Related papers: Compact Factorization of Matrices Using Generalize…
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…
Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical…
We consider whether algorithmic choices in over-parameterized linear matrix factorization introduce implicit regularization. We focus on noiseless matrix sensing over rank-$r$ positive semi-definite (PSD) matrices in $\mathbb{R}^{n \times…
In this paper, we introduce and formalize a rank-one partitioning learning paradigm that unifies partitioning methods that proceed by summarizing a data set using a single vector that is further used to derive the final clustering…
Matrix representations are a powerful tool for designing efficient algorithms for combinatorial optimization problems such as matching, and linear matroid intersection and parity. In this paper, we initiate the study of matrix…
In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…
We present a very fast algorithm for general matrix factorization of a data matrix for use in the statistical analysis of high-dimensional data via latent factors. Such data are prevalent across many application areas and generate an…
The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…
Because of the limitations of matrix factorization, such as losing spatial structure information, the concept of low-rank tensor factorization (LRTF) has been applied for the recovery of a low dimensional subspace from high dimensional…
Generalized singular values (GSVs) play an essential role in the comparative analysis. In the real world data for comparative analysis, both data matrices are usually numerically low-rank. This paper proposes a randomized algorithm to first…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…
In this work, we analyze a sublinear-time algorithm for selecting a few rows and columns of a matrix for low-rank approximation purposes. The algorithm is based on an initial uniformly random selection of rows and columns, followed by a…
This manuscript describes a technique for computing partial rank-revealing factorizations, such as, e.g, a partial QR factorization or a partial singular value decomposition. The method takes as input a tolerance $\varepsilon$ and an…
Matrix factorization is a simple and natural test-bed to investigate the implicit regularization of gradient descent. Gunasekar et al. (2017) conjectured that Gradient Flow with infinitesimal initialization converges to the solution that…
Multi-view clustering is an important yet challenging task in machine learning and data mining community. One popular strategy for multi-view clustering is matrix factorization which could explore useful feature representations at…
Matrix factorization (MF) is a widely used collaborative filtering (CF) algorithm for recommendation systems (RSs), due to its high prediction accuracy, great flexibility and high efficiency in big data processing. However, with the…
The selection of most informative and discriminative features from high-dimensional data has been noticed as an important topic in machine learning and data engineering. Using matrix factorization-based techniques such as nonnegative matrix…