  Constrained tensor and matrix factorization models allow to extract
interpretable patterns from multiway data. Therefore identifiability properties
and efficient algorithms for constrained low-rank approximations are nowadays
important research topics. This work deals with columns of factor matrices of a
low-rank approximation being sparse in a known and possibly overcomplete basis,
a model coined as Dictionary-based Low-Rank Approximation (DLRA). While earlier
contributions focused on finding factor columns inside a dictionary of
candidate columns, i.e. one-sparse approximations, this work is the first to
tackle DLRA with sparsity larger than one. I propose to focus on the
sparse-coding subproblem coined Mixed Sparse-Coding (MSC) that emerges when
solving DLRA with an alternating optimization strategy. Several algorithms
based on sparse-coding heuristics (greedy methods, convex relaxations) are
provided to solve MSC. The performance of these heuristics is evaluated on
simulated data. Then, I show how to adapt an efficient MSC solver based on the
LASSO to compute Dictionary-based Matrix Factorization and Canonical Polyadic
Decomposition in the context of hyperspectral image processing and
chemometrics. These experiments suggest that DLRA extends the modeling
capabilities of low-rank approximations, helps reducing estimation variance and
enhances the identifiability and interpretability of estimated factors.
