IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v297y2022i3p853-865.html
   My bibliography  Save this article

Maximal-Sum submatrix search using a hybrid contraint programming/linear programming approach

Author

Listed:
  • Derval, Guillaume
  • Schaus, Pierre

Abstract

A Maximal-Sum Submatrix (MSS) maximizes the sum of the entries corresponding to the Cartesian product of a subset of rows and columns from an original matrix (with positive and negative entries). Despite being NP-hard, this recently introduced problem was already proven to be useful for practical data-mining applications. It was used for identifying bi-clusters in gene expression data or to extract a submatrix that is then visualized in a circular plot. The state-of-the-art results for MSS are obtained using an advanced Constraint Programing approach that combines a custom filtering algorithm with a Large Neighborhood Search. We improve the state-of-the-art approach by introducing new upper bounds based on linear and mixed-integer programming formulations, along with dedicated pruning algorithms. We experiment on both synthetic and real-life data, and show that our approach outperforms the previous methods.

Suggested Citation

  • Derval, Guillaume & Schaus, Pierre, 2022. "Maximal-Sum submatrix search using a hybrid contraint programming/linear programming approach," European Journal of Operational Research, Elsevier, vol. 297(3), pages 853-865.
    • Handle: RePEc:eee:ejores:v:297:y:2022:i:3:p:853-865
    DOI: 10.1016/j.ejor.2021.06.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221721005142
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2021.06.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Thu Hien DAO & Frédéric DOCQUIER & Mathilde MAUREL & Pierre SCHAUS, 2017. "Global Migration in the 20th and 21st Centuries: the Unstoppable Force of Demography," Working Paper 96d89f28-0e80-4703-9b33-6, Agence française de développement.
    2. Laura J. van 't Veer & Hongyue Dai & Marc J. van de Vijver & Yudong D. He & Augustinus A. M. Hart & Mao Mao & Hans L. Peterse & Karin van der Kooy & Matthew J. Marton & Anke T. Witteveen & George J. S, 2002. "Gene expression profiling predicts clinical outcome of breast cancer," Nature, Nature, vol. 415(6871), pages 530-536, January.
    3. Peeters, M.J.P., 2003. "The maximum edge biclique problem is NP-complete," Other publications TiSEM 3e340431-37b3-4bc5-9b14-9, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tibshirani Robert J., 2009. "Univariate Shrinkage in the Cox Model for High Dimensional Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-20, April.
    2. Jing Zhang & Qihua Wang & Xuan Wang, 2022. "Surrogate-variable-based model-free feature screening for survival data under the general censoring mechanism," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 379-397, April.
    3. Gaorong Li & Liugen Xue & Heng Lian, 2012. "SCAD-penalised generalised additive models with non-polynomial dimensionality," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 681-697.
    4. Zemin Zheng & Jie Zhang & Yang Li, 2022. "L 0 -Regularized Learning for High-Dimensional Additive Hazards Regression," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2762-2775, September.
    5. Lian, Heng & Du, Pang & Li, YuanZhang & Liang, Hua, 2014. "Partially linear structure identification in generalized additive models with NP-dimensionality," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 197-208.
    6. Jan, Budczies & Kosztyla, Daniel & von Törne, Christian & Stenzinger, Albrecht & Darb-Esfahani, Silvia & Dietel, Manfred & Denkert, Carsten, 2014. "cancerclass: An R Package for Development and Validation of Diagnostic Tests from High-Dimensional Molecular Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i01).
    7. Zhaoliang Wang & Liugen Xue & Gaorong Li & Fei Lu, 2019. "Spline estimator for ultra-high dimensional partially linear varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 657-677, June.
    8. Lian, I.B. & Chang, C.J. & Liang, Y.J. & Yang, M.J. & Fann, C.S.J., 2007. "Identifying differentially expressed genes in dye-swapped microarray experiments of small sample size," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2602-2620, February.
    9. Sumit Kunnumkal & Kalyan Talluri, 2019. "Choice Network Revenue Management Based on New Tractable Approximations," Transportation Science, INFORMS, vol. 53(6), pages 1591-1608, November.
    10. Konstantin Boss & Andre Groeger & Tobias Heidland & Finja Krueger & Conghan Zheng, 2023. "Forecasting Bilateral Refugee Flows with High-dimensional Data and Machine Learning Techniques," Working Papers 1387, Barcelona School of Economics.
    11. Grace Y. Yi & Wenqing He & Raymond. J. Carroll, 2022. "Feature screening with large‐scale and high‐dimensional survival data," Biometrics, The International Biometric Society, vol. 78(3), pages 894-907, September.
    12. Alejandra Casado & Sergio Pérez-Peló & Jesús Sánchez-Oro & Abraham Duarte, 2022. "A GRASP algorithm with Tabu Search improvement for solving the maximum intersection of k-subsets problem," Journal of Heuristics, Springer, vol. 28(1), pages 121-146, February.
    13. GILLIS, Nicolas & GLINEUR, François, 2010. "On the geometric interpretation of the nonnegative rank," LIDAM Discussion Papers CORE 2010051, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Khan Md Hasinur Rahaman & Bhadra Anamika & Howlader Tamanna, 2019. "Stability selection for lasso, ridge and elastic net implemented with AFT models," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(5), pages 1-14, October.
    15. Michał Burzyński & Christoph Deuster & Frédéric Docquier & Jaime de Melo, 2022. "Climate Change, Inequality, and Human Migration," Journal of the European Economic Association, European Economic Association, vol. 20(3), pages 1145-1197.
    16. Zhang, Shucong & Zhou, Yong, 2018. "Variable screening for ultrahigh dimensional heterogeneous data via conditional quantile correlations," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 1-13.
    17. Rémi DE BERCEGOL & Jérémie CAVE & Arch NGUYEN THAI HUYEN, 2018. "Informal Recycling vs municipal Waste Service in Asian cities: Opposition or Integration?," Working Paper 07c154f8-d6a3-4480-907b-1, Agence française de développement.
    18. Cipolli III, William & Hanson, Timothy & McLain, Alexander C., 2016. "Bayesian nonparametric multiple testing," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 64-79.
    19. Guan-Hua Huang & Su-Mei Wang & Chung-Chu Hsu, 2011. "Optimization-Based Model Fitting for Latent Class and Latent Profile Analyses," Psychometrika, Springer;The Psychometric Society, vol. 76(4), pages 584-611, October.
    20. Foucher Yohann & Danger Richard, 2012. "Time Dependent ROC Curves for the Estimation of True Prognostic Capacity of Microarray Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(6), pages 1-22, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:297:y:2022:i:3:p:853-865. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.