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I've been working with high-dimensional binary tensors (e.g., tensors with entries that are only 0s and 1s) and I'm looking for an efficient way to decompose them into rank-1 components. The tensors I'm dealing with are also quite sparse, meaning they have a lot of zeros.

I came across traditional methods like CANDECOMP/PARAFAC (CP), Tucker, and HOSVD decompositions, but they seem to be quite computationally expensive, especially for large and sparse tensors.

Has anyone here worked on or come across an algorithm specifically designed for binary and sparse tensors? How do these methods compare in terms of computational efficiency with the traditional ones? Any insights or suggestions for efficient decomposition techniques would be greatly appreciated!

Thanks!

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  • $\begingroup$ Do you need/want the rank-1 components to be sparse too, or can they be arbitrary? $\endgroup$ Commented Jul 23, 2024 at 20:23
  • $\begingroup$ I need the rank-1 components to be sparse too $\endgroup$ Commented Aug 13, 2024 at 4:06
  • $\begingroup$ Please edit your post to state all requirements, including this one. Please don't just put additional information in the comments -- instead, revise the question so it contains all necessary information and reads well for someone who experiences it for the first time. Part of our purpose is to build an archive of knowledge, so we want questions to be self-contained and tidy so they will be useful for others. Thank you! $\endgroup$ Commented Aug 13, 2024 at 6:12
  • $\begingroup$ If you can provide any information about typical parameter settings (e.g., number of rank-1 components, dimensions of the tensors, number of non-zero entries in each component and the overall tensor), that might help others to provide more useful answers. $\endgroup$ Commented Aug 13, 2024 at 6:13

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