Microbe–disease associations prediction by graph regularized non‐negative matrix factorization with L2,1$$ {L}_{2,1} $$ norm regularization terms

Microbes are involved in a wide range of biological processes and are closely associated with disease. Inferring potential disease-associated microbes as the biomarkers or drug targets may help prevent, diagnose and treat complex human diseases. However, biological experiments are time-consuming and expensive. In this study, we introduced a new method called iPALM-GLMF, which modelled microbe-disease association prediction as a problem of non-negative matrix factorization with graph dual regularization terms and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>L</mml:mi> <mml:mrow><mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {L}_{2,1} $$</mml:annotation></mml:semantics> </mml:math> norm regularization terms. The graph dual regularization terms were used to capture potential features in the microbe and disease space, and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>L</mml:mi> <mml:mrow><mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {L}_{2,1} $$</mml:annotation></mml:semantics> </mml:math> norm regularization terms were used to ensure the sparsity of the feature matrices obtained from the non-negative matrix factorization and to improve the interpretability. To solve the model, iPALM-GLMF used a non-negative double singular value decomposition to initialize the matrix factorization and adopted an inertial Proximal Alternating Linear Minimization iterative process to obtain the final matrix factorization results. As a result, iPALM-GLMF performed better than other existing methods in leave-one-out cross-validation and fivefold cross-validation. In addition, case studies of different diseases demonstrated that iPALM-GLMF could effectively predict potential microbial-disease associations. iPALM-GLMF is publicly available at https://github.com/LiangzheZhang/iPALM-GLMF.