PMID- 28957024
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20181218
LR  - 20181218
IS  - 1530-888X (Electronic)
IS  - 0899-7667 (Linking)
VI  - 29
IP  - 11
DP  - 2017 Nov
TI  - Sparse Covariance Matrix Estimation by DCA-Based Algorithms.
PG  - 3040-3077
LID - 10.1162/neco_a_01012 [doi]
AB  - This letter proposes a novel approach using the [Formula: see text]-norm 
      regularization for the sparse covariance matrix estimation (SCME) problem. The 
      objective function of SCME problem is composed of a nonconvex part and the 
      [Formula: see text] term, which is discontinuous and difficult to tackle. 
      Appropriate DC (difference of convex functions) approximations of [Formula: see 
      text]-norm are used that result in approximation SCME problems that are still 
      nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex 
      programming framework, are investigated. Two DC formulations are proposed and 
      corresponding DCA schemes developed. Two applications of the SCME problem that 
      are considered are classification via sparse quadratic discriminant analysis and 
      portfolio optimization. A careful empirical experiment is performed through 
      simulated and real data sets to study the performance of the proposed algorithms. 
      Numerical results showed their efficiency and their superiority compared with 
      seven state-of-the-art methods.
FAU - Phan, Duy Nhat
AU  - Phan DN
AD  - Laboratory of Theoretical and Applied Computer Science EA 3097, University of 
      Lorraine, Ile du Saulcy, 57045 Metz, France duy-nhat.phan@univ-loraine.fr.
FAU - Le Thi, Hoai An
AU  - Le Thi HA
AD  - Laboratory of Theoretical and Applied Computer Science EA 3097, University of 
      Lorraine, Ile du Saulcy, 57045 Metz, France hoai-an.le-thi@univ-lorraine.fr.
FAU - Dinh, Tao Pham
AU  - Dinh TP
AD  - Laboratory of Mathematics, INSA-Rouen, University of Normandie, 76801 
      Saint-Etienne-du-Rouvray cedex, France pham@insa-rouen.fr.
LA  - eng
PT  - Journal Article
DEP - 20170928
PL  - United States
TA  - Neural Comput
JT  - Neural computation
JID - 9426182
EDAT- 2017/09/29 06:00
MHDA- 2017/09/29 06:01
CRDT- 2017/09/29 06:00
PHST- 2017/09/29 06:00 [pubmed]
PHST- 2017/09/29 06:01 [medline]
PHST- 2017/09/29 06:00 [entrez]
AID - 10.1162/neco_a_01012 [doi]
PST - ppublish
SO  - Neural Comput. 2017 Nov;29(11):3040-3077. doi: 10.1162/neco_a_01012. Epub 2017 
      Sep 28.