Tensor Decompositions
CP, Tucker, tensor-train and hierarchical tensor formats for high-dimensional data.
Tensor Decompositions. CP, Tucker, tensor-train and hierarchical tensor formats for high-dimensional data.
Foundations and canonical references
The standard treatments of tensor decompositions approach the subject from complementary angles. Landsberg, Tensors: Geometry and Applications (2012) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Recent technical contributions
A handful of recent papers carry the methodological frontier of tensor decompositions forward. Tensor Decompositions and Applications (Kolda et al., 2009) is a primary reference for this area and develops new techniques or results that downstream work builds on.
Open methodological questions for tensor decompositions include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
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- textbook · primary · 2012Tensors: Geometry and Applicationslandsberg-2012
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