Oblivious subspace embeddings for compressed Tucker decompositions

arXiv:2406.09387v1 Announce Type: new
Abstract: Emphasis in the tensor literature on random embeddings (tools for low-distortion dimension reduction) for the canonical polyadic (CP) tensor decomposition has left analogous results for the more expressive Tucker decomposition comparatively lacking. This work establishes general Johnson-Lindenstrauss (JL) type guarantees for the estimation of Tucker decompositions when an oblivious random embedding is applied along each mode. When these embeddings are drawn from a JL-optimal family, the decomposition can be estimated within $\varepsilon$ relative error under …

abstract arxiv canonical embeddings general johnson literature low random results stat.co stat.me stat.ml tensor tools tucker type work