Digital holograms of real-world three-dimensional objects have been captured using phase-shift digital holography. These holograms have complex-valued pixels and a white noise appearance. Uniform and nonuniform scalar quantisation compression have already been applied to the hologram data with some success. Although each complex-valued pixel can itself be treated as a vector of length two, we extend the analysis using a multidimensional vector quantisation technique based on k-means clustering. This involves an a-by-b blockwise decomposition of the data and mapping it to an ab-dimensional space. Degradation due to lossy compression is measured in the reconstruction domain.