TY - GEN
T1 - Sparse null space basis pursuit and analysis dictionary learning for high-dimensional data analysis
AU - Bian, Xiao
AU - Krim, Hamid
AU - Bronstein, Alex
AU - Dai, Liyi
N1 - Publisher Copyright: © 2015 IEEE.
PY - 2015/8/4
Y1 - 2015/8/4
N2 - Sparse models in dictionary learning have been successfully applied in a wide variety of machine learning and computer vision problems, and have also recently been of increasing research interest. Another interesting related problem based on a linear equality constraint, namely the sparse null space problem (SNS), first appeared in 1986, and has since inspired results on sparse basis pursuit. In this paper, we investigate the relation between the SNS problem and the analysis dictionary learning problem, and show that the SNS problem plays a central role, and may be utilized to solve dictionary learning problems. Moreover, we propose an efficient algorithm of sparse null space basis pursuit, and extend it to a solution of analysis dictionary learning. Experimental results on numerical synthetic data and real-world data are further presented to validate the performance of our method.
AB - Sparse models in dictionary learning have been successfully applied in a wide variety of machine learning and computer vision problems, and have also recently been of increasing research interest. Another interesting related problem based on a linear equality constraint, namely the sparse null space problem (SNS), first appeared in 1986, and has since inspired results on sparse basis pursuit. In this paper, we investigate the relation between the SNS problem and the analysis dictionary learning problem, and show that the SNS problem plays a central role, and may be utilized to solve dictionary learning problems. Moreover, we propose an efficient algorithm of sparse null space basis pursuit, and extend it to a solution of analysis dictionary learning. Experimental results on numerical synthetic data and real-world data are further presented to validate the performance of our method.
KW - Sparse null space problem
KW - analysis dictionary learning
KW - high dimensional signal processing
KW - sparse representation
UR - http://www.scopus.com/inward/record.url?scp=84946044765&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2015.7178678
DO - 10.1109/ICASSP.2015.7178678
M3 - منشور من مؤتمر
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3781
EP - 3785
BT - 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
T2 - 40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
Y2 - 19 April 2014 through 24 April 2014
ER -