A ROBUST SPECTRAL METHOD FOR FINDING LUMPINGS AND META STABLE STATES OF NON-REVERSIBLE MARKOV CHAINS

被引：0
作者：
Jacobi, Martin Nilsson [1 ]
机构：
[1] Chalmers Univ Technol, Complex Syst Grp, Environm & Energy Dept, S-41296 Gothenburg, Sweden
来源：
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2010年 / 37卷
关键词：
Markov chain; stochastic matrix; metastable states; lumping; aggregation; modularity; block diagonal dominance; block stochastic;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A spectral method for identifying lumping in large Markov chains is presented. The identification of meta stable states is treated as a special case. The method is based on the spectral analysis of a self-adjoint matrix that is a function of the original transition matrix. It is demonstrated that the technique is more robust than existing methods when applied to noisy non-reversible Markov chains.
引用
收藏
页码：296 / 306
页数：11
相关论文
共 17 条
[1]  
[Anonymous], 1976, Denumerable Markov Chains
[2]   GRAPH-COLORING USING EIGENVALUE DECOMPOSITION [J].
ASPVALL, B ;
GILBERT, JR .
SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1984, 5 (04) :526-538
[3]   EIGENVECTOR CONDITION FOR MARKOV-CHAIN LUMPABILITY [J].
BARR, DR ;
THOMAS, MU .
OPERATIONS RESEARCH, 1977, 25 (06) :1028-1031
[4]   Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains [J].
Deuflhard, P ;
Huisinga, W ;
Fischer, A ;
Schütte, C .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 315 (1-3) :39-59
[5]   Robust Perron cluster analysis in conformation dynamics [J].
Deuflhard, P ;
Weber, M .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 398 :161-184
[6]  
FIEDLER M, 1973, CZECH MATH J, V23, P298
[7]  
Fritzsche D, 2007, ELECTRON T NUMER ANA, V29, P46
[8]   Statistically optimal almost-invariant sets [J].
Froyland, G .
PHYSICA D-NONLINEAR PHENOMENA, 2005, 200 (3-4) :205-219
[9]   A SPECTRAL METHOD FOR AGGREGATING VARIABLES IN LINEAR DYNAMICAL SYSTEMS WITH APPLICATION TO CELLULAR AUTOMATA RENORMALIZATION [J].
Jacobi, Martin Nilsson ;
Gornerup, Olof .
ADVANCES IN COMPLEX SYSTEMS, 2009, 12 (02) :131-155
[10]   Sensitivity of peptide conformational dynamics on clustering of a classical molecular dynamics trajectory [J].
Jensen, Christian H. ;
Nerukh, Dmitry ;
Glen, Robert C. .
JOURNAL OF CHEMICAL PHYSICS, 2008, 128 (11)
12