Related papers: Approximate Guarantees for Dictionary Learning
In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$…
Dictionary learning is a popular approach for inferring a hidden basis or dictionary in which data has a sparse representation. Data generated from the dictionary A (an n by m matrix, with m > n in the over-complete setting) is given by Y =…
We present theoretical guarantees for an alternating minimization algorithm for the dictionary learning/sparse coding problem. The dictionary learning problem is to factorize vector samples $y^{1},y^{2},\ldots, y^{n}$ into an appropriate…
A dictionary is a database of standard vectors, so that other vectors / signals are expressed as linear combinations of dictionary vectors, and the task of learning a dictionary for a given data is to find a good dictionary so that the…
Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular…
In "dictionary learning" we observe $Y = AX + E$ for some $Y\in\mathbb{R}^{n\times p}$, $A \in\mathbb{R}^{m\times n}$, and $X\in\mathbb{R}^{m\times p}$. The matrix $Y$ is observed, and $A, X, E$ are unknown. Here $E$ is "noise" of small…
The efficient sparse coding and reconstruction of signal vectors via linear observations has received a tremendous amount of attention over the last decade. In this context, the automated learning of a suitable basis or overcomplete…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical…
In the synthesis model signals are represented as a sparse combinations of atoms from a dictionary. Dictionary learning describes the acquisition process of the underlying dictionary for a given set of training samples. While ideally this…
In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$. This is a central notion in signal processing, statistics and machine learning. But in…
We consider the problem of dictionary learning under the assumption that the observed signals can be represented as sparse linear combinations of the columns of a single large dictionary matrix. In particular, we analyze the minimax risk of…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via $\ell_1$-minimisation. The problem can also be seen as factorising a $\ddim \times \nsig$ matrix $Y=(y_1 >... y_\nsig),…
Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
It is well known that sparse approximation problem is \textsf{NP}-hard under general dictionaries. Several algorithms have been devised and analyzed in the past decade under various assumptions on the \emph{coherence} $\mu$ of the…
Given an overcomplete dictionary $A$ and a signal $b = Ac^*$ for some sparse vector $c^*$ whose nonzero entries correspond to linearly independent columns of $A$, classical sparse signal recovery theory considers the problem of whether…
We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear…
Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the…