An algorithm for simultaneous computation of the adjoint G(s) and determinant d(s) of the matrix polynomial s2J-sA 1-A 2 is presented, where J is a singular matrix. Both G(s) and d(s) are expressed relative to a basis...An algorithm for simultaneous computation of the adjoint G(s) and determinant d(s) of the matrix polynomial s2J-sA 1-A 2 is presented, where J is a singular matrix. Both G(s) and d(s) are expressed relative to a basis of Laguerre orthogonal polynomials. This algorithm is a new extension of Leverrier-Fadeev algorithm..展开更多
Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research. However, rank determination problem has not received so much emphasis as sparseness regularization pr...Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research. However, rank determination problem has not received so much emphasis as sparseness regularization problem. Usually, the rank of base matrix needs to be assumed. In this paper, we propose an unsupervised multi-level non-negative matrix factorization model to extract the hidden data structure and seek the rank of base matrix. From machine learning point of view, the learning result depends on its prior knowledge. In our unsupervised multi-level model, we construct a three-level data structure for non-negative matrix factorization algorithm. Such a construction could apply more prior knowledge to the algorithm and obtain a better approximation of real data structure. The final bases selection is achieved through L2-norm optimization. We implement our experiment via binary datasets. The results demonstrate that our approach is able to retrieve the hidden structure of data, thus determine the correct rank of base matrix.展开更多
文摘An algorithm for simultaneous computation of the adjoint G(s) and determinant d(s) of the matrix polynomial s2J-sA 1-A 2 is presented, where J is a singular matrix. Both G(s) and d(s) are expressed relative to a basis of Laguerre orthogonal polynomials. This algorithm is a new extension of Leverrier-Fadeev algorithm..
文摘Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research. However, rank determination problem has not received so much emphasis as sparseness regularization problem. Usually, the rank of base matrix needs to be assumed. In this paper, we propose an unsupervised multi-level non-negative matrix factorization model to extract the hidden data structure and seek the rank of base matrix. From machine learning point of view, the learning result depends on its prior knowledge. In our unsupervised multi-level model, we construct a three-level data structure for non-negative matrix factorization algorithm. Such a construction could apply more prior knowledge to the algorithm and obtain a better approximation of real data structure. The final bases selection is achieved through L2-norm optimization. We implement our experiment via binary datasets. The results demonstrate that our approach is able to retrieve the hidden structure of data, thus determine the correct rank of base matrix.
