The Researc Of Active Inductive Matrix Completion

In recent years,matrix completion has been widely used in the fields of recommendation systems,image processing,and pattern recognition.Matrix completion learn low-rank structures from high-dimensional data,to estimate unknown elements based on known elements,and recover matrix missing items.Matrix completion involves interdisciplinary subject such as polynomial optimization,matrix analysis,manifold geometry,etc.,which is of great significance for dealing with practical engineering problems.Deal with the high complexity of matrix completion,this dissertation proposes a fixed rank submanifold optimization algorithm,with adaptive rank estimation based on manifold optimization.The algorithm uses the iterative subspace tracking strategy to quickly predict the rank of the matrix to determine the optimal fixed rank submanifold solution space.Gradient descent Riemann optimization solves the matrix completion which estimated rank is not accurate.Deal with the matrix completion distortion for too much missing items,combined with the idea of active induction,this dissertation proposes a matrix linear decomposition active induction algorithm with optimized minimum rank.The algorithm designs the active induction strategy with multivariate Gaussian distribution and manually labels the missing matrix items with large information.The matrix decomposition is performed by the gradient descent algorithm based on the Grassmann manifold,which solves the problem that the low rank matrix decomposition is not unique.In this dissertation,the proposed algorithm is validated on image restoration,image denoising and collaborative filtering,which shows that the algorithm has improved in time complexity,convergence speed and matrix completion accuracy.The algorithm proposed in this dissertation is suitable for the matrix completion problem in practical applications.