Article
Mathematics, Applied
Hong Zhu, Michael K. Ng, Guang-Jing Song
Summary: A new approximate method for solving nonnegative low-rank matrix approximation problem is developed in this study. It involves alternately projecting onto fixed-rank matrix manifold and nonnegative matrix manifold to ensure convergence, with numerical results demonstrating its performance.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Artificial Intelligence
Nan Zhang, Shiliang Sun
Summary: Multiview clustering is an important research topic, and incomplete views of data instances are common in real-world scenarios. To address this issue, we propose an effective incomplete multiview nonnegative representation learning framework that can handle incomplete multiview clustering in various situations and achieves better results compared to other state-of-the-art algorithms.
PATTERN RECOGNITION
(2022)
Article
Mathematics, Applied
Damjana Kokol Bukovsek, Helena Smigoc
Summary: The Symmetric Nonnegative Matrix Trifactorization (SN-Trifactorization) is a factorization of a nonnegative symmetric matrix A into the form BCBT, where C is a symmetric matrix of smaller size and B and C are nonnegative. This work introduces the concept of SNT-rank, the minimum size of C for which such factorization exists. The paper explores the properties of SNT-rank for low rank matrices and studies the class of nonnegative symmetric matrices with SNT-rank equal to rank. It concludes with a completion problem related to finding matrices with the smallest possible SNT-rank among all nonnegative symmetric matrices with given diagonal blocks.
LINEAR ALGEBRA AND ITS APPLICATIONS
(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
Mathematics, Applied
Francois Moutier, Arnaud Vandaele, Nicolas Gillis
Summary: ODsymNMF is a variant of symmetric nonnegative matrix factorization that has three key advantages over symNMF: it is theoretically more sound, more practical, and easier to solve optimization problems. Coordiante descent algorithms based on l(1) and l(2) norms are proposed for ODsymNMF and compared with symNMF on synthetic and document datasets.
NUMERICAL ALGORITHMS
(2021)
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
Computer Science, Artificial Intelligence
Jingxing Yin, Siyuan Peng, Zhijing Yang, Badong Chen, Zhiping Lin
Summary: A new semi-supervised symmetric nonnegative matrix factorization (SNMF) method, called hypergraph based semi-supervised SNMF (HSSNMF), is proposed for image clustering. HSSNMF constructs a similarity matrix using a predefined hypergraph and propagates pairwise constraints using a hypergraph-based algorithm. The discriminative assignment matrix is obtained through optimization. Experimental results demonstrate the superiority of HSSNMF compared to other state-of-the-art methods.
PATTERN RECOGNITION
(2023)
Article
Computer Science, Artificial Intelligence
Jiewen Guan, Bilian Chen, Xin Huang
Summary: Community detection aims to find densely connected communities in a network, which is a fundamental tool for various applications. Nonnegative matrix factorization (NMF)-based methods have gained attention, but they often neglect multihop connectivity patterns. In this article, we propose a novel method called multihop NMF (MHNMF) that considers these patterns and outperforms state-of-the-art methods.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Mathematics, Applied
Nicoletta Del Buono, Flavia Esposito, Laura Selicato, Rafal Zdunek
Summary: Learning approaches rely on hyperparameters that impact algorithm performance and affect data knowledge extraction. Nonnegative Matrix Factorization (NMF) has gained interest as a learning algorithm for capturing latent information in large datasets while maintaining feature properties. Tuning the penalty hyperparameters in NMF is an open challenge. This study proposes a bi-level optimization framework for addressing the penalty hyperparameters problem in NMF and introduces a novel algorithm called Alternating Bi-level (AltBi) that incorporates hyperparameters tuning into NMF updates. The study investigates the existence and convergence of numerical solutions under certain assumptions and presents numerical experiments.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Engineering, Electrical & Electronic
Yuheng Jia, Hui Liu, Junhui Hou, Sam Kwong, Qingfu Zhang
Summary: This paper introduces a self-supervised symmetric nonnegative matrix factorization (SNMF) method to improve data clustering performance. By exploiting the sensitivity to initialization of SNMF, without relying on additional information, the method progressively enhances clustering results. Experimental results demonstrate its superiority over 14 state-of-the-art methods in terms of multiple quantitative metrics.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY
(2022)
Article
Computer Science, Artificial Intelligence
Benhui Zhang, Xiaoke Ma
Summary: Multi-view clustering aims to assign objects into clusters with multiple heterogeneous features. However, current methods fail to capture the latent information of heterogeneous features, leading to suboptimal clustering performance. To address this issue, a novel algorithm is proposed to jointly learn the common representation and similarity structure in the embedding space, improving the performance of multi-view clustering.
KNOWLEDGE-BASED SYSTEMS
(2022)
Article
Computer Science, Information Systems
Mingyu Zhao, Weidong Yang, Feiping Nie
Summary: This paper proposes a novel multi-view clustering model called AONGR, which integrates spectral clustering and nonnegative matrix factorization into a joint framework to reconstruct the similarity graphs. The reconstructed graph not only owns a clear structure but offers the interpretation for cluster assignment. Experimental results demonstrate the superiority of our AONGR in comparison with the state-of-the-art baselines on eight real-world datasets.
INFORMATION SCIENCES
(2023)
Article
Computer Science, Information Systems
Chong Peng, Zhilu Zhang, Zhao Kang, Chenglizhao Chen, Qiang Cheng
Summary: High-dimensional data is common in the learning community, making it crucial to find a suitable data representation to reveal latent data structures for further processing. Matrix factorization techniques are widely used to handle high-dimensional data by seeking low-dimensional matrices to approximate and represent the original data. Existing nonnegative matrix factorization methods focus on learning global structures of the data, but a new method proposed in this paper enhances local similarity and clustering, resulting in a more representative representation of the data with improved capability in discovering nonlinear structures.
INFORMATION SCIENCES
(2021)
Article
Automation & Control Systems
Kexin Zhang, Xuezhuan Zhao, Siyuan Peng
Summary: A novel multiple graph regularized semi-supervised NMF method, MSNMF, is proposed in this paper, which combines limited supervised information in the form of pairwise constraints with multiple graph regularization to capture discriminative data representation. Experimental results on eight practical image datasets demonstrate that MSNMF can achieve better clustering results than several related NMF methods.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2021)
Article
Engineering, Electrical & Electronic
Siyuan Peng, Jingxing Yin, Zhijing Yang, Badong Chen, Zhiping Lin
Summary: This paper proposes a framework named MVCHSS for multiview data clustering, which improves clustering performance by constructing a set of informative similarity matrices and incorporating graph regularization without the need for additional post-processing.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY
(2023)