Abstract
In this paper we study the identifiability of the Paralind model with sparse interaction matrices (i.e. S-Paralind). We provide some theoretical results on how to obtain the sparsest interaction matrices in some particular configurations and when these matrices are unique. These results could be use for the design and analysis of \(\ell _0\)-based decomposition algorithms.
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Notes
- 1.
PARAllel profiles with LINear Dependencies.
- 2.
CONstrained FACtor decomposition.
- 3.
The Kruskal-rank of a matrix \(\mathbf {A}\) (denoted \(k_\mathbf {A}\)) is the maximum number \(\ell \) such that every \(\ell \) columns of \(\mathbf {A}\) are linearly independent.
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Miron, S., Brie, D. (2015). Some Rank Conditions for the Identifiability of the Sparse Paralind Model. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2015. Lecture Notes in Computer Science(), vol 9237. Springer, Cham. https://doi.org/10.1007/978-3-319-22482-4_5
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