A Novel Method Based on Non-Negative Matrix Factorization for Dimensions Reduction

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.