Subset selection in noise based on diversity measure minimization

By Bhaskar D. Rao, Kjersti Engan, Shane F. Cotter, Jason A. Palmer, Kenneth Kreutz-Delgado. IEEE Transactions on Signal Processing, 2003

342 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/d40c7f467b5e60a6363f70add2540f8a7cec6fa3

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Citations in the corpus

Connections with Robust PCA and the Role of Emergent Sparsity in Variational Autoencoder Models (2018, background): “Consequently, the ‖µz‖22 factor from (3) serves as the only relevant influence, pushing these values to be exactly zero even though `2 norms in most regularization contexts tend to favor diverse, non-sparse representations (Rao et al., 2003).”
Dictionary Learning Algorithms for Sparse Representation (2003, methodology): “The L-curve method works well, but it requires solving a one-dimensional optimization for each λ k , which becomes computationally expensive for large problems.”
A unified Bayesian framework for MEG/EEG source imaging (2009, positive): “While details and assumptions may differ γ-MAP, S-MAP, and VB can all be leveraged to obtain a point estimate of S expressed in the Tikhonov regularized form (Rao et al., 2003)”
Iterative Reweighted 1 and 2 Methods for Finding Sparse Solutions (2010, methodology): “Many recent sparse approximation algorithms rely on iterative reweighting schemes that produce more focal estimates as optimization progresses [3], [4], [5], [11], [17], [18].”
Sparse Signal Recovery With Temporally Correlated Source Vectors Using Sparse Bayesian Learning (2011, methodology): “This suggests the use of methods such as the modified L-curve procedure [55] or the cross-validation [37], [38] to choose λ specially in strongly noisy environments.”
A sparse signal reconstruction perspective for source localization with sensor arrays (2005, background): “An attempt to apply the L-curve to a subset selection problem in noise has been made in [36], but the authors have to make an assumption that the SNR is approximately known.”
Variational EM Algorithms for Non-Gaussian Latent Variable Models (2005, methodology): “This algorithm has also been derived in the image restoration literature [12] as the “halfquadratic” algorithm, and it is the basis for the FOCUSS algorithms derived in [26, 25].”
Sparse Methods for Direction-of-Arrival Estimation (2016, methodology): “A regularized FOCUSS algorithm for (27) was developed in [28] by using the same main idea as in FOCUSS.”
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images (2009, methodology): “A simple strategy to attack ( Q λ 1 ) is the iteratively reweighted least squares (IRLS) algorithm [97, 139, 138].”
Sparse regression using mixed norms (2009, methodology): “FOCUSS and the above generalization can be modiﬁed as in [23] to take the noise into account; however, this does not seem to be the most eﬃcient algorithm in this case, as we shall see in the next section, where an alternative approach is also proposed.”
Compressing Neural Networks using the Variational Information Bottleneck (2018, background): “this type of sparsity archetype instead prefers pushing some percentage to exactly zero while leaving others mostly unchanged (Rao et al., 2003).”
Hidden Talents of the Variational Autoencoder. (2017, background): “Consequently, the ‖μz‖(2)2 factor from (3) serves as the only relevant influence, pushing these values to be exactly zero even though `2 norms in most regularization contexts tend to favor diverse, non-sparse representations [34].”
Sparse Bayesian learning for basis selection (2004, methodology): “where we have assumed a Gaussian likelihood model, and represents a trade-off parameter balancing sparsity with quality of fit [1], [20].”
An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem (2007, methodology): “Third, we weigh in the M-FOCUSS algorithm derived in [7], [40] based on the generalized FOCUSS algorithm of [41].”
Sparse solutions to linear inverse problems with multiple measurement vectors (2005, methodology): “Fortunately, the modified -curve method described in [28] and [29] as a method of choosing the regularization parameter also performs well in this context.”
$rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation (2006, methodology): “The focal underdetermined system solver (FOCUSS) is very similar, using the -norm with as a replacement for the -norm [18]–[21].”