TY - GEN
T1 - Lp Quasi-norm Minimization
AU - Ashour, M. E.
AU - Lagoa, C. M.
AU - Aybat, N. S.
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/11
Y1 - 2019/11
N2 - The ℓp (0 < p < 1) quasi-norm is used as a sparsity-inducing function, and has applications in diverse areas, e.g., statistics, machine learning, and signal processing. This paper proposes a heuristic based on a two-block ADMM algorithm for tackling ℓp quasi-norm minimization problems. For p = s/q < 1, s, q +, the proposed algorithm requires solving for the roots of a scalar degree 2q polynomial as opposed to applying a soft thresholding operator in the case of ℓ1. We show numerical results for two example applications, sparse signal reconstruction from few noisy measurements and spam email classification using support vector machines. Our method obtains significantly sparser solutions than those obtained by ℓ1 minimization while achieving similar level of measurement fitting in signal reconstruction, and training and test set accuracy in classification.
AB - The ℓp (0 < p < 1) quasi-norm is used as a sparsity-inducing function, and has applications in diverse areas, e.g., statistics, machine learning, and signal processing. This paper proposes a heuristic based on a two-block ADMM algorithm for tackling ℓp quasi-norm minimization problems. For p = s/q < 1, s, q +, the proposed algorithm requires solving for the roots of a scalar degree 2q polynomial as opposed to applying a soft thresholding operator in the case of ℓ1. We show numerical results for two example applications, sparse signal reconstruction from few noisy measurements and spam email classification using support vector machines. Our method obtains significantly sparser solutions than those obtained by ℓ1 minimization while achieving similar level of measurement fitting in signal reconstruction, and training and test set accuracy in classification.
UR - http://www.scopus.com/inward/record.url?scp=85083345957&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85083345957&partnerID=8YFLogxK
U2 - 10.1109/IEEECONF44664.2019.9048923
DO - 10.1109/IEEECONF44664.2019.9048923
M3 - Conference contribution
AN - SCOPUS:85083345957
T3 - Conference Record - Asilomar Conference on Signals, Systems and Computers
SP - 726
EP - 730
BT - Conference Record - 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019
A2 - Matthews, Michael B.
PB - IEEE Computer Society
T2 - 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019
Y2 - 3 November 2019 through 6 November 2019
ER -