NMF with feature relationship preservation penalty term for clustering problems

The method proposed in this paper belongs to the family of orthogonal non-negative matrix factorization (ONMF) methods designed to solve clustering problems. Unlike some existing ONMF methods that explicitly constrain the orthogonality of the coefficient matrix in the cost function to derive their clustering models, the proposed method integrates it implicitly, so that it results in a new optimization model with a penalty term. The latter is added to impose a scale relationship between the scatter of the cluster centroids and that of the data points. The solution of the new model involves deriving a new parametrized update scheme for the basis matrix, which makes it possible to improve the performance of the clustering by adjusting a parameter. The proposed clustering algorithm, which we call “pairwise Feature Relationship preservation-based NMF” (FR-NMF), is evaluated on several real-life and synthetic datasets and compared to eight existing NMF-based clustering models. The results obtained show the effectiveness of the proposed algorithm.