Related papers: Dictionary Learning Using Rank-One Atomic Decompos…

In this paper, we propose an analysis mechanism based structured Analysis Discriminative Dictionary Learning (ADDL) framework. ADDL seamlessly integrates the analysis discriminative dictionary learning, analysis representation and analysis…

The aim of this paper is to introduce a novel dictionary learning algorithm for sparse representation of signals defined over combinatorial topological spaces, specifically, regular cell complexes. Leveraging Hodge theory, we embed topology…

This letter proposes a multiple parametric dictionary learning algorithm for direction of arrival (DOA) estimation in presence of array gain-phase error and mutual coupling. It jointly solves both the DOA estimation and array imperfection…

Dictionary learning is a challenge topic in many image processing areas. The basic goal is to learn a sparse representation from an overcomplete basis set. Due to combining the advantages of generic multiscale representations with learning…

Alignment of large language models remains a central challenge in natural language processing. Preference optimization has emerged as a popular and effective method for improving alignment, typically through training-time or prompt-based…

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…

This paper focuses on the noiseless complete dictionary learning problem, where the goal is to represent a set of given signals as linear combinations of a small number of atoms from a learned dictionary. There are two main challenges faced…

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…

For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to…

Dictionary learning is a versatile method to produce an overcomplete set of vectors, called atoms, to represent a given input with only a few atoms. In the literature, it has been used primarily for tasks that explore its powerful…

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…

Dictionary Learning (DL) is one of the leading sparsity promoting techniques in the context of image classification, where the "dictionary" matrix D of images and the sparse matrix X are determined so as to represent a redundant image…

The problem of convex optimization is studied. Usually in convex optimization the minimization is over a d-dimensional domain. Very often the convergence rate of an optimization algorithm depends on the dimension d. The algorithms studied…

Sparse document representations have been widely used to retrieve relevant documents via exact lexical matching. Owing to the pre-computed inverted index, it supports fast ad-hoc search but incurs the vocabulary mismatch problem. Although…

Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…

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…

Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…

Sparse signal representations based on linear combinations of learned atoms have been used to obtain state-of-the-art results in several practical signal processing applications. Approximation methods are needed to process high-dimensional…

In this paper, we propose a supervised dictionary learning algorithm that aims to preserve the local geometry in both dimensions of the data. A graph-based regularization explicitly takes into account the local manifold structure of the…

Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…