The size and site dependences of atomic and electronic structures in isolated and supported gold nanoparticles have been investigated using large-scale density functional theory (DFT) calculations using multi-site support functions. The effects of the substrate on nanoparticles with diameters of 2 nm and several different shapes have been examined. First, isolated gold nanoparticles with diameters of 0.6 nm (13 atoms) to 4.5 nm (2057 atoms), which have comparable sizes to nanoparticles used in experiments, were considered. To analyse huge amounts of data obtained from large-scale DFT calculations, we performed principal component analysis (PCA), which helps systematically and efficiently clarify the electronic structures of large nanoparticles. The PCA results reveal the site dependence of the electronic structures. Notably, the atoms in the surface and subsurface have different electronic structures to those located in the inner layers, especially at the vertexes of the particles. The convergence of local electronic structures with respect to the particle size has also been demonstrated. For supported nanoparticles, PCA helps indicate which atoms are affected, and how much, by the substrate. The correlation between the PCA results and site dependence of reaction activity is also discussed herein.