Article
Computer Science, Information Systems
Siyuan Peng, Zhijing Yang, Bingo Wing-Kuen Ling, Badong Chen, Zhiping Lin
Summary: A new semi-supervised NMF method called dual semi-supervised convex nonnegative matrix factorization (DCNMF) is proposed in this paper. DCNMF incorporates the pointwise and pairwise constraints of labeled samples into convex NMF, resulting in a better low-dimensional data representation. It can process mixed-sign data due to the nonnegative constraint only on the coefficient matrix.
INFORMATION SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Xiaoxia Zhang, Xianjun Zhou, Lu Chen, Yanjun Liu
Summary: Explicable recommendation systems are important for improving the persuasiveness of the system and enhancing user trust. However, the presence of latent features makes it challenging to interpret recommendation results. To address this, a novel method called PE-NMF is proposed, which replaces latent variables with explicit data to help users understand the features of recommended items and make better decisions. Experimental results demonstrate that PE-NMF performs well in rating prediction and top-N recommendation, outperforming FE-NMF and maintaining comparable recommendation ability to NMF.
ARTIFICIAL INTELLIGENCE REVIEW
(2023)
Article
Computer Science, Information Systems
Xiaoxia Zhang, Degang Chen, Hong Yu, Guoyin Wang, Houjun Tang, Kesheng Wu
Summary: Nonnegative Matrix Factorization (NMF) produces interpretable solutions for applications like collaborative filtering. Regularization is needed to address issues like overfitting and interpretability. Existing regularizers are constructed from factorization results, but this study proposes a more holistic graph regularizer based on a linear projection of the rating matrix, named LPGNMF. Experimental results show the superiority of LPGNMF on different datasets.
INFORMATION SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Nicolas Nadisic, Jeremy E. Cohen, Arnaud Vandaele, Nicolas Gillis
Summary: This paper introduces a new form of sparse MNNLS problem and a two-step algorithm to solve it. By dividing the problem into subproblems and selecting Pareto front solutions, a matrix that satisfies the sparsity constraint is constructed. Experimental results show that this method is more accurate than existing heuristic algorithms.
Article
Computer Science, Artificial Intelligence
Junjun Pan, Nicolas Gillis
Summary: Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data, which can be efficiently computed under the separability assumption. The algorithm operates by finding data points that contain basis vectors for decomposition.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2021)
Article
Computer Science, Software Engineering
Alberto Del Pia, Aida Khajavirad
Summary: This paper discusses the definition of the multilinear polytope and its relation to the acyclicity degree of the underlying hypergraph. It also provides a polynomial-size extended formulation for the multilinear polytope of ss-acyclic hypergraphs, characterizing the hypergraphs for which such a formulation can be constructed.
MATHEMATICAL PROGRAMMING
(2023)
Article
Operations Research & Management Science
Ja'far Dehghanpour, Nezam Mahdavi-Amiri
Summary: This article proposes an approach to convert the orthogonal nonnegative matrix factorization problem into a non-convex constraint problem and applies a penalty function to handle the non-convex constraints. The method performs well in partitioning clustering problems.
ANNALS OF OPERATIONS RESEARCH
(2022)
Article
Computer Science, Artificial Intelligence
Xiaoxia Zhang, Lu Chen, Ye Wang, Guoyin Wang
Summary: In this paper, a new recommendation algorithm called Three-way Decision Recommendations Based on Incremental Non-negative Matrix Factorization (3WD-INMF) is proposed, which leverages the concept of positive, negative, and boundary regions to update new samples' features. Experimental results show that the error induced by 3WD-INMF decreases with the addition of new samples and outperforms existing recommendation algorithms, indicating its superior performance and efficiency.
COGNITIVE COMPUTATION
(2022)
Article
Computer Science, Software Engineering
Yong Sheng Soh, Antonios Varvitsiotis
Summary: This paper introduces the application of the symmetric-cone multiplicative update algorithm to the cone factorization problem in the case of symmetric cones. The proposed algorithm updates each iterate by applying a chosen automorphism of the cone, ensuring that iterates remain within the interior of the cone. The algorithm utilizes a generalization of the geometric mean on symmetric cones. It has important applications in computing nonnegative matrix factorizations and hybrid lifts.
MATHEMATICAL PROGRAMMING
(2023)
Article
Biochemistry & Molecular Biology
Marc Elosua-Bayes, Paula Nieto, Elisabetta Mereu, Ivo Gut, Holger Heyn
Summary: SPOTlight is a computational tool that integrates spatial transcriptomics with single-cell RNA sequencing data to infer the location of cell types and states within complex tissues. Its high prediction accuracy and flexible application spectrum were demonstrated through applications in mouse brain and human pancreatic cancer.
