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weighted nonnegative matrix factorization for Image Inpainting and Clustering

INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2020年第1期13卷 734-743页

作者： Dai, Xiangguang Zhang, Nian Zhang, Keke Xiong, Jiang Chongqing Three Gorges Univ Key Lab Intelligent Informat Proc & Control Chong Chongqing 40044 Peoples R China Univ Dist Columbia Dept Elect & Comp Engn Washington DC 20008 USA

Conventional nonnegative matrix factorization and its variants cannot separate the noise data space into a clean space and learn an effective low-dimensional subspace from Salt and Pepper noise or Contiguous Occlusion. This paper proposes a weighted nonnegative matrix factorization (WNMF) to improve the robustness of existing nonnegative matrix factorization. In WNMF, a weighted graph is constructed to label the uncorrupted data as 1 and the corrupted data as 0, and an effective matrix factorization model is proposed to recover the noise data and achieve clustering from the recovered data. Extensive experiments on the image datasets corrupted by Salt and Pepper noise or Contiguous Occlusion are presented to demonstrate the effectiveness and robustness of the proposed method in image inpainting and clustering. (C) 2020 The Authors. Published by Atlantis Press SARL.

关键词： Recovery Dimensionality reduction weighted nonnegative matrix factorization Noise

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Graph regularization weighted nonnegative matrix factorization for link prediction in weighted complex network

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NEUROCOMPUTING 2019年 369卷 50-60页

作者： Chen, Guangfu Xu, Chen Wang, Jingyi Feng, Jianwen Feng, Jiqiang Shenzhen Univ Coll Elect & Informat Engn Shenzhen 518060 Peoples R China Shenzhen Univ Coll Math & Stat Shenzhen 518060 Peoples R China

In weight networks, both link weights and topological structure are important features for link prediction. Currently, almost all existing weighted network link prediction algorithms only focused on naturally existed link weight but ignored the topological structure information. Therefore, these methods will suffer from the challenge of network sparsity and insufficient topology information. In this paper, we propose a novel Graph Regularization weighted nonnegative matrix factorization(GWNMF) model to integrate local topology information with link weights information for link prediction. Specifically, this model integrates two types of information: local topology and link weight information, and utilizes the weighted cosine similarity(WCS) method to calculate the weight similarity between local nodes. The WCS score matrix as the indicator weighted matrix to capture more useful link weight information. While graph regularization technology combines WCS score matrix to capture the local information. Besides, we derive the multiplicative updating rules to learn the parameter of this model. Empirically, we conduct the experiments on eight real-world weighted networks demonstrate that GWNMF remarkably outperforms the state-of-the-arts methods for weighted link prediction tasks. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Link prediction weighted nonnegative matrix factorization weighted cosine similarity Link weight

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Iterative algorithm for the Q-weighted nonnegative matrix factorization

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LINEAR & MULTILINEAR ALGEBRA 2021年第11期69卷 2130-2142页

作者： Li, Chun-Mei Lu, Lin-Zhang Chen, Zhen Guizhou Normal Univ Sch Math Sci Guiyang 550001 Guizhou Peoples R China Xiamen Univ Sch Math Sci Xiamen Fujian Peoples R China

nonnegative matrix factorization, which decomposes a target matrix into the product of two matrices with nonnegative elements, has been widely used in various fields of science, engineering and technology. In this paper, we consider the more general Q-weighted nonnegative matrix factorization (QWNMF) problem. By using the additive representation of the Q-weighted norm, the QWNMF problem is transformed into an unconstraint optimization problem, and then a new iterative algorithm is designed to solve it. The numerical analysis of this algorithm is also given. Numerical examples show that the new method is feasible and effective.

关键词： weighted nonnegative matrix factorization Q-weighted norm Iterative algorithm

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Change Detection of Remote Sensing Images Based on weighted nonnegative matrix factorization 10

Change Detection of Remote Sensing Images Based on Weighted ...

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10th International Workshop on the Analysis of Multitemporal Remote Sensing Images (MultiTemp)

作者： Wu, Hui Li, Heng-Chao Yang, Gang Yang, Wen Southwest Jiaotong Univ Sichuan Prov Key Lab Informat Coding & Transmiss Chengdu Peoples R China Wuhan Univ Sch Elect Informat Wuhan Peoples R China

ISBN: (纸本)9781728146157

In this paper, a change detection method of multitemporal remote sensing (RS) images based on weighted nonnegative matrix factorization (WNMF) is proposed. Firstly, difference image is generated according to the different types of input images. Then, in order to effectively explore the change information in two original RS images, WNMF is applied to extract features from the resulting difference image, in which a new weight matrix is designed by using difference values of the corresponding pixels. In addition, sparse constraint based on l(1/2)-norm regularization is enforced into WNMF to learn sparser features. Finally, a binary change mask (CM) is achieved by partitioning the extracted features with the k-means clustering. Experimental results on two pairs of RS images demonstrate the effectiveness of the proposed algorithm.

关键词： Change detection remote sensing images weighted nonnegative matrix factorization sparse constraint

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RANDOM PROJECTION STREAMS FOR (weighted) nonnegative matrix factorization

RANDOM PROJECTION STREAMS FOR (WEIGHTED) NONNEGATIVE MATRIX ...

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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Yahaya, Farouk Puigt, Matthieu Delmaire, Gilles Roussel, Gilles Univ Littoral Cote dOpale LISIC EA 4491 F-62228 Calais France

ISBN: (纸本)9781728176055

Random projections recently became popular tools to process big data. When applied to nonnegative matrix factorization (NMF), it was shown that, in practice, with the same compression level, structured random projections were more efficient than classical strategies based on, e.g., Gaussian compression. However, as they are data-dependent, they remain costly and might not fully benefit from recent very fast random projection techniques. In this paper, we thus investigate an alternative framework to structured random projections-named random projection streams (RPS)-which (i) are based on classical random compression strategies only-and are thus data-independent-and (ii) can benefit from the above fast techniques. We experimentally show that, under some mild conditions, RPS allow the same NMF performance as structured random projection along iterations. We also show that even a CPU implementation of Gaussian Compression Streams allows a faster convergence than structured random projections when applied to weighted NMF.

