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Learning overcomplete, low coherence dictionaries with linear inference [article]

Jesse A. Livezey and Alejandro F. Bujan and Friedrich T. Sommer
2018 arXiv   pre-print
Specifically, the coherence control in existing ICA algorithms, necessary to prevent the formation of duplicate dictionary features, is ill-suited in the overcomplete case.  ...  All told, this study contributes new insights into and methods for coherence control for linear ICA, some of which are applicable to many other, potentially nonlinear, unsupervised learning methods.  ...  Here, we investigated potential and limitations of linear inference methods in overcomplete dictionary learning.  ... 
arXiv:1606.03474v4 fatcat:uw2wqyuhpne5nii2nmrzarfd6i

Simultaneous Sensing Matrix and Sparsifying Dictionary Optimization for Block-sparse Compressive Sensing

Shuang Li, Qiuwei Li, Gang Li, Xiongxiong He, Liping Chang
2013 2013 IEEE 10th International Conference on Mobile Ad-Hoc and Sensor Systems  
Index Terms-Compressive sensing, projection matrix optimization, overcomplete dictionary learning, block-sparsity, CBKSVD.  ...  Simulation results show that our novel method can significantly improve the dictionary recovery ability and lower the representation error compared with other dictionary learning methods in block-sparse  ...  In previous work, the sensing matrix in a block-sparse CS system is usually optimized with a given dictionary and the overcomplete dictionary is learned separately [6] .  ... 
doi:10.1109/mass.2013.98 dblp:conf/mass/LiLLHC13 fatcat:y57sjwx3mree7dgn3mxowldl3m

Covariance-domain Dictionary Learning for Overcomplete EEG Source Identification [article]

Ozgur Balkan, Kenneth Kreutz-Delgado, Scott Makeig
2015 arXiv   pre-print
Our overcomplete source identification algorithm, Cov-DL, leverages dictionary learning methods applied in the covariance-domain.  ...  This is contrary to straight-forward dictionary learning methods that are based on the assumption of sparsity, which is not a satisfied condition in the case of low-density EEG systems.  ...  D with dictionary learning Infer columns of A from columns of D, in a one-toone manner Learn N-dimensional subspace R(U) that "vectorized outer products" live in.  ... 
arXiv:1512.00156v1 fatcat:h5n4nvdd6fgqddawaczvu7bumu

Inference via Sparse Coding in a Hierarchical Vision Model [article]

Joshua Bowren, Luis Sanchez-Giraldo, Odelia Schwartz
2022 arXiv   pre-print
Higher degrees of sparsity allowed for inference over larger deleted image regions. The mechanism that allows for this inference capability in sparse coding is described here.  ...  The contributions of the models were assessed with image classification tasks, specifically tasks associated with mid-level vision including figure-ground classification, texture classification, and angle  ...  Acknowledgments We thank Hauro Hosoya for publicly providing his hierarchical overcomplete ICA model code (Hosoya and Hyvärinen, 2015) .  ... 
arXiv:2108.01548v3 fatcat:so47koxdvndxnakfng25n6zrgm

Dictionary Learning

Ivana Tosic, Pascal Frossard
2011 IEEE Signal Processing Magazine  
We describe methods for learning dictionaries that are appropriate for the representation of given classes of signals and multisensor data.  ...  The benefits of dictionary learning clearly show that a proper understanding of causes underlying the sensed world is key to task-specific representation of relevant information in high-dimensional data  ...  The probabilistic inference approach in overcomplete dictionary learning has subsequently been adopted by other researchers.  ... 
doi:10.1109/msp.2010.939537 fatcat:yvxjzm5margvncs73m2jjjyfhy

Exploiting Restricted Boltzmann Machines and Deep Belief Networks in Compressed Sensing

Luisa F. Polania, Kenneth E. Barner
2017 IEEE Transactions on Signal Processing  
The parameters of the prior distribution are learned from training data.  ...  The motivation behind this approach is to model the higher-order statistical dependencies between the coefficients of the sparse representation, with the final goal of improving the reconstruction.  ...  In the case of overcomplete dictionaries, a training stage is employed with dual purpose. First, it learns an overcomplete dictionary to sparsely represent the signal of interest.  ... 
doi:10.1109/tsp.2017.2712128 fatcat:42blog4fzresfj7zmtyvubf5nq

The Sparse Manifold Transform [article]

Yubei Chen, Dylan M. Paiton, Bruno A. Olshausen
2018 arXiv   pre-print
It turns non-linear transformations in the primary sensory signal space into linear interpolations in a representational embedding space while maintaining approximate invertibility.  ...  The sparse manifold transform is an unsupervised and generative framework that explicitly and simultaneously models the sparse discreteness and low-dimensional manifold structure found in natural scenes  ...  High overcompleteness with a positive-only constraint makes the relative geometry of the dictionary elements more explicit.  ... 
arXiv:1806.08887v2 fatcat:zmurlcmff5f7pokdnpochlhlaq

