Recommender systems are one of the most used tools for knowledge discovery in databases, and they have become extremely popular in recent years. These systems have been applied in many internet-based communities and businesses to make personalized recommendations and acquire higher profits. Core entities in Recommender systems are ratings given by users to items. However, there is much additional information which using it can result in better performance. The personality of each user is one of the most useful data that can help the system produce more accurate and suitable recommendations for active users. It is noteworthy that the characteristics of a person can directly affect his/her behavior. Therefore, in this paper, the personality of users is identified, and a novel mathematical and algorithmic approach is proposed in order to utilize this information for making suitable recommendations. The base model in our proposed approach is matrix factorization, which is one of the most powerful methods in model-based Recommender systems. Experimental results on MovieLens dataset demonstrate the positive impact of using personality information in the matrix factorization technique, and also reveal better performance by comparing them with the state-of-the-art algorithms.

With the expansion of social networks, the use of Recommender systems in these networks has attracted considerable attention. Recommender systems have become an important tool for alleviating the information that overload problem of users by providing personalized recommendations to a user who might like based on past preferences or observed behavior about one or various items. In these systems, the users’ behavior is dynamic and their preferences change over time for different reasons. The adaptability of Recommender systems to capture the evolving user preferences, which are changing constantly, is essential. Recent studies point out that the modeling and capturing the dynamics of user preferences lead to significant improvements in recommendation accuracy. In spite of the importance of this issue, only a few approaches recently proposed that take into account the dynamic behavior of the users in making recommendations. Most of these approaches are based on the matrix factorization scheme. However, most of them assume that the preference dynamics are homogeneous for all users, whereas the changes in user preferences may be individual and the time change pattern for each user differs. In addition, because the amount of numerical ratings dramatically reduced in a specific time period, the sparsity problem in these approaches is more intense. Exploiting social information such as the trust relations between users besides the users’ rating data can help to alleviate the sparsity problem. Although social information is also very sparse, especially in a time period, it is complementary to rating information. Some works use tensor factorization to capture user preference dynamics. Despite the success of these works, the processing and solving the tensor decomposition is hard and usually leads to very high computing costs in practice, especially when the tensor is large and sparse. In this paper, considering that user preferences change individually over time, and based on the intuition that social influence can affect the users’ preferences in a Recommender system, a social Recommender system is proposed. In this system, the users’ rating information and social trust information are jointly factorized based on a matrix factorization scheme. Based on this scheme, each users and items is characterized by a sets of features indicating latent factors of the users and items in the system. In addition, it is assumed that user preferences change smoothly, and the user preferences in the current time period depend on his/her preferences in the previous time period. Therefore, the user dynamics are modeled into this framework by learning a transition matrix of user preferences between two consecutive time periods for each individual user. The complexity analysis implies that this system can be scaled to large datasets with millions of users and items. Moreover, the experimental results on a dataset from a popular product review website, Epinions, show that the proposed system performs better than competitive methods in terms of MAE and RMSE.

In this paper, we tackle two important problems in low-rank learning, which are partial singular value decomposition  and numerical rank estimation of huge matrices. By using the concepts of Krylov subspaces such as  Golub-Kahan  bidiagonalization (GK-bidiagonalization) as well as Ritz vectors, we propose two methods for solving these problems in a fast and accurate way. Our experiments show the advantages of the proposed methods compared to the traditional and randomized singular value decomposition methods. The proposed methods are appropriate for applications involving huge matrices where the accuracy of the desired singular values and also all of their corresponding singular vectors are essential. As a real application, we evaluate the performance of our methods on the problem of Riemannian similarity learning between two different image datasets of MNIST and USPS.

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.

Non-negative matrix factorization (NMF) is a part-based image representation method. It comes from the intuitive idea that entire face image can be constructed by combining several parts. In this paper, we propose a framework for face recognition by finding localized, part-based representations, denoted “ Iterative weighted non-smooth non-negative matrix factorization” (IWNS-NMF). A new cost function is proposed in order to incorporate sparsity which is controlled by a specific parameter and weights of feature coefficients. This method extracts highly localized patterns, which generally improves the capability of face recognition. After extracting patterns by IWNS-NMF, we use principle component analysis to reduce dimension for classification by linear SVM. The Recognition rates on ORL, YALE and JAFFE datasets were 97. 5, 93. 33 and 87. 8%, respectively. Comparisons to the related methods in the literature indicate that the proposed IWNS-NMF method achieves higher face recognition performance than NMF, NS-NMF, Local NMF and SNMF.

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.

Haplotype estimates based on DNA information are used to detect human genetic diseases. This problem can be modeled in the genomic processing of signals as a low-rank matrix in which only a few elements are observed. As a result, an effective way to estimate the haplotype from incomplete observations is to use matrix completion methods. In this paper, using matrix completion methods, an attempt has been made to estimate the haplotype through matrix factorization. In references, the reduction gradient method has been used to solve the problem. However, in the previous methods, outliers were also included in the calculations, which caused an error in the haplotype estimation. In other words, these methods do not pay attention to the existing conditions for haplotype matrices, and this has led to outdated estimates for haplotypes. In this paper, with the matrix completion method and considering these conditions in the haplotype matrix, we introduce a new cost function as a penalty expression for haplotype estimation. The new expression added to the cost function reduces the effect of skewed data and thus increases the accuracy of haplotype estimates. The simulation results confirm the need to reduce the haplotype retrieval error