Learning dictionaries/atomic sets that induce structured representation on data. Applications are still explosively emerging, especially of deep learning, where one allows multi-level nonlinear cascading of representation. Hence formulations to the problems are fairly diverse. We will roughly organize the references according to the problem they try to solve, concentrated on recent literature of theoretical nature. (Update: Jan 07 2018)

[S] indicates my contribution.

Theory

$\mathbf{Y} = \mathbf{A} \mathbf{X}$, $\mathbf{A}$ Square, Invertible, Global Recovery

This problem can be reduced to a sequence of problems, each taking the form of finding sparsest vector in a linear subspace. See also Structured Element Pursuit.

$\mathbf{Y} = \mathbf{A} \mathbf{X}$, $\mathbf{A}$ Overcomplete, Incoherent, Global Recovery

$\mathbf{Y} = \mathbf{A} \mathbf{X}$ Local Correctness

Single-Kernel Convolutional (aka Blind Deconvolution): $\mathbf{y} = \mathbf{a} \otimes \mathbf{x}$

Multi-Kernel Convolutional: $\mathbf{Y} = \sum_i \mathbf{a}_i \otimes \mathbf{x}_i$

Wavelet/General Scattering Network

Provable Learning of Deep Structure

Algorithms and Applications

Dictionary Learning

Convolutional Dictionary Learning

Deep Learning

Disclaimer - This page is meant to serve a hub for references on this problem, and does not represent in any way personal endorsement of papers listed here. So I do not hold any responsibility for quality and technical correctness of each paper listed here. The reader is advised to use this resource with discretion.

If you’d like your paper to be listed here - Just drop me a few lines via email (which can be found on “Welcome” page). If you don’t bother to spend a word, just deposit your paper on arXiv. I get email alert about new animals there every morning,  and will be happy to hunt one for this zoo if it seems fit.