相关论文: Maximum Volume Inscribed Ellipsoid: A New Simplex-…
Recent multi-view subspace clustering achieves impressive results utilizing deep networks, where the self-expressive correlation is typically modeled by a fully connected (FC) layer. However, they still suffer from two limitations. i) The…
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…
Nonnegative matrix factorization (NMF) methods have proved to be powerful across a wide range of real-world clustering applications. Integrating multiple types of measurements for the same objects/subjects allows us to gain a deeper…
Objective: Global Maxwell Tomography (GMT) is a noninvasive inverse optimization method for the estimation of electrical properties (EP) from magnetic resonance (MR) measurements. GMT uses the volume integral equation (VIE) in the forward…
Nonnegative matrix factorization (NMF) has been shown to be identifiable under the separability assumption, under which all the columns(or rows) of the input data matrix belong to the convex cone generated by only a few of these columns(or…
Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that…
Among optimal hierarchical algorithms for the computational solution of elliptic problems, the Fast Multipole Method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and…
Learning suitable latent representations for observed, high-dimensional data is an important research topic underlying many recent advances in machine learning. While traditionally the Gaussian normal distribution has been the go-to latent…
Low dimensional nonlinear structure abounds in datasets across computer vision and machine learning. Kernelized matrix factorization techniques have recently been proposed to learn these nonlinear structures for denoising, classification,…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\mathbb{Q}^d$. We give a deterministic approximation algorithm for this problem…
Unsupervised integrative analysis of multiple data sources has become common place and scalable algorithms are necessary to accommodate ever increasing availability of data. Only few currently methods have estimation speed as their focus,…
Parametric optimization is an important product design technique, especially in the context of the modern parametric feature-based CAD paradigm. Realizing its full potential, however, requires a closed loop between CAD and CAE (i.e.,…
Nonnegative matrix factorization (NMF) based topic modeling methods do not rely on model- or data-assumptions much. However, they are usually formulated as difficult optimization problems, which may suffer from bad local minima and high…
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…
Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations. They aim to extract complex hierarchies of features within high-dimensional datasets. Most of the loss…
Non-negative Matrix Factorization (NMF) is a useful method to extract features from multivariate data, but an important and sometimes neglected concern is that NMF can result in non-unique solutions. Often, there exist a Set of Feasible…
Compressed Sensing Magnetic Resonance Imaging (CS-MRI) significantly accelerates MR data acquisition at a sampling rate much lower than the Nyquist criterion. A major challenge for CS-MRI lies in solving the severely ill-posed inverse…
Latest federated learning (FL) methods started to focus on how to use unlabeled data in clients for training due to users' privacy concerns, high labeling costs, or lack of expertise. However, current Federated…
Vision-language foundation models such as CLIP have achieved tremendous results in global vision-language alignment, but still show some limitations in creating representations for specific image regions. % To address this problem, we…