# Dictionary-based Tensor Canonical Polyadic Decomposition

arXiv: https://arxiv.org/abs/1704.00541 · HTML: https://mlsanity.com/paper/1704.00541/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2017.

## Built on by (most cited first, 4 of 4)

- [Multi-Dictionary Tensor Decomposition](https://mlsanity.com/paper/2309.09717/) (2023)
- [Tensor Decomposition with Unaligned Observations](https://mlsanity.com/paper/2410.14046/) (2024)
- [Multi-Channel Automatic Music Transcription Using Tensor Algebra](https://mlsanity.com/paper/2107.11250/) (2021)
- [Dictionary-based Low-Rank Approximations and the Mixed Sparse Coding problem](https://mlsanity.com/paper/2111.12399/) (2021)

## Abstract (arXiv)

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.