Optimization for L1-Norm Error Fitting via Data Aggregation

We propose a data aggregation-based algorithm with monotonic convergence to a global optimum for a generalized version of the L1-norm error fitting model with an assumption of the fitting function....

[1]  Yongjia Song,et al.  Adaptive Partition-Based Level Decomposition Methods for Solving Two-Stage Stochastic Programs with Fixed Recourse , 2018, INFORMS J. Comput..

[2]  Diego Klabjan,et al.  Three iteratively reweighted least squares algorithms for $$L_1$$L1-norm principal component analysis , 2017, Knowledge and Information Systems.

[3]  Panos P. Markopoulos,et al.  Optimal Algorithms for L1-subspace Signal Processing , 2014, IEEE Transactions on Signal Processing.

[4]  Yongjia Song,et al.  An Adaptive Partition-based Level Decomposition for Solving Two-stage Stochastic Programs with Fixed Recourse , 2016 .

[5]  J. Tropp,et al.  Two proposals for robust PCA using semidefinite programming , 2010, 1012.1086.

[6]  Tommi S. Jaakkola,et al.  Weighted Low-Rank Approximations , 2003, ICML.

[7]  Alexandra M. Newman,et al.  Using aggregation to optimize long-term production planning at an underground mine , 2007, Eur. J. Oper. Res..

[8]  Hiroshi Konno,et al.  Choosing the best set of variables in regression analysis using integer programming , 2009, J. Glob. Optim..

[9]  José H. Dulá,et al.  The L1-norm best-fit hyperplane problem , 2013, Appl. Math. Lett..

[10]  Andreas Bärmann,et al.  Solving network design problems via iterative aggregation , 2015, Math. Program. Comput..

[11]  Richard W. Taylor,et al.  Solving large-scale linear programs by aggregation , 1987, Comput. Oper. Res..

[12]  D. Bertsimas,et al.  Best Subset Selection via a Modern Optimization Lens , 2015, 1507.03133.

[13]  Peter Sanders,et al.  Exact Routing in Large Road Networks Using Contraction Hierarchies , 2012, Transp. Sci..

[14]  Diego Klabjan,et al.  An aggregate and iterative disaggregate algorithm with proven optimality in machine learning , 2016, Machine Learning.

[15]  James R. Evans.  A network decomposition/aggregation procedure for a class of multicommodity transportation problems , 1983, Networks.

[16]  I. Litvinchev,et al.  Aggregation in Large-Scale Optimization , 2003 .

[17]  I. Vakhutinsky,et al.  Iterative Aggregation--A New Approach to the Solution of Large-Scale Problems , 1979 .

[18]  Taesik Lee,et al.  Demand point aggregation method for covering problems with gradual coverage , 2015, Comput. Oper. Res..

[19]  Jiawei Han,et al.  Making SVMs Scalable to Large Data Sets using Hierarchical Cluster Indexing , 2005, Data Mining and Knowledge Discovery.

[20]  Feiping Nie,et al.  Robust Principal Component Analysis with Non-Greedy l1-Norm Maximization , 2011, IJCAI.

[21]  J. Current,et al.  Analysis of Errors Due to Demand Data Aggregation in the Set Covering and Maximal Covering Location Problems , 2010 .

[22]  Massimiliano Pontil,et al.  Support Vector Machines with Clustering for Training with Very Large Datasets , 2002, SETN.

[23]  P. Hammer,et al.  Aggregation of inequalities in integer programming. , 1975 .

[24]  E. Balas.  Solution of Large-Scale Transportation Problems Through Aggregation , 1965 .

[25]  G. Alistair Watson,et al.  The ℓ1 oblique procrustes problem , 2004, Stat. Comput..

[26]  Young Woong Park.  Optimization for Regression, PCA, and SVM: Optimality and Scalability , 2015 .

[27]  James R. Evans,et al.  Aggregation and Disaggregation Techniques and Methodology in Optimization , 1991, Oper. Res..

[28]  José H. Dulá,et al.  A pure L1L1-norm principal component analysis , 2013, Comput. Stat. Data Anal..

[29]  Diego Klabjan,et al.  Subset selection for multiple linear regression via optimization , 2017, Journal of Global Optimization.

[30]  Dimitris Bertsimas,et al.  Algorithm for cardinality-constrained quadratic optimization , 2009, Comput. Optim. Appl..

[31]  Andreas Bärmann.  Solving Network Design Problems via Decomposition, Aggregation and Approximation , 2016 .

[32]  Diego Klabjan,et al.  Iteratively Reweighted Least Squares Algorithms for L1-Norm Principal Component Analysis , 2016, 2016 IEEE 16th International Conference on Data Mining (ICDM).

[33]  Gaël Varoquaux,et al.  Scikit-learn: Machine Learning in Python , 2011, J. Mach. Learn. Res..

[34]  Panos P. Markopoulos,et al.  Efficient L1-Norm Principal-Component Analysis via Bit Flipping , 2016, IEEE Transactions on Signal Processing.

[35]  Cláudio Alves,et al.  Iterative aggregation and disaggregation algorithm for pseudo-polynomial network flow models with side constraints , 2017, Eur. J. Oper. Res..

[36]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[37]  Takeo Kanade,et al.  Robust L/sub 1/ norm factorization in the presence of outliers and missing data by alternative convex programming , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[38]  Jiawei Han,et al.  Classifying large data sets using SVMs with hierarchical clusters , 2003, KDD '03.

[39]  Nickolay T. Trendafilov,et al.  On the l1 Procrustes problem , 2003, Future Gener. Comput. Syst..

[40]  Sverre Storøy,et al.  Aggregation and Disaggregation in Integer Programming Problems , 1990, Oper. Res..

[41]  Gene H. Golub,et al.  Matrix computations , 1983 .

[42]  Roy Mendelssohn.  Technical Note - Improved Bounds for Aggregated Linear Programs , 1980, Oper. Res..

[43]  James R. Luedtke,et al.  An Adaptive Partition-Based Approach for Solving Two-Stage Stochastic Programs with Fixed Recourse , 2015, SIAM J. Optim..

[44]  Nojun Kwak,et al.  Principal Component Analysis Based on L1-Norm Maximization , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.