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This paper introduces sparse coding and dictionary learning for Symmetric Positive Definite (SPD) matrices, which are often used in machine learning, computer vision and related areas. Unlike traditional sparse coding schemes that work in…
Many applications like audio and image processing show that sparse representations are a powerful and efficient signal modeling technique. Finding an optimal dictionary that generates at the same time the sparsest representations of data…
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…
Sparse representations using learned dictionaries are being increasingly used with success in several data processing and machine learning applications. The availability of abundant training data necessitates the development of efficient,…
We propose an sparse Bayesian learning (SBL)-based method that leverages group sparsity and multiple parameterized dictionaries to detect the relevant dictionary entries and estimate their continuous parameters by combining data from…
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 paper studies distributed Dictionary Learning (DL) problems where the learning task is distributed over a multi-agent network with time-varying (nonsymmetric) connectivity. This formulation is relevant, for instance, in big-data…
Data encoded as symmetric positive definite (SPD) matrices frequently arise in many areas of computer vision and machine learning. While these matrices form an open subset of the Euclidean space of symmetric matrices, viewing them through…
Dictionary learning methods continue to gain popularity for the solution of challenging inverse problems. In the dictionary learning approach, the computational forward model is replaced by a large dictionary of possible outcomes, and the…
Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…
Dictionary learning and sparse coding have been widely studied as mechanisms for unsupervised feature learning. Unsupervised learning could bring enormous benefit to the processing of hyperspectral images and to other remote sensing data…
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…
As AI models achieve remarkable capabilities across diverse domains, understanding what representations they learn and how they encode concepts has become increasingly important for both scientific progress and trustworthy deployment.…
Dictionary learning algorithms have been successfully used in both reconstructive and discriminative tasks, where the input signal is represented by a linear combination of a few dictionary atoms. While these methods are usually developed…
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…
Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major…
Sparse representation, which uses dictionary atoms to reconstruct input vectors, has been studied intensively in recent years. A proper dictionary is a key for the success of sparse representation. In this paper, an active dictionary…
In this paper, we propose supervised dictionary learning (SDL) by incorporating information on class labels into the learning of the dictionary. To this end, we propose to learn the dictionary in a space where the dependency between the…
Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can…
While deep learning (DL)-based methods have achieved remarkable success in continuous wireless resource allocation, efficient solutions for problems involving discrete variables remain challenging. This is primarily due to the zero-gradient…