Electron Energy Loss Spectroscopy (EELS) in a transmission electron microscope offers the possibility of extracting high accuracy maps of composition and electronic properties through EELS spectrum images (EELS-SI). Acquiring EELS-SI for different tilt angles, a 3D tomographic reconstruction of EELS information can be achieved. In the present work we show that an EELS spectrum volume (EELS-SV), a 4D dataset where every voxel contains a full EELS spectrum, can be reconstructed from the EELS-SI tilt series by the application of multivariate analysis. We apply this novel approach to characterize a nanocomposite material consisting of CoFe2O4 nanocolumns embedded in a BiFeO3 matrix grown on a LaNiO3 buffered LaAlO3 (001) substrate.