arXiv research

ZNMF improves facial recognition performance using data-dependent penalties.

The paper introduces MU for NMF with $β$-divergences and disjoint constraints.

An algorithm simplifies optimization with nonnegative and orthogonal constraints.

We demonstrate a new deep learning autoencoder network, trained by a nonnegativity constraint algorithm (NCAE), that learns features which show part-based representation of data. The learning algorithm is based on constraining negative weights. The performance of the algorithm is assessed based on decomposing data into…

New NMF algorithm uses Toeplitz matrix for facial recognition.

In this paper, we propose a new fast and robust recursive algorithm for near-separable nonnegative matrix factorization, a particular nonnegative blind source separation problem. This algorithm, which we refer to as the successive nonnegative projection algorithm (SNPA), is closely related to the popular successive pro…

For certain manifolds, nonnegative Ricci curvature limits dimension and forces almost abelian fundamental group.

A Bayesian approach termed BAyesian Least Squares Optimization with Nonnegative L1-norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be a Dirichlet distribution. With the Bayes rule, searching for the optimal parame…

Enforces physical constraints in GP regression models.

Study shows curvature constraints force submanifolds to have specific topology or geometry.

Modeling variability in tensor decomposition methods is one of the challenges of source separation. One possible solution to account for variations from one data set to another, jointly analysed, is to resort to the PARAFAC2 model. However, so far imposing constraints on the mode with variability has not been possible.…

Nonnegative matrix factorization (NMF), a dimensionality reduction and factor analysis method, is a special case in which factor matrices have low-rank nonnegative constraints. Considering the stochastic learning in NMF, we specifically address the multiplicative update (MU) rule, which is the most popular, but which h…

Motivated by the problem of optimal portfolio liquidation under transient price impact, we study the minimization of energy functionals with completely monotone displacement kernel under an integral constraint. The corresponding minimizers can be characterized by Fredholm integral equations of the second type with cons…

Bayesian NMF model improves predictions and avoids overfitting.

This paper introduces a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model, but also allows for possible nonlinear effects to be easily handled, relying on mild assumptions regarding…

Paper introduces a novel matrix-wise sparse MNNLS formulation and algorithm.

Stacked regressions improve predictive accuracy by combining estimators.

A new algorithm solves nonnegative least squares faster with nonnegative data.

Symmetric nonnegative matrix factorization has found abundant applications in various domains by providing a symmetric low-rank decomposition of nonnegative matrices. In this paper we propose a Frank-Wolfe (FW) solver to optimize the symmetric nonnegative matrix factorization problem under a simplicial constraint, whic…

The paper tackles tensor factorization and completion from noisy data.

New algorithm learns interpretable CP-basis from streaming tensor data under Markovian constraints.

Williams and Beer (2010) proposed a nonnegative mutual information decomposition, based on the construction of redundancy lattices, which allows separating the information that a set of variables contains about a target variable into nonnegative components interpretable as the unique information of some variables not p…

Enhances tensor regression for interpretability and performance.

We present an improved Bayesian framework for performing inference of affine transformations of constrained functions. We focus on quadrature with nonnegative functions, a common task in Bayesian inference. We consider constraints on the range of the function of interest, such as nonnegativity or boundedness. Although …

In curved spaces, isoperimetric sets don't exist for small volumes.

This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems with singular terminal state constraint and possibly unbounded cost coefficients. The existence result is based on a novel comparison principle for…

Paper develops compact formulations for optimization problems with rank-one convex functions and indicator variables.

Local Linear embedding (LLE) is a popular dimension reduction method. In this paper, we first show LLE with nonnegative constraint is equivalent to the widely used Laplacian embedding. We further propose to iterate the two steps in LLE repeatedly to improve the results. Thirdly, we relax the kNN constraint of LLE and p…

The paper explores curvature constraints on Kodaira dimension for specific almost Hermitian manifolds.

This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to express the remaining features. More precisely, given a data matrix X, the algorithm…

Method improves clarity in forecasting spatio-temporal data.

Inexact Riemannian optimization converges to stationary points efficiently.

Study critical quasilinear equations on Riemannian manifolds with curvature constraints.

Compositional data have two unique characteristics compared to typical multivariate data: the observed values are nonnegative and their summand is exactly one. To reflect these characteristics, a specific regularized regression model with linear constraints is commonly used. However, linear constraints incur additional…

Proposes CRG_IMSC for better clustering of multi-view data.

Paper reviews and compares NMF, PLSA, LBA, EMA, and LCA models.

Binary data matrices can represent many types of data such as social networks, votes, or gene expression. In some cases, the analysis of binary matrices can be tackled with nonnegative matrix factorization (NMF), where the observed data matrix is approximated by the product of two smaller nonnegative matrices. In this …

We propose a unified and systematic framework for performing online nonnegative matrix factorization in the presence of outliers. Our framework is particularly suited to large-scale data. We propose two solvers based on projected gradient descent and the alternating direction method of multipliers. We prove that the se…

Nonnegative matrix factorization (NMF) with group sparsity constraints is formulated as a probabilistic graphical model and, assuming some observed data have been generated by the model, a feasible variational Bayesian algorithm is derived for learning model parameters. When used in a supervised learning scenario, NMF …

The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes, when deflated by it, supermartingales. The numeraire portfolio depends on market characteristics, which include: (a) the information flow available to acting agents, given by a filtrati…

Study optimal consumption and portfolio strategies with no-borrowing constraint in financial markets.

The goal of this paper is to study weakly Einstein critical metrics of the volume functional on a compact manifold $M$ with smooth boundary $\partial M$. Here, we will give the complete classification for an $n$-dimensional, $n=3$ or $4,$ weakly Einstein critical metric of the volume functional with nonnegative scalar …

State spaces of multifactor approximations of nonnegative Volterra processes are linear transformations of the nonnegative orthant.

Derives matrix Harnack inequalities for semilinear heat equations on manifolds.

Fixed points of nonnegative neural networks are analyzed using fixed point theory.

Study Euler characteristic of manifolds with almost nonnegative curvature operator, showing nonnegativity under certain conditions.

Study open Alexandrov spaces with nonnegative curvature, proving structural results.

Sharp inequalities for manifolds with nonnegative curvature.