and improve the stability of model convergence. Additionally, we add an adaptive optimized affinity matrix based on spectral constraint, which overcomes the limitations of static Gaussian kernels, and improves the performance and stability of spectral constraint. Experimental results on both synthetic and real datasets demonstrate that our model outperforms existing methods in clustering performance, computational efficiency, and stability.

In the past era of explosive data growth, how to deal with large-scale, unlabeled remote sensing images (RSIs) has become a concern. Due to the lack of data labels, unsupervised methods are usually used to deal with them. As one of the best unsupervised algorithms, spectral clustering (SC) is a very effective data processing and analysis technology. However, the scalability of SC affects its development in the era of big data. Deep network technology has developed rapidly in the past, and it is often used to solve the problem of out-of-sample expansion (OOSE) that traditional machine learning cannot solve. However, because RSI is usually high-dimensional data, it is easy to cause dimension explosion in deep networks. The main motivation of this work is to solve the above problems. We have designed a new algorithm called deep SC with projected adaptive feature selection (DSCFS), which benefits from deep learning theory and feature projection technology. We use a neural network to map RSI data and then further process the data through regularization embedding. At the same time, adaptive feature projection is applied to extract the main features of RSI, and the loss feedback network is calculated through these two steps. A large number of experiments show that the performance of our proposed method is better than other mainstream methods.