Hyperspectral Image Unmixing Based on Fast Kernel Archetypal Analysis

Restricted by the associated factors to spatial resolution in remote sensing, mixed pixels and relative pure pixels may both exist in hyperspectral images. In this paper, Kernel Archetypal Analysis (KAA) is investigated for flexible endmember extraction which implicitly takes the intraclass variability into account in relative pure pixel mapping and mixed pixel unmixing. As kernel matrix in KAA brings high computational cost, fast KAA (FKAA) is proposed in this study to relieve KAA's memory issue and reduce KAA's processing time using the Nyström method. Nyström method is used to realize low-rank approximation of the high-dimensional kernel matrix in KAA by using a small portion of informative samples obtained by K-means. Experiments were conducted on both synthetic and real hyperspectral images. The results show that both KAA and FKAA can generate representative endmembers from the mixed data. With proper parameter setting, they can address the intraclass endmember variability in endmember extraction and achieve more realistic unmixing results than conventional geometric methods. In particular, FKAA is able to speed up KAA without significant reduction in unmixing accuracy.