Related papers: An Incidence Geometry approach to Dictionary Learn…
Given a hypergraph $H$ with $m$ hyperedges and a set $Q$ of $m$ \emph{pinning subspaces}, i.e.\ globally fixed subspaces in Euclidean space $\mathbb{R}^d$, a \emph{pinned subspace-incidence system} is the pair $(H, Q)$, with the constraint…
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…
This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing…
Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of…
In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies,…
The dictionary learning problem concerns the task of representing data as sparse linear sums drawn from a smaller collection of basic building blocks. In application domains where such techniques are deployed, we frequently encounter…
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…
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…
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…
Given a hypergraph $H$ with $m$ hyperedges and a set $X$ of $m$ \emph{pins}, i.e.\ globally fixed subspaces in Euclidean space $\mathbb{R}^d$, a \emph{pinned subspace-incidence system} is the pair $(H, X)$, with the constraint that each pin…
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…
Neural network-based language models deal with data sparsity problems by mapping the large discrete space of words into a smaller continuous space of real-valued vectors. By learning distributed vector representations for words, each…
Learning dictionaries suitable for sparse coding instead of using engineered bases has proven effective in a variety of image processing tasks. This paper studies the optimization of dictionaries on image data where the representation is…
Sparse representation-based classifiers have shown outstanding accuracy and robustness in image classification tasks even with the presence of intense noise and occlusion. However, it has been discovered that the performance degrades…
Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As…
In this paper, it is proved that dictionary learning and sparse representation is invariant to a linear transformation. It subsumes the special case of transforming/projecting the data into a discriminative space. This is important because…
Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of…
In sparse recovery, the unique sparsest solution to an under-determined system of linear equations is of main interest. This scheme is commonly proposed to be applied to signal acquisition. In most cases, the signals are not sparse…
Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points…
In this work, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions). Unlike the traditional DL and SC framework, our new…