# Solving the Order-Preserving Submatrix Problem via Integer Programming

@article{Trapp2010SolvingTO, title={Solving the Order-Preserving Submatrix Problem via Integer Programming}, author={Andrew C. Trapp and Oleg A. Prokopyev}, journal={INFORMS J. Comput.}, year={2010}, volume={22}, pages={387-400} }

In this paper we consider the order-preserving submatrix (OPSM) problem. This problem is known to be NP-hard. Although in recent years some heuristic methods have been presented to find OPSMs, they lack the guarantee of optimality. We present exact solution approaches based on linear mixed 0--1 programming formulations and develop algorithmic enhancements to aid in solvability. Encouraging computational results are reported both for synthetic and real biological data. In addition, we discuss…

## 14 Citations

### A Fixed Parameter Tractable Integer Program for Finding the Maximum Order Preserving Submatrix

- Computer Science2011 IEEE 11th International Conference on Data Mining
- 2011

This paper proposes a novel exact algorithm to find maximum order preserving sub matrices which is fixed parameter tractable with respect to the number of columns of the provided gene expression data and exhibits better guarantees as well as better runtime performance as compared to the state of the art exact algorithms.

### An apriori-based algorithm for mining semi-order-preserving submatrix

- Computer Science, MathematicsInt. J. Comput. Sci. Eng.
- 2016

Order-preserving submatrices OPSMs find objects that exhibit a coherent pattern with the same linear ordering in subspace. In general, this problem can be reducible to a special case of the…

### On solving selected nonlinear integer programming problems in data mining, computational biology, and sustainability

- Computer Science
- 2011

This thesis consists of three essays concerning the use of optimization techniques to solve four problems in the fields of data mining, computational biology, and sustainable energy devices, and demonstrates that each problem can be modeled as a nonlinear (mixed) integer program.

### Recovering all generalized order-preserving submatrices: new exact formulations and algorithms

- Computer ScienceAnn. Oper. Res.
- 2018

Two exact mathematical programming formulations are provided that generalize the OPSM formulation by allowing for the reverse linear ordering, known as the generalized OPSM pattern, or GOPSM, and two novel algorithms to recover, for any given level of significance, all GOPSMs from a given data matrix, by iteratively solving mathematical programming formulation to global optimality.

### Towards Order-Preserving SubMatrix Search and Indexing

- Computer ScienceDASFAA
- 2015

This paper investigates the issues of indexing two datasets above and presents a naive solution pfTree by applying prefix-Tree and gives an optimization indexing method pIndex, which employs row and column header tables to traverse related branches in a bottom-up manner.

### Mining order-preserving submatrices from probabilistic matrices

- Computer ScienceACM Trans. Database Syst.
- 2014

This article defines new probabilistic matrix representations to model uncertain data with continuous distributions and uses two biological datasets to illustrate that the POPSM model better captures the characteristics of the expression levels of biologically correlated genes and greatly promotes the discovery of patterns with high biological significance.

### A new approach for the deep order preserving submatrix problem based on sequential pattern mining

- Computer ScienceInternational Journal of Machine Learning and Cybernetics
- 2015

This paper proposes a new exact algorithm, capable of mining all the deep OPSMs over a small support, and reveals better performance than the traditional sequential pattern mining algorithms.

### A new approach for the deep order preserving submatrix problem based on sequential pattern mining

- Computer ScienceInt. J. Mach. Learn. Cybern.
- 2018

This paper proposes a new exact algorithm, capable of mining all the deep OPSMs over a small support, and reveals better performance than the traditional sequential pattern mining algorithms.

### Recovering all generalized order-preserving submatrices: new exact formulations and algorithms

- Computer ScienceAnnals of Operations Research
- 2016

Two exact mathematical programming formulations are provided that generalize the OPSM formulation by allowing for the reverse linear ordering, known as the generalized OPSM pattern, or GOPSM, and provide two novel algorithms to recover, for any given level of significance, all GOPSMs from a given data matrix, by iteratively solving mathematical programming formulation to global optimality.

### A common-subsequence-based approach for mining deep order preserving submatrix

- Computer Science2014 11th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)
- 2014

A new exact algorithm is proposed, which obtain all the deep OPSMs by finding the common subsequences shared by every two rows, which is suitable for the full mining of deep OPSM with a small support, which could even find all theDeep OPSMs with a minimum support threshold of 2.

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