Feature extraction plays a crucial role in dimensionality reduction in machine learning applications. Nonnegative matrix factorization (NMF) has emerged as a powerful technique for dimensionality reduction; however, its equal treatment of all features may limit accuracy. To address this challenge, this paper introduces Graph-Regularized Entropy-Weighted Nonnegative matrix factorization (GEWNMF) for enhanced feature representation. The proposed method improves feature extraction through two key innovations: optimizable feature weights and graph regularization. GEWNMF uses optimizable weights to prioritize the extraction of crucial features that best describe the underlying data structure. These weights, determined using entropy measures, ensure a diverse selection of features, thereby enhancing the fidelity of the data representation. This adaptive weighting not only improves interpretability but also strengthens the model against noisy or outlier-prone datasets. Furthermore, GEWNMF integrates robust graph regularization techniques to preserve local data relationships. By constructing an adjacency graph that captures these relationships, the method enhances its ability to discern meaningful patterns amid noise and variability. This regularization not only stabilizes the method but also ensures that nearby data points appropriately influence feature extraction. Thus, GEWNMF produces representations that capture both global trends and local nuances, making it applicable across various domains. Extensive experiments on four widely used datasets validate the efficacy of GEWNMF compared to existing methods, demonstrating its superior performance in capturing meaningful data patterns and enhancing interpretability.

This paper presents a modified digital image watermarking method based on Nonnegative matrix factorization. Firstly, host image is factorized to the product of three Nonnegative matrices. Then, the centric matrix is transferred to discrete cosine transform domain. Watermark is embedded in low frequency band of this matrix and next, the reverse of the transform is computed. Finally, watermarked image is obtained by multiplying Nonnegative matrix components. The experimental results show that the proposed method is transparent and also is high robust against JPEG compression, scaling and median filter attacks.

Nonnegative matrix factorization (NMF) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. Methods in alternating least square (ALS) approach usually used to solve this non-convex minimization problem. At each step of ALS algorithms two convex least square problems should be solved, which causes high computational cost. In this paper, based on the properties of norms and orthogonal transformations we propose a framework to project NMF’ s convex sub-problems to smaller problems. This projection reduces the time of finding NMF factors. Also every method on ALS class can be used with our proposed framework.

Recommender systems has shown as effective tools that are proposed for helping users to select their interested items. Collaborative filtering is a well-known and frequently used recommender system applied successfully in many e-commerce websites. However, these systems have poor performance while facing cold-start users (items). To address such issues, in this paper, a social regularization method is proposed which combines the social network information of users in a Nonnegative matrix factorization framework. The proposed method integrates multiple information sources such as user-item ratings and trust statements to reduce the cold-start and data sparsity issues. Moreover, the alternating direction method is used to improve the convergence speed and reduce the computational cost. We use two well-known datasets to show that the proposed method performs much better, especially for cold start users, than state-of-the-art recommendation methods for recommendation in social networks.

Images material identification plays an important role in remotely sensed image processing and its applications. Hyperspectral images، which contain a lot of narrow spectral bands of the electromagnetic spectrum، have a great potential for information extraction from remotely sensed images and material identification. Due to the low spatial resolution of hyperspectral cameras، material mixing، and light multi scattering، these images usually contain a lot of mixed pixels which face material identification with many problems. Recently، hyperspectral unmixing methods have been widely considered by the researchers as a powerful tool for identifying materials in the mixed pixels. Some of the algorithms، proposed for hyperspectral unmixing، are based on the linear mixture model (LMM) and the others are based on nonlinear mixture model (NLMM). LMM-based algorithms are more simple and commonly used methods for hyperspectral unmixing. Among various algorithms، based on LMM، non-negative matrix factorization (NMF) has attracted the most attention due to essentially implying non-negativity of the endmembers and their corresponding abundances، and moreover، simultaneously extracting spectral signature and abundances of the endmembers. In spite of these capabilities، NMF leads to local minima due to its non-convex objective function. In this regards، various studies have attempted to lead NMF results to the global optimum by imposing some additional constraint to the main objective function of NMF. However، NMF-based methods still suffer from the problem of falling into local minima. To tackle this problem، an iterative post-processing procedure، based on an ensemble learning technique، has been presented in this paper. The main goal of this paper is to demonstrate the ability of ensemble learning to improve the hyperspectral unmixing results in a simple and non-parametric manner. To this end، NMF with sparse constraint is performed in several iterations، and then، the results of each of these iterations are weightened on the basis of identifying a primary endmember that certainly exists in the image. Weightening is done with calculating spectral angle distance (SAD) metric between the true and extracted spectral signatures of the primary endmember. Usually، there is prior information about the hyperspectral images such as some existed materials or the number of materials in the images. Therefore، it is always possible to find a primary endmember in an image. The accuracy of identifying primary endmember is extended the accuracy of identifying other endmembers of their corresponding abundances. Final mixing and abundances matrices are determined using weighted combinations of the mixing and abundances matrices، extracted from each of the iterations. The proposed procedure is nonparametric and mathematically clear which can be extended to more advanced algorithms of hyperspectral unmixing. The performance of the proposed method for extraction of endmembers and their corresponding abundances has been evaluated using various synthetic and real hyperspectral data sets. Synthetic hyperspectral images constructed using USGS spectral library with several numbers of endmembers in the different signal to noise ratio (SNR) levels. Cuprite hyperspectral image، acquired by the AVIRIS sensor in 1997 from the Nevada Desert in the United States، has been used in this study as a real hyperspectral data set. The results of the experiments on both types of hyperspectral data illustrate the superiority of the proposed method over state-of-the-art competing methods.

Unmixing of remote-sensing data using Nonnegative matrix factorization has been considered recently. To improve performance, additional constraints are added to the cost function. The main challenge is to introduce constraints that lead to better results for unmixing.Correlation between bands of Hyperspectral images is the problem that is paid less attention to it in the unmixing algorithms. In this paper, we have proposed a new method for unmixing of Hyperspectral data using semi-Nonnegative matrix factorization and principal component analysis. In the proposed method, spectral and spatial unmixing is performed simultaneously. Physical constraints applied based on Linear Mixing Model. In addition to physical constraints, characteristics of Hyperspectral data have been exploited in the unmixing process. Sparseness of the abundance is one of the important features of Hyperspectral data, which is applied using the nsNMF matrix. In the proposed method update rules is derived using the ALS algorithm. In the final section of this paper, real and synthetic Hyperspectral data is used to verify the effectiveness of the proposed algorithm. Obtained results show the superiority of the proposed algorithm in comparison with some unmixing algorithms.