non-negative matrix factorization

Recommender systems help users to extract useful information from a large volume of complex data, and their use has received significant attention in recent years. In practice, the interests of users and the characteristics of items in these systems change over time, and therefore, adapting recommender systems to these types of changes is necessary and helps to provide more accurate recommendations to users. However, most temporal recommender systems are only based on the dynamics of users' preferences over time and do not consider changes in item characteristics.In this paper, we propose a non-negative matrix factorization-based recommender system that uses both dynamics of users' interests and the changes in item characteristics over time in predicting users' ratings of items. In the proposed model, in order to reduce the data sparsity problem, in addition to users' ratings, trust between users is also used. The evaluation results on the Epinions dataset show that the proposed model is more accurate than the compared methods.

Clustering or community detection is a powerfrul tool for ‎analayzing complex networks which is widely used for ‎modeling complex systems. Modularity is a ‎comprehensive criterion for evaluating the quality of ‎clusters (or communities). However, it has some ‎limitations and challenges such as being a NP-hard ‎problem and not using prior information. So, Modularity-‎based community detection cannot be extended as a ‎semi-supervised community detection method. On the ‎other hand, one of the most common semi-supervised ‎methods which can use prior knowledge for clustering is ‎community detection based on non negative matrix ‎factorization (NMF). But, this method is not able to ‎consider the features of the networks. Therefore, in this ‎paper to overcome the mentioned limitations and ‎challenges and by presenting a new proof, a structure ‎similar to community detection based on NMF is ‎presented for modularity-based community detection ‎which can employ prior knowledge and iterative ‎solution. Therefore, a novel semi-supervised community ‎detection based on modularity (SSNMF-Q) criteria is ‎developed by utilizing prior information and iterative ‎solution instead of solving a NP-hard problem. To ‎evaluate SSNMF-Q, five real world networks are used ‎and it is shown that the SSNMF-Q had better ‎performance compared to other semi-supervised ‎community detection methods based on NMF.‎

Machine learning has been widely used over the past decades due to its wide range of applications. In most machine learning applications such as clustering and classification, data dimensions are large and the use of data reduction methods is essential. Non-negative matrix factorization reduces data dimensions by extracting latent features from large dimensional data. Non-negative matrix factorization only considers how to model each feature vector in the decomposed matrices and ignores the relationships between feature vectors. The relationships between feature vectors provide better factorization for machine learning applications. In this paper, a new method based on non-negative matrix factorization is proposed to reduce the dimensions of the data, which sets constraints on each feature vector pair using distance-based criteria. The proposed method uses the Frobenius norm as a cost function to create update rules. The results of experiments on the data sets show that the proposed multiplicative update rules converge rapidly and give better results than other algorithms.