Highly Scalable Parallel Algorithms for Sparse Matrix Factorization
IEEE Transactions on Parallel and Distributed Systems
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Sparse representations are most likely to be the sparsest possible
EURASIP Journal on Applied Signal Processing
Robust Face Recognition via Sparse Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sparse and Redundant Modeling of Image Content Using an Image-Signature-Dictionary
SIAM Journal on Imaging Sciences
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Blind separation of speech mixtures via time-frequency masking
IEEE Transactions on Signal Processing
An affine scaling methodology for best basis selection
IEEE Transactions on Signal Processing
A Frame Construction and a Universal Distortion Bound for Sparse Representations
IEEE Transactions on Signal Processing
Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors
IEEE Transactions on Signal Processing - Part I
Convolutive Blind Source Separation in the Frequency Domain Based on Sparse Representation
IEEE Transactions on Audio, Speech, and Language Processing
Sparse representations in unions of bases
IEEE Transactions on Information Theory
Recovery of exact sparse representations in the presence of bounded noise
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
Stable Recovery of Sparse Signals Via Regularized Minimization
IEEE Transactions on Information Theory
On the Uniqueness of Nonnegative Sparse Solutions to Underdetermined Systems of Equations
IEEE Transactions on Information Theory
Fast Solution of -Norm Minimization Problems When the Solution May Be Sparse
IEEE Transactions on Information Theory
Sparse Representation for Color Image Restoration
IEEE Transactions on Image Processing
Fast Sparse Approximation for Least Squares Support Vector Machine
IEEE Transactions on Neural Networks
Neural associative memories and sparse coding
Neural Networks
A new index based on sparsity measures for comparing fuzzy partitions
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Sparse activity and sparse connectivity in supervised learning
The Journal of Machine Learning Research
Modulation domain blind speech separation in noisy environments
Speech Communication
Towards high-dimensional data analysis in air quality research
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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Sparsity of representations of signals has been shown to be a key concept of fundamental importance in fields such as blind source separation, compression, sampling and signal analysis. The aim of this paper is to compare several commonly-used sparsity measures based on intuitive attributes. Intuitively, a sparse representation is one in which a small number of coefficients contain a large proportion of the energy. In this paper, six properties are discussed: (Robin Hood, Scaling, Rising Tide, Cloning, Bill Gates, and Babies), each of which a sparsity measure should have. The main contributions of this paper are the proofs and the associated summary table which classify commonly-used sparsity measures based on whether or not they satisfy these six propositions. Only two of these measures satisfy all six: the pq-mean with p ≤ 1, q 1 and the Gini Index.