Low-Rank Approximation for Efficient Compression of Gaussian Splatting Spherical Harmonics

3D Gaussian Splatting (3DGS) enables real-time, high-fidelity rendering but suffers from large model sizes, mainly due to the Spherical Harmonics (SH) coefficients used for view-dependent appearance modeling, whose parameter count scales quadratically(O(L2))with the degreeL. This paper presents the first systematic study that reveals and leverages the intrinsic low-rank structure of SH coefficients in 3DGS. Unlike prior approaches that truncate spectral energy, the proposed low-rank paradigm compactly preserves spectral information, achieving high visual quality with substantially reduced storage. Two complementary approaches are introduced. (1) SHAC-PCA (Principal Component Analysis) is a plug-and-play post-hoc compressor that retains principal spectral variance for high-fidelity compression. (2) SHAC-LST (Learned Subset Transformation) is a training-integrated approach that decomposes Alternating Current (AC) of SH coefficients into low-dimensional subset coefficients and a shared transformation matrix, offering superior compression and even quality improvements through regularization. Both methods effectively reduce SH coefficients storage complexity toO(L). Extensive experiments demonstrate that our approaches significantly reduce memory usage while maintaining or even improving rendering quality. The proposed techniques are highly versatile: SHAC-PCA can be applied to any pre-trained 3DGS model, while SHAC-LST supports end-to-end training or fine-tuning. Both methods are compatible with existing 3DGS compression pipelines, providing a practical and general solution for efficient compression of SH coefficients in 3DGS.