HierarchicalMamba: A Multiscale State Space Model With Dual Transitions for Hyperspectral Image Classification

Hyperspectral image (HSI) classification faces fundamental challenges: existing convolutional neural networks capture only local spatial patterns while neglecting spectral sequence dependencies, recurrent neural networks suffer from gradient vanishing and computational inefficiency, and Transformer architectures encounter quadratic computational complexity O(L²) limiting scalability for sequences with hundreds of spectral bands. This paper proposes the HierarchicalMamba algorithm, which addresses these challenges through three core innovations leveraging State Space Models (SSMs) with linear complexity O(L). First, we design a unified spatial-sequential modeling framework that encodes two-dimensional spatial coordinate information into one-dimensional sequence positional indices, enabling simultaneous modeling of spectral correlations and spatial neighborhood relationships within a single SSM framework while avoiding the complexity of traditional dual-stream architectures. Second, we develop a multi-scale SSM decomposition theory through heterogeneous parallel branches and combinations of different activation functions, comprehensively capturing multi-granularity features in hyperspectral data and introducing adaptive fusion weights to achieve optimal feature combination. Third, we innovatively propose a dual state transition(DST) mechanism that applies the state transition matrix twice within each computational cycle, significantly enhancing the modeling capability for higher-order state dependencies and complex nonlinear dynamics. Comprehensive experiments on five benchmark datasets including Indian Pines, Pavia University, Salinas Valley, Kennedy Space Center, and Houston2018 demonstrate that HierarchicalMamba achieves overall accuracies of 96.11%, 98.03%, 97.06%, 95.34%, and 82.35% respectively, significantly outperforming existing methods while maintaining linear computational complexity and featuring 3.04M parameters, training time of 5.87 seconds per epoch on Pavia University (approximately 53× faster than TRANSF_uniformer_tiny at 313.33 seconds per epoch), and inference time of 2.51 milliseconds per image. This method provides a new theoretical framework and technical pathway for HSI classification. The source code for HierarchicalMamba will be made publicly available at: https://github.com/Jason20155/HierarchicalMamba ¹.