Multi-view clustering guided by unconstrained non-negative matrix factorization

Multi-view clustering based on non-negative matrix factorization (NMFMvC) is a well-known method for handling high-dimensional multi-view data. To satisfy the non-negativity constraint of the matrix, NMFMvC is usually solved using the Karush–Kuhn–Tucker (KKT) conditions. However, this optimization method is poorly scalable. To this end, we propose an unconstrained non-negative matrix factorization multi-view clustering (uNMFMvC) model. First, the objective function was constructed by decoupling the elements of the matrix and combining the elements with a non-linear mapping function in a non-negative value domain. The objective function was then optimized using the stochastic gradient descent (SGD) algorithm. Subsequently, three uNMFMvC methods were constructed based on different mapping functions and detailed reasoning was provided. Finally, experiments were conducted on eight public datasets and compared with cutting-edge multi-view clustering methods. The experimental results demonstrate that the proposed model has significant advantages.