A Difference of Convex Functions Algorithm for Switched Linear Regression
被引:23
作者:
Tao Pham Dinh
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机构:
Normandie Univ, Natl Inst Appl Sci Rouen, Math Lab, F-76801 St Etienne Du Rouvray, FranceNormandie Univ, Natl Inst Appl Sci Rouen, Math Lab, F-76801 St Etienne Du Rouvray, France
Tao Pham Dinh
[1
]
Hoai Minh Le
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机构:
Univ Lorraine, Lab Theoret & Appl Comp Sci LITA EA 3097, F-57045 Metz, FranceNormandie Univ, Natl Inst Appl Sci Rouen, Math Lab, F-76801 St Etienne Du Rouvray, France
Hoai Minh Le
[2
]
Hoai An Le Thi
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h-index: 0
机构:
Univ Lorraine, Lab Theoret & Appl Comp Sci LITA EA 3097, F-57045 Metz, FranceNormandie Univ, Natl Inst Appl Sci Rouen, Math Lab, F-76801 St Etienne Du Rouvray, France
Hoai An Le Thi
[2
]
论文数: 引用数:
h-index:
机构:
Lauer, Fabien
[3
]
机构:
[1] Normandie Univ, Natl Inst Appl Sci Rouen, Math Lab, F-76801 St Etienne Du Rouvray, France
[2] Univ Lorraine, Lab Theoret & Appl Comp Sci LITA EA 3097, F-57045 Metz, France
[3] Univ Lorraine, CNRS, LORIA, Inria, F-54506 Vandoeuvre Les Nancy, France
DC programming;
DCA;
nonconvex optimization;
nonsmooth optimization;
piecewise affine systems;
switched linear systems;
switched regression;
system identification;
IDENTIFICATION;
OPTIMIZATION;
D O I:
10.1109/TAC.2014.2301575
中图分类号:
TP [自动化技术、计算机技术];
学科分类号:
0812 ;
摘要:
This technical note deals with switched linear system identification and more particularly aims at solving switched linear regression problems in a large-scale setting with both numerous data and many parameters to learn. We consider the recent minimum-of-error framework with a quadratic loss function, in which an objective function based on a sum of minimum errors with respect to multiple submodels is to be minimized. The technical note proposes a new approach to the optimization of this nonsmooth and nonconvex objective function, which relies on Difference of Convex (DC) functions programming. In particular, we formulate a proper DC decomposition of the objective function, which allows us to derive a computationally efficient DC algorithm. Numerical experiments show that the method can efficiently and accurately learn switching models in large dimensions and from many data points.