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The integration of hyperspectral imaging (HSI) and LiDAR data within new linear feature spaces offers a promising solution to the challenges posed by the high-dimensionality and redundancy inherent in HSIs. This study introduces a dual linear fused space framework that capitalizes on bidirectional reversed convolutional neural network (CNN) pathways, coupled with a specialized spatial analysis block. This approach combines the computational efficiency of CNNs with the adaptability of attention mechanisms, facilitating the effective fusion of spectral and spatial information. The proposed method not only enhances data processing and classification accuracy, but also mitigates the computational burden typically associated with advanced models such as Transformers. Evaluations of the Houston 2013 dataset demonstrate that our approach surpasses existing state-of-the-art models. This advancement underscores the potential of the framework in resource-constrained environments and its significant contributions to the field of remote sensing.