Characterizing Multi-Energy X-ray Transmission (XRT) hyperspectral images presents significant challenges for traditional classification frameworks due to high-dimensional redundancy and non-linear spectral overlaps. Although manifold learning techniques such as UMAP enhance spectral representation by preserving non-linear correlations, they do not explicitly utilize the geometric structure of the embedded manifold for segmentation. This study introduces a hybrid architecture that integrates topological features derived from persistent homology with convolutional and graph neural networks. The approach computes Vietoris-Rips persistent homology on UMAP-projected superpixel point clouds to capture H 1 cyclic structures that encode spectral heterogeneity. These topological descriptors are combined with pixel-level CNN features through a broadcasting mechanism that propagates superpixel-level graph representations to full spatial resolution. Experimental results on XRT multi-energy imagery demonstrate that the proposed hybrid model significantly outperforms both CNN-only and superpixel-pooling fusion baselines, suggesting that topological features provide complementary discriminative information to local spectralspatial descriptors.