179 citations · 420 across the 27 of their papers we have counts for
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stat.ML2012
Approximate Rank-Detecting Factorization of Low-Rank Tensors
Franz J. Király, Andreas Ziehe
We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for t…
cs.LG2012
The Algebraic Combinatorial Approach for Low-Rank Matrix Completion
Franz J. Király, Louis Theran, Ryota Tomioka
We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theor…
cs.LG2012★ 33 cited
A Combinatorial Algebraic Approach for the Identifiability of Low-Rank Matrix Completion
Franz Kiraly, Ryota Tomioka
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary…