arXiv research

Paper provides conditions for local recovery of tensor data's Kronecker-structured dictionaries.

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…

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…

Method selects interpretable circular coordinates from data.

Proposes a new method for time series classification and clustering.

Detects financial fraud schemes in networks using graph structure learning.

Study shows unique sharp local minimum in $\ell_1$-minimization for dictionary learning.

Isometry pursuit identifies orthonormal submatrices from wide matrices.

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…

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

The paper tackles automatic interpretation of manifold coordinates.

A distributed algorithm learns patterns in large images and signals.

A summary introduction of the Weil-Petersson metric space geometry is presented. Teichmueller space and its augmentation are described in terms of Fenchel-Nielsen coordinates. Formulas for the gradients and Hessians of geodesic-length functions are presented. Applications are considered. A description of the Weil-Peter…

The goal of the present paper is to propose an enhanced ordinary differential equations solver by exploitation of the powerful equivalence method of Élie Cartan. This solver returns a target equation equivalent to the equation to be solved and the transformation realizing the equivalence. The target ODE is a member of …

Paper studies SDL for better document and medical classification.

Robot learns to manipulate objects using multiple geometric representations.

DeepCAM learns convolutional dictionaries for image processing.

Bayesian method improves dictionary learning for complex problems.

Paper improves dictionary learning by addressing local and global coherence issues.

We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficient…

This work learns sparse tensor representations using mixtures of separable dictionaries.

NOODL solves dictionary and coefficient recovery for online learning.

DeepAM optimizes deep neural networks for image super-resolution.

We present a two-stage approach for learning dictionaries for object classification tasks based on the principle of information maximization. The proposed method seeks a dictionary that is compact, discriminative, and generative. In the first stage, dictionary atoms are selected from an initial dictionary by maximizing…

We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy. Our algorithms can decompose a 4-tensor with $n$-dimensional orthonormal components in the…

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…

CRsAE auto-encoder recovers convolutional dictionary from noisy signals.

Efficient algorithm selects atoms from dictionaries with complex sparsity constraints.

Paper proposes robust dictionary learning using concave losses.

We give a new approach to the dictionary learning (also known as "sparse coding") problem of recovering an unknown $n\times m$ matrix $A$ (for $m \geq n$) from examples of the form \[ y = Ax + e, \] where $x$ is a random vector in $\mathbb R^m$ with at most $τm$ nonzero coordinates, and $e$ is a random noise vector in …

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 signal class by iteratively computing an approximate factorization of a training …

A dictionary connects symplectic to contact geometry, with applications to complex and G-structures.

A parallel algorithm learns efficient Kronecker product dictionaries.

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

In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate …

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, robust and provably good dictionary learning algorithms. Algorithmic stability an…

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

The paper tackles dictionary learning with almost sure error constraints.

We study the Dictionary Learning (aka Sparse Coding) problem of obtaining a sparse representation of data points, by learning \emph{dictionary vectors} upon which the data points can be written as sparse linear combinations. We view this problem from a geometry perspective as the spanning set of a subspace arrangement,…

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

The paper proposes a method to learn discriminative multilevel dictionaries for supervised image classification.

New algorithm reduces dictionary learning complexity.

Unified analysis for robust PCA decomposition with sparse components in known dictionaries.

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 …

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 …

This article addresses the issue of representing electroencephalographic (EEG) signals in an efficient way. While classical approaches use a fixed Gabor dictionary to analyze EEG signals, this article proposes a data-driven method to obtain an adapted dictionary. To reach an efficient dictionary learning, appropriate s…

A new tree-based method for adaptive dictionary learning.

The kernel least-mean-square (KLMS) algorithm is an appealing tool for online identification of nonlinear systems due to its simplicity and robustness. In addition to choosing a reproducing kernel and setting filter parameters, designing a KLMS adaptive filter requires to select a so-called dictionary in order to get a…