Subspace Quantization on the Grassmannian

摘要

We extend the K-means and LBG algorithms to the framework of the Grassmann manifold to perform subspace quantization. For K-means it is possible to move a subspace in the direction of another using Grassmannian geodesics. For LBG the centroid computation is now done using a flag mean algorithm for averaging points on the Grassmannian. The resulting unsupervised algorithms are applied to the MNIST digit data set and the AVIRIS Indian Pines hyperspectral data set.