arXiv research

Researchers find optimal dictionaries for minimizing average squared coefficients in random vector representations.

Dictionaries are collections of vectors used for representations of random vectors in Euclidean spaces. Recent research on optimal dictionaries is focused on constructing dictionaries that offer sparse representations, i.e., $\ell_0$-optimal representations. Here we consider the problem of finding optimal dictionaries …

DeepAM optimizes deep neural networks for image super-resolution.

NOODL solves dictionary and coefficient recovery for online learning.

Proposes a new method for time series classification and clustering.

New method learns histograms using optimal transport barycenters.

Paper learns dictionaries for sparse signal recovery using automatic differentiation.

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 in this paper utilize dictionaries instead of a canonical basis used in the coord…

Paper proposes a novel R-JDRDL method for SPD manifolds.

Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a suitable training set. While analytic dictionaries permit to capture the global st…

Two algorithms converge to dictionary learning with geometric rate for non-uniform data.

We consider the problem of distributed dictionary learning, where a set of nodes is required to collectively learn a common dictionary from noisy measurements. This approach may be useful in several contexts including sensor networks. Diffusion cooperation schemes have been proposed to solve the distributed linear regr…

CRsAE auto-encoder recovers convolutional dictionary from noisy signals.

The paper provides guarantees for an alternating minimization algorithm in dictionary learning.

Subgradient descent learns orthogonal dictionaries efficiently.

STARK learns structured dictionaries for tensor data.

We develop methods to learn dictionaries invariant under group symmetries, useful in cryo-EM and tracking.

Dictionary learning is a cutting-edge area in imaging processing, that has recently led to state-of-the-art results in many signal processing tasks. The idea is to conduct a linear decomposition of a signal using a few atoms of a learned and usually over-completed dictionary instead of a pre-defined basis. Determining …

Novel algorithm learns sparse signal representations over topological spaces.

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 the dictionary learning problem which governs the mean squared error (MSE) perf…

This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential (Riemannian) geometry can be appli…

Paper develops DLTF to learn optimized dictionaries for efficient thresholded feature recovery.

New method improves dictionary recovery from over-realized models.

Bayesian optimization for high-dimensional combinatorial spaces using embeddings.

Data sets are often modeled as point clouds in $R^D$, for $D$ large. It is often assumed that the data has some interesting low-dimensional structure, for example that of a $d$-dimensional manifold $M$, with $d$ much smaller than $D$. When $M$ is simply a linear subspace, one may exploit this assumption for encoding ef…

Learning optimal dictionaries for sparse coding has exposed characteristic sparse features of many natural signals. However, universal guarantees of the stability of such features in the presence of noise are lacking. Here, we provide very general conditions guaranteeing when dictionaries yielding the sparsest encoding…

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 under $\ell_1$ sparsity constrain (prior) in the input domain, recent studies hav…

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 data. In order to overcome this drawback, we propose an algorithm aimed at learn…

This work combines deep learning and sparse coding for CT image reconstruction.

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 would be achieved by optimizing the expectation of the factors over the underlyin…

This paper is a survey of dictionary screening for the lasso problem. The lasso problem seeks a sparse linear combination of the columns of a dictionary to best match a given target vector. This sparse representation has proven useful in a variety of subsequent processing and decision tasks. For a given target vector, …

The paper tackles energy disaggregation by improving dictionary learning with deep neural models.

The paper proposes efficient dictionary learning algorithms that avoid multiplications for sparse representations.

The paper tackles MSDA by learning dictionary atoms in Wasserstein space.

A-DLISTA and VLISTA learn dictionaries and sparse representations under varying sensing matrices.

Unified model combines neural networks and dictionary learning for clinical predictions from brain data.

A distributed algorithm learns patterns in large images and signals.

Probabilistic model for weakly supervised analysis dictionary learning.

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse representations, it is now well established that these models are well suited t…

PUDLE method analyzes and improves unrolled sparse coding networks for dictionary learning.

Graph-Dictionary model for sparse multivariate signal representation.

Dictionary learning algorithms have been successfully used for both reconstructive and discriminative tasks, where an input signal is represented with a sparse linear combination of dictionary atoms. While these methods are mostly developed for single-modality scenarios, recent studies have demonstrated the advantages …

A novel dictionary-based approach for predicting functions.

In this paper, we focus on online representation learning in non-stationary environments which may require continuous adaptation of model architecture. We propose a novel online dictionary-learning (sparse-coding) framework which incorporates the addition and deletion of hidden units (dictionary elements), and is inspi…

We present a sparse estimation and dictionary learning framework for compressed fiber sensing based on a probabilistic hierarchical sparse model. To handle severe dictionary coherence, selective shrinkage is achieved using a Weibull prior, which can be related to non-convex optimization with $p$-norm constraints for $0…

New method learns complete orthogonal dictionary from samples with theoretical guarantees and efficiency.

We present a theoretical analysis and empirical evaluations of a novel set of techniques for computational cost reduction of classifiers that are based on learned transform and soft-threshold. By modifying optimization procedures for dictionary and classifier training, as well as the resulting dictionary entries, our t…

DeepCAM learns convolutional dictionaries for image processing.