VHR Multispectral Satellite Image Classification with Kolmogorov-Arnold Networks for Urban Applications

Abstract. The Kolmogorov-Arnold Network (KAN) is a computational framework rooted in the Kolmogorov-Arnold representation theorem, which states that any continuous function of multiple variables can be expressed as a superposition of univariate functions. KAN leverages this theoretical foundation to decompose complex functions into simpler and lower-dimensional ones. Function decomposition makes KAN particularly suitable for challenging tasks in image classification, where separating data into distinct categories often requires approximating intricate and multi-dimensional boundaries. In practice, KAN, relying on function decomposition, offers an alternative to multilayer perceptron (MLP) architectures. By efficiently encoding nonlinear relationships among features, KAN demonstrates potential in multilayered data analysis tasks such as multi and hyper-spectral remotely sensed image classification. As a result, KAN finds significant applications in remote sensing image processing, particularly in Land Cover and Land Use (LCLU) mapping using Very High-Resolution (VHR) satellite imageries. Due to their fine detail, VHR images provide an exceptional basis for accurately distinguishing between various land cover types. When multispectral data is incorporated, KAN excels by leveraging its ability to model nonlinear relationships, allowing for highly accurate classifications. KAN's performance is validated using ground-truth data collected from field surveys or random reference points visually picked from images. Additionally, KAN is benchmarked against other methods like traditional Shallow Neural Networks (SNNs). Obtained KAN classification accuracy and computational efficiency are evaluated compared to SNN, highlighting its strengths in modelling complexity with optimized key model parameters. A Python-based implementation of KAN is developed for flexible integration into existing geospatial analysis workflows and highlighting its compatibility with cloud computing environments such as Google Colab. This integration enhances scalability, makes it practical for processing large-scale satellite datasets efficiently, and facilitates high-resolution mapping and reproducibility in environmental monitoring and urban applications. The reliability of KAN and the potential classification accuracy of different model architectures were verified. The KAN model with a 10-neuron mid-layer achieved an overall accuracy of 88.89%, outperforming the SNN results with a maximum accuracy of 87.84 for a model with 20 & 20-neuron hidden layers.