The why and how of nonnegative matrix factorization
N Gillis - … , optimization, kernels, and support vector machines, 2014 - books.google.com
Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of
high-dimensional data as it automatically extracts sparse and meaningful features from a set …
high-dimensional data as it automatically extracts sparse and meaningful features from a set …
[图书][B] Nonnegative matrix factorization
N Gillis - 2020 - SIAM
Identifying the underlying structure of a data set and extracting meaningful information is a
key problem in data analysis. Simple and powerful methods to achieve this goal are linear …
key problem in data analysis. Simple and powerful methods to achieve this goal are linear …
Training (overparametrized) neural networks in near-linear time
The slow convergence rate and pathological curvature issues of first-order gradient methods
for training deep neural networks, initiated an ongoing effort for developing faster $\mathit …
for training deep neural networks, initiated an ongoing effort for developing faster $\mathit …
Overview of accurate coresets
A coreset of an input set is its small summarization, such that solving a problem on the
coreset as its input, provably yields the same result as solving the same problem on the …
coreset as its input, provably yields the same result as solving the same problem on the …
Low-rank approximation with 1/𝜖1/3 matrix-vector products
We study iterative methods based on Krylov subspaces for low-rank approximation under
any Schatten-p norm. Here, given access to a matrix A through matrix-vector products, an …
any Schatten-p norm. Here, given access to a matrix A through matrix-vector products, an …
Nonmonotone variable projection algorithms for matrix decomposition with missing data
This paper investigates algorithms for matrix factorization when some or many components
are missing, a problem that arises frequently in computer vision and pattern recognition. We …
are missing, a problem that arises frequently in computer vision and pattern recognition. We …
Efficient alternating minimization with applications to weighted low rank approximation
Weighted low rank approximation is a fundamental problem in numerical linear algebra, and
it has many applications in machine learning. Given a matrix $ M\in\mathbb {R}^{n\times n} …
it has many applications in machine learning. Given a matrix $ M\in\mathbb {R}^{n\times n} …
Numerically stable binary coded computations
This paper addresses the gradient coding and coded matrix multiplication problems in
distributed optimization and coded computing. We present a numerically stable binary …
distributed optimization and coded computing. We present a numerically stable binary …
Near-linear time and fixed-parameter tractable algorithms for tensor decompositions
AV Mahankali, DP Woodruff, Z Zhang - arXiv preprint arXiv:2207.07417, 2022 - arxiv.org
We study low rank approximation of tensors, focusing on the tensor train and Tucker
decompositions, as well as approximations with tree tensor networks and more general …
decompositions, as well as approximations with tree tensor networks and more general …
Additive error guarantees for weighted low rank approximation
A Bhaskara, AK Ruwanpathirana… - International …, 2021 - proceedings.mlr.press
Low-rank approximation is a classic tool in data analysis, where the goal is to approximate a
matrix $ A $ with a low-rank matrix $ L $ so as to minimize the error $\norm {AL} _F^ 2 …
matrix $ A $ with a low-rank matrix $ L $ so as to minimize the error $\norm {AL} _F^ 2 …