Spectral unmixing is one of the most important and studied topics in hyperspectral image analysis. By means of spectral unmixing it is possible to decompose a hyperspectral image in its spectral components, the so-called endmembers, and their respective fractional spatial distributions, so-called abundance maps. New hyperspectral missions will allow to acquire hyperspectral images in new ways, for instance, in temporal series or in multi-angular acquisitions. Working with these incoming huge databases of multi-way hyperspec-tral images will raise new challenges to the hyperspectral community. Here, we propose the use of compression-based non-negative tensor canonical polyadic (CP) decompositions to analyze this kind of datasets. Furthermore, we show that the non-negative CP decomposition could be understood as a multi-linear spectral unmixing technique. We evaluate the proposed approach by means of Mars synthetic datasets built upon multi-angular in-lab hyperspectral acquisitions.