Related papers: Matrix factorization with neural networks

Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…

Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource constrained devices such as mobile phones and embedded systems. Compression algorithms have been…

Matrix reordering is a task to permute the rows and columns of a given observed matrix such that the resulting reordered matrix shows meaningful or interpretable structural patterns. Most existing matrix reordering techniques share the…

Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…

Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…

We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…

In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading…

The decomposition of a matrix, as a product of factors with particular properties, is a much used tool in numerical analysis. Here we develop methods for decomposing a matrix $C$ into a product $X Y$, where the factors $X$ and $Y$ are…

This paper revisits the problem of decomposing a positive semidefinite matrix as a sum of a matrix with a given rank plus a sparse matrix. An immediate application can be found in portfolio optimization, when the matrix to be decomposed is…

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…

Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations. The efficiency of its performance depends on various factors, in particular vectorization, data movement and arithmetic…

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…

Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for…

For most problems in science and engineering we can obtain data sets that describe the observed system from various perspectives and record the behavior of its individual components. Heterogeneous data sets can be collectively mined by data…

Nonnegative matrix factorization can be used to automatically detect topics within a corpus in an unsupervised fashion. The technique amounts to an approximation of a nonnegative matrix as the product of two nonnegative matrices of lower…

Most contemporary multi-task learning methods assume linear models. This setting is considered shallow in the era of deep learning. In this paper, we present a new deep multi-task representation learning framework that learns cross-task…

Integer factorization is a famous computational problem unknown whether being solvable in the polynomial time. With the rise of deep neural networks, it is interesting whether they can facilitate faster factorization. We present an approach…

Course enrollment recommendation is a relevant task that helps university students decide what is the best combination of courses to enroll in the next term. In particular, recommender system techniques like matrix factorization and…

Matrix factorization from a small number of observed entries has recently garnered much attention as the key ingredient of successful recommendation systems. One unresolved problem in this area is how to adapt current methods to handle…