关键词： Random projections Big data nonnegative matrix factorization weighted nonnegative matrix factorization Compressive learning

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Improved self-paced learning framework for nonnegative matrix factorization

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PATTERN RECOGNITION LETTERS 2017年 97卷 1-7页

作者： Zhu, Xiangxiang Zhang, Zhuosheng Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China

nonnegative matrix factorization (NMF) has been attracting intensive attention due to its wide applications. However due to the non-convexity of the NMF models, most of the existing methods are easily stuck into a bad local minima, especially in presence of noise or outliers. To alleviate this deficiency, in this paper we propose a novel NMF method by incorporating self-paced learning (SPL) methodology with traditional NMF model, to sequentially include matrix elements into NMF training from easy to complex, which draws the merits of SPL that have been demonstrated to be beneficial in avoiding bad local minima. To make the SPL methodology play a more stable and efficient role in NMF, we suggest to base on multicriteria to select training elements. The effectiveness of the proposed multicriteria self-paced NMF (MSPNMF) method is demonstrated by a series of numerical experiments on synthetic and real face image data. We also discuss the effects of different initializations on MSPNMF. Experimental results show that MSPNMF is sensitive to the starting values and different initializations should be adopted for MSPNMF based on different situations. (C) 2017 Elsevier B.V. All rights reserved.

关键词： nonnegative matrix factorization Self-paced learning Robust weighted nonnegative matrix factorization Initialization analysis

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A novel recommendation system comprising WNMF with graph-based static and temporal similarity estimators

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INTERNATIONAL JOURNAL OF DATA SCIENCE AND ANALYTICS 2023年第1期16卷 27-41页

作者： Gupta, Anshul Shrinath, Pravin NMIMS Univ Dept Comp Engn MPSTME Mumbai Maharashtra India

Users' similarity plays a crucial role in the Collaborative Filtering (CF)-based Recommendation Systems (RS). The CF uses a user-item matrix to estimate this similarity. However, the user-item matrix-based similarity performs poorly during cold-start and temporal variations in users' behavior. To overcome this limitation in this paper, a combined static and temporal similarity- based CF is presented, which estimates the final ratings using a weighted sum of four independent ratings. The first rating is estimated through the similarity estimated using the Affinity Propagation (AP) applied to a reduced rank coefficient matrix generated by factorizing the user-item rating matrix using weighted nonnegative matrix factorization (WNMF). The remaining three ratings are estimated by employing graph-based similarity measures on bipartite graphs made between the user and their static (age and occupation), and temporal (purchasing pattern) characteristics. Finally, the performance of the proposed algorithm is evaluated using the MovieLens1M and Ta-Feng grocery datasets under different scenarios. The results show that the proposed approach not only outperforms the traditional techniques but also outperforms the Google Wide & Deep and CoupledCF models by 22.52, 2.06, and 11.26, 2.75% for Hit Ratio (HR) and Normalized Discounted Cumulative Gain (NDCG), respectively.

关键词： Recommendation system Collaborative filtering Bipartite graph Temporal similarity weighted nonnegative matrix factorization Affinity propagation

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Modeling and Applying Implicit Dormant Features for Recommendation via Clustering and Deep factorization

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SENSORS 2022年第21期22卷 8224页

作者： Kutlimuratov, Alpamis Abdusalomov, Akmalbek Bobomirzaevich Oteniyazov, Rashid Mirzakhalilov, Sanjar Whangbo, Taeg Keun Gachon Univ Dept Comp Engn Seongnam Si 461701 South Korea Tashkent Univ Informat Technol Dept Telecommun Engn Nukus Branch Nukus 230100 Uzbekistan Tashkent Univ Informat Technol Dept Informat Comp Technol & Programming Tashkent 100200 Uzbekistan

E-commerce systems experience poor quality of performance when the number of records in the customer database increases due to the gradual growth of customers and products. Applying implicit hidden features into the recommender system (RS) plays an important role in enhancing its performance due to the original dataset's sparseness. In particular, we can comprehend the relationship between products and customers by analyzing the hierarchically expressed hidden implicit features of them. Furthermore, the effectiveness of rating prediction and system customization increases when the customer-added tag information is combined with hierarchically structured hidden implicit features. For these reasons, we concentrate on early grouping of comparable customers using the clustering technique as a first step, and then, we further enhance the efficacy of recommendations by obtaining implicit hidden features and combining them via customer's tag information, which regularizes the deep-factorization procedure. The idea behind the proposed method was to cluster customers early via a customer rating matrix and deeply factorize a basic WNMF (weighted nonnegative matrix factorization) model to generate customers preference's hierarchically structured hidden implicit features and product characteristics in each cluster, which reveals a deep relationship between them and regularizes the prediction procedure via an auxiliary parameter (tag information). The testimonies and empirical findings supported the viability of the proposed approach. Especially, MAE of the rating prediction was 0.8011 with 60% training dataset size, while the error rate was equal to 0.7965 with 80% training dataset size. Moreover, MAE rates were 0.8781 and 0.9046 in new 50 and 100 customer cold-start scenarios, respectively. The proposed model outperformed other baseline models that independently employed the major properties of customers, products, or tags in the prediction process.

关键词： recommendation system clustering-based recommendation system heterogeneous information weighted nonnegative matrix factorization implicit features tag information deep factorization

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