A latent space perturbation algorithm for Boolean Matrix completion based on weighted Frobenius norm

The problem of matrix completion has been gaining increasing attention among the data mining, knowledge discovery and related research communities. Factorization is one approach to solve the problem. There are good factorization methods, such as Singular value decomposition (SVD) and Non-negative matrix factorization (NMF) which could get a rather satisfied results when dealing with real-valued data. However when comes to binary data, we need a different handling strategy. In this paper, we use the Boolean Matrix Factorization (BMF) method based on weighted Frobenius norm to predict the missing values in a binary matrix. Because BMF is an NP-hard problem, we propose a recursive method that updates the rank-one matrix in latent space in each step to maximum the coverage of the known values of the input matrix. To speed up computations, we use a Heaviside step function, which allows us to decompose the recursive computing process into normal non-negative matrices and get the results by mapping them back into a Boolean matrix. The Simulation results from an actual test show that the proposed method outperforms the existing method.