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Subspace Quantization on the Grassmannian

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Advances in Self-Organizing Maps, Learning Vector Quantization, Clustering and Data Visualization (WSOM 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 976))

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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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Author information

Authors and Affiliations

  1. Colorado State University, Fort Collins, CO, 80523, USA

    Shannon Stiverson, Michael Kirby & Chris Peterson

Authors
  1. Shannon Stiverson
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  2. Michael Kirby
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  3. Chris Peterson
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Corresponding author

Correspondence to Shannon Stiverson .

Editor information

Editors and Affiliations

  1. Department of Computer Science, UPC BarcelonaTech, Barcelona, Spain

    Alfredo Vellido

  2. Knowledge Engineering and Machine Learning Group (KEMLG) at Intelligent Data Science and Artificial Intelligence Research Center, UPC BarcelonaTech, Barcelona, Spain

    Karina Gibert

  3. Department of Automatic Control, UPC BarcelonaTech, Barcelona, Spain

    Cecilio Angulo

  4. Departament d'Enginyeria Electrònica, Universitat de València, Burjassot, Valencia, Spain

    José David Martín Guerrero

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Stiverson, S., Kirby, M., Peterson, C. (2020). Subspace Quantization on the Grassmannian. In: Vellido, A., Gibert, K., Angulo, C., Martín 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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