Dictionary-based Tensor Canonical Polyadic Decomposition
This work addresses interpretability in tensor decomposition for applications like hyperspectral imaging, but it appears incremental as it builds on existing decomposition methods by incorporating a dictionary constraint.
The paper tackled the problem of ensuring interpretability in tensor decomposition by introducing a dictionary-based canonical polyadic decomposition that enforces one factor to belong to a known dictionary, and it evaluated performance on simulated data and hyperspectral image unmixing.
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.