Nonnegative Matrix Factorization and Hash Bit Selection Based on Collaborative Neurodynamic Optimization
Student thesis: Doctoral Thesis
Related Research Unit(s)
Due to the explosive growth of data, the storage capacity and computational efficiency of a given computing resource bring huge challenges to the task. Nonnegative matrix factorization (NMF) and hash bit selection (HBS) are two important dimension-reduction techniques in modern data analysis. However, the problems and their variations are hard to solve due to their combinatorial natures. This thesis presents collaborative neurodynamic approaches (CNO) to sparse nonnegative matrix factorization, Boolean matrix factorization, and hash bit selection. In the first part of the thesis, sparse NMF is equivalently reformulated as a mixed-integer optimization problem with sparsity as binary constraints. A discrete neurodynamic optimization approach is applied to solve the reformulated problem. In the second part, the performance of four commonly used mutation operators on CNO is empirically studied. In the third part, CNO with projection neural networks is applied for solving the HBS problem by equivalently reformulating the problem as a quadratic constraint quadratic programming problem. In the fourth part, CNO with discrete Hopfield networks is applied to the HBS problem by directly searching in the discrete solution space. In the fifth part, CNO with Boltzmann machines is applied to solve the Boolean matrix factorization problem. The stability and the convergence of the algorithms are theoretically characterized. Experimental results on benchmark datasets are discussed to demonstrate the superior performance of the proposed approaches to state-of-the-art methods.