Feature representation is a key step for the classification of histopathological images. The principal component analysis network (PCANet) offers a new unsupervised feature learning algorithm for images via a simple deep network architecture. However, PCA is sensitive to noise and outliers, which may depress the representation learning of PCANet. Grassmann averages (GA) is a newly proposed dimensionality reduction algorithm, which is more robust and effective than PCA. Therefore, in this paper, we propose a GA network (GANet) algorithm to improve the robustness of learned features from images. Moreover, since quaternion algebra provides a mathematically elegant tool to well handle color images, a quaternion representation based GANet (QGANet) is developed to fuse color information and learn a superior representation for color histopathological images. The experimental results on two histopathological image datasets show that GANet outperforms PCANet, while QGANet achieves the best performance for the classification of color histopathological images.
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