Symmetric nonnegative matrix factorization (symNMF) is a variant of (NMF) that allows handling symmetric input matrices and has been shown to be particularly well suited for clustering tasks. In this paper, we present new model, dubbed off-diagonal symNMF (ODsymNMF), does not take into account the diagonal entries in objective function. ODsymNMF three key advantages compared symNMF. First, theo...

Symmetric nonnegative matrix factorization (SNMF) has demonstrated to be a powerful method for data clustering. However, SNMF is mathematically formulated as non-convex optimization problem, making it sensitive the initialization of variables. Inspired by ensemble clustering that aims seek better result from set results, we propose self-supervised (S <sup xmlns:mml="http://www.w3.org/1998/Math/...

We consider the eigenvectors of symmetric matrices with independent heavy tailed entries, such as matrices with entries in the domain of attraction of α-stable laws, or adjacency matrices of Erdös-Rényi graphs. We denote by U = [uij ] the eigenvectors matrix (corresponding to increasing eigenvalues) and prove that the bivariate process B s,t := 1 √ n ∑ 1≤i≤ns 1≤j≤nt (|uij | − 1 n ) (0 ≤ s, t ≤ ...

in this article the general non-symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids have been investigated to present a semi analytical sensitivity analysis approach for geometric nonlinear shape optimization. to approach this aim the analytical formulas of secant stiffness matrix are presented. the models were validated and used to perform inve...

In this paper, we develop a novel and effective algorithm for the construction of perfect reconstruction filter banks (PRFBs) with linear phase. In the algorithm, the key step is the symmetric Laurent polynomial matrix extension (SLPME). There are two typical problems in the construction: (1) For a given symmetric finite low-pass filter a with the polyphase, to construct a PRFBs with linear pha...

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...