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This study proposes revised axioms for defining inconsistency indicators in pairwise comparisons. It is based on the new findings that "PC submatrix cannot have a worse inconsistency indicator than the PC matrix containing it" and that…

Other Computer Science · Computer Science 2023-07-25 W. W. Koczkodaj , J. -P. Magnot

In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…

Machine Learning · Computer Science 2012-07-03 Franz Kiraly , Ryota Tomioka

The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…

Machine Learning · Computer Science 2014-12-01 Vassilis Kalofolias , Xavier Bresson , Michael Bronstein , Pierre Vandergheynst

Pairwise comparison matrix as a crucial component of AHP, presents the prefer- ence relations among alternatives. However, in many cases, the pairwise comparison matrix is difficult to complete, which obstructs the subsequent operations of…

Optimization and Control · Mathematics 2016-07-28 Xinyi Zhou , Yong Hu , Yong Deng , Felix T. S. Chan , Alessio Ishizak

Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…

Machine Learning · Statistics 2020-03-23 Xiaojun Mao , Raymond K. W. Wong , Song Xi Chen

This paper studies decision-making and statistical inference for two-sided matching markets via matrix completion. In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise…

Methodology · Statistics 2025-10-31 Congyuan Duan , Wanteng Ma , Dong Xia , Kan Xu

While the matrix completion problem has attracted considerable attention over the decades, few works address the nonignorable missing issue and all have their limitations. In this article, we propose a nuclear norm regularized row- and…

Machine Learning · Statistics 2025-06-30 Yuanhong A , Guoyu Zhang , Yongcheng Zeng , Bo Zhang

In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group $G$, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided.…

Logic · Mathematics 2018-07-12 Waldemar W. Koczkodaj , Jean-Pierre Magnot

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

Machine Learning · Statistics 2024-12-17 Ziyuan Chen , Fang Yao

We consider the problem of matrix completion with graphs as side information depicting the interrelations between variables. The key challenge lies in leveraging the similarity structure of the graph to enhance matrix recovery. Existing…

Machine Learning · Computer Science 2025-02-13 Yao Wang , Yiyang Yang , Kaidong Wang , Shanxing Gao , Xiuwu Liao

This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…

Information Theory · Computer Science 2016-11-15 Yudong Chen

The main contribution of this paper is the development of a new decision tree algorithm. The proposed approach allows users to guide the algorithm through the data partitioning process. We believe this feature has many applications but in…

Machine Learning · Statistics 2020-10-27 Cédric Beaulac , Jeffrey S. Rosenthal

Handling missing values in training datasets for constructing learning models or extracting useful information is considered to be an important research task in data mining and knowledge discovery in databases. In recent years, lot of…

Databases · Computer Science 2009-04-22 Shariq Bashir , Saad Razzaq , Umer Maqbool , Sonya Tahir , Abdul Rauf Baig

We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise…

Optimization and Control · Mathematics 2022-07-11 Nikolai Krivulin , Sergei Sergeev

In this paper, paired comparison models with stochastic background are investigated. We focus on the models that allow three options for choice. We estimate all parameters, the strength of the objects and the boundaries of equal decision,…

Optimization and Control · Mathematics 2025-02-20 László Gyarmati , Csaba Mihálykó , Eva Orbán-Mihálykó , András Mihálykó

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

Numerical Analysis · Mathematics 2014-07-01 Gil Shabat , Yaniv Shmueli , Amir Averbuch

Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…

Machine Learning · Statistics 2020-07-06 Jesús Arroyo , Daniel L. Sussman , Carey E. Priebe , Vince Lyzinski

We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise…

Optimization and Control · Mathematics 2018-02-01 N. Krivulin , S. Sergeev

We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching…

Machine Learning · Statistics 2019-06-11 Yameng Liu , Aw Dieng , Sudeepa Roy , Cynthia Rudin , Alexander Volfovsky

Techniques of matrix completion aim to impute a large portion of missing entries in a data matrix through a small portion of observed ones. In practice including collaborative filtering, prior information and special structures are usually…

Statistics Theory · Mathematics 2022-03-09 Ji Chen , Xiaodong Li , Zongming Ma