The spatial pixel resolution of common multispectral and hyperspectral sensors is generally not sufficient to avoid thatmultiple elementary materials contribute to the observed spectrum of a single pixel. To alleviate this limitation, spectral unmixingis a by-pass procedure which consists in decomposing the observed spectra associated with these mixed pixels into a set ofcomponent spectra, or endmembers, and a set of corresponding proportions, or abundances, that represent the proportion ofeach endmember in these pixels. In this study, a spectral unmixing technique is proposed to handle the challenging scenario of non-linear mixtures. This algorithm relies on a dedicated implementation of multiple-kernel learning using self-organising mapproposed as a solver for the non-linear unmixing problem. Based on a priori knowledge of the endmember spectra, it aims atestimating their relative abundances without specifying the non-linear model under consideration. It is compared to state-of-the-art algorithms using synthetic yet realistic and real hyperspectral images. Results obtained from experiments conducted onsynthetic and real hyperspectral images assess the potential and the effectiveness of this unmixing strategy. Finally, therelevance and potential parallel implementation of the proposed method is demonstrated.