Electron energy-loss spectroscopy (EELS) in the transmission electron microscope (TEM) is used to obtain high-resolution information on the composition and the type of chemical bonding of materials. Spectrum imaging, where a full EEL spectrum is acquired and stored at each pixel in the image, gives an exact correlation of spatial and spectral features. However, determining and extracting the important spectral components from the large amount of information contained in a spectrum image (SI) can be difficult. This paper demonstrates that principal component analysis of EEL SIs can be used to extract chemically relevant components. With weighted or two-way scaled principal component analysis, both compositional and bonding information can be extracted. Mapping of the chemical variations in a partially reduced titanium dioxide sample and the orientation-dependent bonding in boron nitride and carbon nanotubes are given as examples.