  In this paper, we introduce a new algorithm based on archetypal analysis for
blind hyperspectral unmixing, assuming linear mixing of endmembers. Archetypal
analysis is a natural formulation for this task. This method does not require
the presence of pure pixels (i.e., pixels containing a single material) but
instead represents endmembers as convex combinations of a few pixels present in
the original hyperspectral image. Our approach leverages an entropic gradient
descent strategy, which (i) provides better solutions for hyperspectral
unmixing than traditional archetypal analysis algorithms, and (ii) leads to
efficient GPU implementations. Since running a single instance of our algorithm
is fast, we also propose an ensembling mechanism along with an appropriate
model selection procedure that make our method robust to hyper-parameter
choices while keeping the computational complexity reasonable. By using six
standard real datasets, we show that our approach outperforms state-of-the-art
matrix factorization and recent deep learning methods. We also provide an
open-source PyTorch implementation: https://github.com/inria-thoth/EDAA.
