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- W4387156661 abstract "We study the algebraic complexity of Euclidean distance minimization from a generic tensor to a variety of rank-one tensors. The Euclidean Distance (ED) degree of the Segre-Veronese variety counts the number of complex critical points of this optimization problem. We regard this invariant as a function of inner products and conjecture that it achieves its minimal value at Frobenius inner product. We prove our conjecture in the case of matrices. We discuss the above optimization problem for other algebraic varieties, classifying all possible values of the ED degree. Our approach combines tools from Singularity Theory, Morse Theory, and Algebraic Geometry." @default.
- W4387156661 created "2023-09-30" @default.
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- W4387156661 date "2023-09-26" @default.
- W4387156661 modified "2023-09-30" @default.
- W4387156661 title "On the minimal algebraic complexity of the rank-one approximation problem for general inner products" @default.
- W4387156661 doi "https://doi.org/10.48550/arxiv.2309.15105" @default.
- W4387156661 hasPublicationYear "2023" @default.
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