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The initial stages of growth of the nanostructured cerium oxide deposited on the polycrystalline tungsten surface by pulsed laser deposition are studied using XPS technique. The population of Ce (III) and Ce (IV) oxidation states in the deposited CeO2−x layers is determined applying factor analysis method. Tungsten atoms react with oxygen from the cerium oxide nanoparticles already at the room temperature, and a layer of tungsten trioxide is formed at the interface. Gradual heating of the samples up to 900 K leads to the increase of the thickness of WO3 oxide layer and a partial reduction of Ce (IV) to Ce (III). The spectra of O (1s) photoelectrons are composed from a signal originating from metal oxides and a signal of surface superoxide and hydroxyl groups. Factor analysis was performed on the spectra of Ce (3d) photoelectrons to determine the position, shape, and intensity of the spectral components belonging to Ce (III) and Ce (IV) oxidation states. We propose a new simple method to generate components of the spectroscopic meaning. The basic idea of our method consists in the use of the slightly positive values instead of zeros to the needle test vector. Two components are required to reproduce the original data within the experimental errors. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]