Complex symmetric matrices arise from many applications, such as chemical exchange in nuclear magnetic resonance and power systems. Singular value decomposition (SVD) reveals a great deal of properties of a matrix. A complex symmetric matrix has a symmetric SVD (SSVD), also called Takagi Factorization, which exploits the symmetry [3]. Let A be a complex symmetric matrix, its Takagi factorizatio...

The matrix factorization algorithms such as the matrix factorization technique (MF), singular value decomposition (SVD) and the probability matrix factorization (PMF) and so on, are summarized and compared. Based on the above research work, a kind of improved probability matrix factorization algorithm called MPMF is proposed in this paper. MPMF determines the optimal value of dimension D of bot...

Stochastic gradient methods are effective to solve matrix factorization problems. However, it is well known that the performance of stochastic gradient method highly depends on the learning rate schedule used; a good schedule can significantly boost the training process. In this paper, motivated from past works on convex optimization which assign a learning rate for each variable, we propose a ...

Nonnegative matrix factorization (NMF) is one of the most frequently-used matrix factorization models in data analysis. A significant reason to the popularity of NMF is its interpretability and the ‘parts of whole’ interpretation of its components. Recently, max-times, or subtropical, matrix factorization (SMF) has been introduced as an alternative model with equally interpretable ‘winner takes...

This paper presents a new kernel framework for hyperspectral images classification. In this paper, a new feature extraction algorithm based on wavelet kernel non-negative matrix factorization (WKNMF) for hyperspectral remote sensing images is proposed. By using the feature of multi-resolution analysis, the new method can improve the nonlinear mapping capability of kernel non-negative matrix fac...

A new preconditioner for symmetric positive definite systems is proposed, analyzed, and tested. The preconditioner, compressed incomplete modified Gram–Schmidt (CIMGS), is based on an incomplete orthogonal factorization. CIMGS is robust both theoretically and empirically, existing (in exact arithmetic) for any full rank matrix. Numerically it is more robust than an incomplete Cholesky factoriza...

Matrix factorization is a core technique in many machine learning problems, yet also presents a nonconvex and often difficult-to-optimize problem. In this paper we present an approach based upon polynomial optimization techniques that both improves the convergence time of matrix factorization algorithms and helps them escape from local optima. Our method is based on the realization that given a...

By relating the projective camera model to the perspective one, the intrinsic camera parameters give rise to what is called the calibration matrix. This paper presents two new methods to retrieve the calibration matrix from the projective camera model. In both methods, a collective approach was adopted, using matrix representation. The calibration matrix was retrieved from a quadratic matrix te...

This paper presents a class of preconditioning techniques which exploit rational function approximations to the original matrix. The matrix is rst shifted and then an incomplete LU factorization of the resulting matrix is computed. The resulting factors are then used to compute a better preconditioner to the original matrix. Since the incomplete factorization is made on a shifted matrix, a good...

In order to solve the problem of algorithm convergence in projective non-negative matrix factorization (P-NMF), a method, called convergent projective non-negative matrix factorization (CP-NMF), is proposed. In CP-NMF, an objective function of Frobenius norm is defined. The Taylor series expansion and the Newton iteration formula of solving root are used. An iterative algorithm for basis matrix...