Abstract
We study the problem of finding a subspace representative of multiple datasets by minimizing the maximal dissimilarity between this subspace and all the subspaces generated by those datasets. After arguing for the choice of the dissimilarity function, we derive some properties of the corresponding formulation. We propose an adaptation of an algorithm used for a similar problem on Riemannian manifolds. Experiments on synthetic data show that the subspace recovered by our algorithm is closer to the true common subspace than the solution obtained using an SVD.
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Part of this work was performed while the second author was a visiting professor at Université catholique de Louvain.
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Renard, E., Gallivan, K.A., Absil, PA. (2018). A Grassmannian Minimum Enclosing Ball Approach for Common Subspace Extraction. In: Deville, Y., Gannot, S., Mason, R., Plumbley, M., Ward, D. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2018. Lecture Notes in Computer Science(), vol 10891. Springer, Cham. https://doi.org/10.1007/978-3-319-93764-9_7
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DOI: https://doi.org/10.1007/978-3-319-93764-9_7
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