On partial and generic uniqueness of block term tensor decompositions

TL;DR

This paper establishes conditions under which certain tensor decompositions are uniquely identifiable, using geometric methods to analyze the properties of joins of subspace varieties.

Contribution

It provides new geometric criteria for the generic and partial uniqueness of block term tensor decompositions with specific multilinear ranks.

Findings

Joins of relevant subspace varieties are not tangentially weakly defective.

Conditions are given for partial uniqueness based on non-defectiveness of joins.

The results advance understanding of tensor decomposition identifiability.

Abstract

We present several conditions for generic uniqueness of tensor decompositions of multilinear rank (1,L_{1}, L_{1}),..., (1, L_{R}, L_{R}) terms. In geometric language, we prove that the joins of relevant subspace varieties are not tangentially weakly defective. We also give conditions for partial uniqueness of block term tensor decompositions by proving that the joins of relevant subspace varieties are not defective.