NUCLEIC ACIDS RESEARCH
(2021)
Article
Computer Science, Information Systems
Qing Yang, Xuesong Yin, Simin Kou, Yigang Wang
Summary: The paper introduces a new matrix factorization method called RSCNMF, which can achieve meaningful factorizations of mixed-sign data and learn discriminative representations by leveraging local and global structures. It utilizes L-2, L-1-norm loss function and regularizer to handle noise and select discriminative features, and its convergence and performance are theoretically proven and empirically verified on eight real-world data sets.
Article
Multidisciplinary Sciences
John Golden, Daniel O'Malley
Summary: This study found that combining forward annealing with reverse annealing in matrix factorization algorithms can significantly improve performance.
Article
Multidisciplinary Sciences
Matthias Ruediger, David Antons, Amol M. Joshi, Torsten-Oliver Salge
Summary: This paper examines the application of topic modeling in exploring large document collections, identifying the challenges in algorithm selection and result evaluation. Through analysis and comparison, the study presents a ranking of algorithm accuracy and identifies the conditions under which these algorithms can be effectively utilized.
Article
Engineering, Electrical & Electronic
Olivier Vu Thanh, Nicolas Gillis, Fabian Lecron
Summary: In this article, a new low-rank matrix factorization model called bounded simplex-structured matrix factorization (BSSMF) is proposed. BSSMF seeks to find matrices W and H such that X approximate to WH, with the entries in each column of W bounded and the columns of H belonging to the probability simplex. BSSMF generalizes nonnegative matrix factorization and simplex-structured matrix factorization, and is particularly suitable for cases where the entries of the input matrix X belong to a given interval.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2023)
Article
Remote Sensing
Feixia Yang, Fei Ma, Shuai Huo, Yanwei Wang
Summary: This article introduces a method that fuses hyperspectral and multispectral data by incorporating sparse and low-rank regularization to address the issues of spectral shadows and spatial information redundancy in high-noise environments.
INTERNATIONAL JOURNAL OF REMOTE SENSING
(2021)
Article
Mathematics
Kristof Berczi, Endre Boros, Kazuhisa Makino
Summary: This paper introduces the characteristics and representations of hypergraph Horn functions and matroid Horn functions, and studies the Boolean minimization problem of matroid Horn functions. We determine the size of an optimal representation for binary matroids and investigate the strong connection between our problem and Turán systems.
JOURNAL OF COMBINATORIAL THEORY SERIES A
(2024)
Article
Mathematics
Pavel Galashin, Gleb Nenashev, Alexander Postnikov
Summary: This article introduces a new approach to dealing with the triangulations of a product of two simplices and root polytopes. It identifies a triangulation of a root polytope with a specific bijection between lattice points of two generalized permutohedra. In order to study such bijections, trianguloids are defined as edge-colored graphs satisfying simple local axioms. It is proved that trianguloids are in correspondence with triangulations of root polytopes.
JOURNAL OF COMBINATORIAL THEORY SERIES A
(2024)
Article
Mathematics
Sergey Avgustinovich, Sergey Kitaev, Jeffrey Liese, Vladimir Potapov, Anna Taranenko
Summary: This paper introduces the notion of mesh patterns in multidi-mensional permutations and initiates a systematic study of singleton mesh patterns (SMPs), which are multidimensional mesh patterns of length 1. It provides a complete characterization of avoidable SMPs using an invariant called rank. The paper also characterizes SMPs that occur at most once in any d-dimensional permutation and provides enumerative results of certain types of SMPs.
JOURNAL OF COMBINATORIAL THEORY SERIES A
(2024)
Article
Mathematics
A. C. Burgess, P. Danziger, A. Pastine, T. Traetta
Summary: In this paper, the concept of a row-sum matrix over an arbitrary group G is formally introduced. Row-sum matrices over generalized dihedral groups are constructed, and they are used to solve open cases of the Hamilton-Waterloo problem, filling up a large part of the spectrum of orders for which such factorizations are known to exist.
JOURNAL OF COMBINATORIAL THEORY SERIES A
(2024)
Article
Mathematics
Gary R. W. Greaves, Jeven Syatriadi
Summary: This study shows that the maximum cardinality of an equiangular line system in R18 is at most 59. The proof includes a novel application of the Jacobi identity for complementary subgraphs, and demonstrates the non-existence of a graph with a given characteristic polynomial.
JOURNAL OF COMBINATORIAL THEORY SERIES A
(2024)
Article
Mathematics
Jozsef Solymosi, Joshua Zahl
Summary: We prove a new estimate on the size of the intersection of a Cartesian product with an algebraic surface and improve upon the previous bound. We also obtain an expanding polynomial estimate with exponent 3/2. These results have important applications in combinatorial geometry.
JOURNAL OF COMBINATORIAL THEORY SERIES A
(2024)
