Related papers: Factorization of a class of matrix-functions with …
We introduce negative binomial matrix factorization (NBMF), a matrix factorization technique specially designed for analyzing over-dispersed count data. It can be viewed as an extension of Poisson matrix factorization (PF) perturbed by a…
A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis…
In this paper we give an asymptotic formula for a matrix integral which plays a crucial role in the approach of Diaconis et al. to random matrix eigenvalues. The choice of parameter for the asymptotic analysis is motivated by an invariant…
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…
In this paper, we introduce a new class of optimization problems whose objective functions are weakly homogeneous relative to the constraint sets. By using the normalization argument in asymptotic analysis, we prove two criteria for the…
A non-iterative method is presented for the factorization step of sector decomposition method, which separates infrared divergent part from loop integration. This method is based on a classification of asymptotic behavior of polynomials.…
In this paper, we discuss on the linearized stability of the trivial solution for a class of nonlinear Caputo fractional differential systems of order $\alpha\in(1,2)$. We show that some recent existing results in this direction are wrong.…
Factorization -- a simple form of standardization -- is concerned with reduction strategies, i.e. how a result is computed. We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which…
This paper introduces the "Target Polish," a robust and computationally efficient framework for Non-Negative Matrix Factorization (NMF). Although conventional weighted NMF approaches are resistant to outliers, they converge slowly due to…
Non-negative matrix factorization (NMF) is a fundamental non-convex optimization problem with numerous applications in Machine Learning (music analysis, document clustering, speech-source separation etc). Despite having received extensive…
Non-negative matrix factorization (NMF) is a key technique for feature extraction and widely used in source separation. However, existing algorithms may converge to poor local minima, or to one of several minima with similar objective value…
The functional empirical process is a very powerful tool for deriving asymptotic laws for almost any kind of statistics whenever we know how to express them into functions of the sample. Since this method seems to be applied more and more…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…
Let $f(n)$ be an arithmetic function with $f(1)\neq0$ and let $f^{-1}(n)$ be its reciprocal with respect to the Dirichlet convolution. We study the asymptotic behaviour of $|f^{-1}(n)|$ with regard to the asymptotic behaviour of $|f(n)|$…
Nonnegative matrix factorization (NMF) has been widely studied in recent years due to its effectiveness in representing nonnegative data with parts-based representations. For NMF, a sparser solution implies better parts-based…
This paper is devoted to prove the existence and nonexistence of positive solutions for a class of fractional Schrodinger equation in RN of the We apply a new methods to obtain the existence of positive solutions when f(u) is asymptotically…
Monte Carlo simulations of a system whose action has an imaginary part are considered to be extremely difficult. We propose a new approach to this `complex-action problem', which utilizes a factorization property of distribution functions.…
Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical…
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as…