TY - GEN
T1 - Phase transition in the hard-margin support vector machines
AU - Sifaou, Houssem
AU - Kammoun, Abla
AU - Alouini, Mohamed-Slim
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2020/3/6
Y1 - 2020/3/6
N2 - This paper establishes a phase transition for convergence of the hard-margin support vector machines (SVM) in high dimensional and numerous data regime, drawn from a Gaussian mixture distribution. Particularly, we characterize the maximum number of training samples that the hard-margin SVM is capable of perfectly separating. Under the assumption that the number of training samples is less than this threshold, we provide a sharp characterization of the margin parameter and the classification error performance of the hard-margin SVM classifier. Our analysis, validated through a set of numerical experiments, is based on the convex Gaussian min-max framework.
AB - This paper establishes a phase transition for convergence of the hard-margin support vector machines (SVM) in high dimensional and numerous data regime, drawn from a Gaussian mixture distribution. Particularly, we characterize the maximum number of training samples that the hard-margin SVM is capable of perfectly separating. Under the assumption that the number of training samples is less than this threshold, we provide a sharp characterization of the margin parameter and the classification error performance of the hard-margin SVM classifier. Our analysis, validated through a set of numerical experiments, is based on the convex Gaussian min-max framework.
UR - http://hdl.handle.net/10754/662445
UR - https://ieeexplore.ieee.org/document/9022461/
UR - http://www.scopus.com/inward/record.url?scp=85082394417&partnerID=8YFLogxK
U2 - 10.1109/CAMSAP45676.2019.9022461
DO - 10.1109/CAMSAP45676.2019.9022461
M3 - Conference contribution
SN - 9781728155494
SP - 415
EP - 419
BT - 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
PB - IEEE
ER -