Abstract
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.
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Stiverson, S., Kirby, M., Peterson, C. (2020). Subspace Quantization on the Grassmannian. In: Vellido, A., Gibert, K., Angulo, C., MartÃn Guerrero, J. (eds) Advances in Self-Organizing Maps, Learning Vector Quantization, Clustering and Data Visualization. WSOM 2019. Advances in Intelligent Systems and Computing, vol 976. Springer, Cham. https://doi.org/10.1007/978-3-030-19642-4_25
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DOI: https://doi.org/10.1007/978-3-030-19642-4_25
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