Related papers: Nonconvex Factorization and Manifold Formulations …

Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the…

Multi-task learning is a widely used technique for harnessing information from various tasks. Recently, the sparse orthogonal factor regression (SOFAR) framework, based on the sparse singular value decomposition (SVD) within the coefficient…

When applying nonnegative matrix factorization (NMF), the rank parameter is generally unknown. This rank, called the nonnegative rank, is usually estimated heuristically since computing its exact value is NP-hard. In this work, we propose…

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to…

Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image…

Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices and has been widely used for unsupervised learning tasks such as product recommendation based on a rating matrix. However, although…

Many image processing tasks involve image-to-image mapping, which can be addressed well by fully convolutional networks (FCN) without any heavy preprocessing. Although empirically designing and training FCNs can achieve satisfactory…

Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian…

We study the Convex Set Disjointness (CSD) problem, where two players have input sets taken from an arbitrary fixed domain~$U\subseteq \mathbb{R}^d$ of size $\lvert U\rvert = n$. Their mutual goal is to decide using minimum communication…

Many matrices appearing in numerical methods for partial differential equations and integral equations are rank-structured, i.e., they contain submatrices that can be approximated by matrices of low rank. A relatively general class of…

Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of…

Parametrizations of data manifolds in shape spaces can be computed using the rich toolbox of Riemannian geometry. This, however, often comes with high computational costs, which raises the question if one can learn an efficient neural…

Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a…

We present a criterion for the stochastic completeness of a submanifold in terms of its distance to a hypersurface in the ambient space. This relies in a suitable version of the Hessian comparison theorem. In the sequel we apply a…

Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…

Motivated by the emerging role of interpolating machines in signal processing and machine learning, this work considers the computational aspects of over-parametrized matrix factorization. In this context, the optimization landscape may…

Empirical studies of the loss landscape of deep networks have revealed that many local minima are connected through low-loss valleys. Yet, little is known about the theoretical origin of such valleys. We present a general framework for…

Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…

Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…