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Hyperspectral unmixing remains one of the most challenging tasks in the analysis of such data. Deep learning has been blooming in the field and proved to outperform other classic unmixing techniques, and can be effectively deployed onboard Earth observation satellites equipped with hyperspectral imagers. In this letter, we follow this research pathway and propose a multi-branch convolutional neural network that benefits from fusing spectral, spatial, and spectral-spatial features in the unmixing process. The results of our experiments, backed up with the ablation study, revealed that our techniques outperform others from the literature and lead to higher-quality fractional abundance estimation. Also, we investigated the influence of reducing the training sets on the capabilities of all algorithms and their robustness against noise, as capturing large and representative ground-truth sets is time-consuming and costly in practice, especially in emerging Earth observation scenarios.