An Improved Method of Training Overcomplete Dictionary Pair

Zhuozheng Wang, John R. Deller, Kebin Jia, Wenli Zhang
2014 Mathematical Problems in Engineering  
Training overcomplete dictionary pair is a critical step of the mainstream superresolution methods.  ...  For the high time complexity and susceptible to corruption characteristics of training dictionary, an improved method based on lifting wavelet transform and robust principal component analysis is reported  ...  In contrast, learning-based methods construct optimally weighted constraints inferred from training overcomplete dictionary pair.  ... 
doi:10.1155/2014/386835 fatcat:wvwvr7hlpbgzvmznkb7othfkeq

Dataless Model Selection with the Deep Frame Potential [article]

Calvin Murdock, Simon Lucey
2020 arXiv   pre-print
Building upon theoretical connections between deep learning and sparse approximation, we propose the deep frame potential: a measure of coherence that is approximately related to representation stability  ...  We validate its use as a criterion for model selection and demonstrate correlation with generalization error on a variety of common residual and densely connected network architectures.  ...  This suggests that architectures' capacities for low validation error can be quantified and compared based on their capacities for inducing dictionaries with low minimum mutual coherence.  ... 
arXiv:2003.13866v1 fatcat:ctvt43qmzrdohk6uti7qm4uscq

Dataless Model Selection With the Deep Frame Potential

Calvin Murdock, Simon Lucey
2020 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
Building upon theoretical connections between deep learning and sparse approximation, we propose the deep frame potential: a measure of coherence that is approximately related to representation stability  ...  We validate its use as a criterion for model selection and demonstrate correlation with generalization error on a variety of common residual and densely connected network architectures.  ...  This suggests that architectures' capacities for low validation error can be quantified and compared based on their capacities for inducing dictionaries with low minimum mutual coherence.  ... 
doi:10.1109/cvpr42600.2020.01127 dblp:conf/cvpr/MurdockL20 fatcat:dnxvxnm6dvbvlp3xgjp75v3mda

Learning block-structured incoherent dictionaries for sparse representation

YongQin Zhang, JinSheng Xiao, ShuHong Li, CaiYun Shi, GuoXi Xie
2015 Science China Information Sciences  
of the overcomplete dictionary.  ...  Keywords dictionary learning, sparse representation, sparse coding, block sparsity, mutual coherence Citation Zhang Y Q, Xiao J S, Li S H, et al.  ...  Therefore, the dictionary learning methods based on the block structure incurs incorrect results at the low SNR values.  ... 
doi:10.1007/s11432-014-5258-6 fatcat:ya6j3v6enjakveej5bbh44wljy

Tensor Least Angle Regression for Sparse Representations of Multidimensional Signals

Ishan Wickramasingha, Ahmed Elrewainy, Michael Sobhy, Sherif S. Sherif
2020 Neural Computation  
separable overcomplete dictionaries, by solving both [Formula: see text] and [Formula: see text] constrained sparse least-squares problems.  ...  However, its memory usage and computation time increase quickly with the number of problem dimensions and iterations.  ...  in dictionaries with higher coherence.  ... 
doi:10.1162/neco_a_01304 pmid:32687768 fatcat:3waxqaoghnafjlydao6zqlbjom

Unsupervised Analysis of Polyphonic Music by Sparse Coding

S.A. Abdallah, M.D. Plumbley
2006 IEEE Transactions on Neural Networks  
Index Terms Learning overcomplete dictionaries, polyphonic music, probabilistic modeling, redundancy reduction, sparse factorial coding, unsupervised learning.  ...  Index Terms-Learning overcomplete dictionaries, polyphonic music, probabilistic modeling, redundancy reduction, sparse factorial coding, unsupervised learning.  ...  Inference Given the latent variable model defined by (1) , (2) , and (3) , the two tasks to be addressed are to infer the optimal encoding of a given vector using a given dictionary , and to learn a  ... 
doi:10.1109/tnn.2005.861031 pmid:16526486 fatcat:7dqv4brfvvbdbg4kgmqudnknce

Discriminative Dictionary Learning based on Statistical Methods [article]

G.Madhuri, Atul Negi
2021 arXiv   pre-print
Training dictionaries such that they represent each class of signals with minimal loss is called Dictionary Learning (DL).  ...  Keywords: Statistical modeling, Dictionary Learning, Discriminative Dictionary, Sparse representation, Gaussian prior, Cauchy prior, Entropy, Hidden Markov model, Hybrid Dictionary Learning  ...  Conclusion The transformation of dictionary learning from orthogonal transforms to overcomplete analytic transforms to overcomplete synthesis dictionaries is followed by parametric dictionary learning.  ... 
arXiv:2111.09027v1 fatcat:zzdz2m3rvfauxjw4eu2mgpk5mu

Editorial

Farokh Marvasti, Ali Mohammad-Djafari, Jonathon Chambers
2012 EURASIP Journal on Advances in Signal Processing  
They use an overcomplete dictionary representation of the spatial covariance matrix model.  ...  They address a difficult nonlinear problem by employing linearization and an over-complete dictionary.  ... 
doi:10.1186/1687-6180-2012-90 fatcat:odv3jhtw35aopips5muxgblkja
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