Publication

Deliverable 3.1: Report on Learning Structured Sparse Models

2011
Reports

Abstract

The aim of this work package (WP) is to explore approaches to learn structured sparse models, that is sparse models where the sparsity assumption seems not to be sufficient, or when there is hope to exploit some additional knowledge together with the sparsity hypothesis. The concept of structured sparsity can denote in fact various types of structure, which are strongly different in nature, yet related and interacting.

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2011
Reports

Abstract

Official source

Related concepts (18)

Sparse approximation

Sparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding these solutions and exploiting them in applications have found wide use in , signal processing, machine learning, medical imaging, and more. Consider a linear system of equations , where is an underdetermined matrix and . The matrix (typically assumed to be full-rank) is referred to as the dictionary, and is a signal of interest.

Sparse dictionary learning

Sparse dictionary learning (also known as sparse coding or SDL) is a representation learning method which aims at finding a sparse representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves. These elements are called atoms and they compose a dictionary. Atoms in the dictionary are not required to be orthogonal, and they may be an over-complete spanning set. This problem setup also allows the dimensionality of the signals being represented to be higher than the one of the signals being observed.

Sparse matrix

In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.

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Deliverable 3.1: Report on Learning Structured Sparse Models

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