arXiv research

New method for hyperparameter tuning in sparse matrix factorization.

Gradient descent proves global convergence for 4-layer matrix factorization.

Unified framework for nonconvex matrix completion with linearly parameterized factors.

This paper analyzes privacy threats in federated matrix factorization.

In this paper, we propose an online algorithm to compute matrix factorizations. Proposed algorithm updates the dictionary matrix and associated coefficients using a single observation at each time. The algorithm performs low-rank updates to dictionary matrix. We derive the algorithm by defining a simple objective funct…

Proposes a robust factor analysis for matrix data.

Federated multi-view matrix factorization learns from multiple data sources without centralizing user data.

Matrix factorization is one of the best approaches for collaborative filtering, because of its high accuracy in presenting users and items latent factors. The main disadvantages of matrix factorization are its complexity, and being very hard to be parallelized, specially with very large matrices. In this paper, we intr…

We want to construct a homological link invariant whose Euler characteristic is MOY polynomial as Khovanov and Rozansky constructed a categorification of HOMFLY polynomial. The present paper gives the first step to construct a categorification of MOY polynomial. For the essential colored planar diagrams with additional…

Develops a fast algorithm for fitting multilevel factor models.

Graph neural networks speed up nonnegative matrix factorization.

Paper proposes algorithms for BMF using integer programming.

New NMF algorithm uses Toeplitz matrix for facial recognition.

Study non-convex matrix factorization using Riemannian geometry.

NIMFA is an open-source Python library that provides a unified interface to nonnegative matrix factorization algorithms. It includes implementations of state-of-the-art factorization methods, initialization approaches, and quality scoring. It supports both dense and sparse matrix representation. NIMFA's component-based…

This article gives matrix factorizations for the trivalent diagrams and double line appearing in $\mathfrak{sl}_n$ quantum link invariant. These matrix factorizations reconstruct Khovanov-Rozansky homology. And we show that the Euler characteristic of the matrix factorization for a double loop equals the quantum dimens…

This project compares MCMC and VI for Bayesian PMF on MovieLens.

Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and…

Proposes a new matrix factorization model for interval-valued matrices.

This paper considers a restriction to non-negative matrix factorization in which at least one matrix factor is stochastic. That is, the elements of the matrix factors are non-negative and the columns of one matrix factor sum to 1. This restriction includes topic models, a popular method for analyzing unstructured data.…

PrecGD restores linear convergence in over-parameterized nonconvex matrix factorization.

Robust method learns nonlinear structures robustly to noise.

This paper develops a new class of nonconvex regularizers for low-rank matrix recovery. Many regularizers are motivated as convex relaxations of the matrix rank function. Our new factor group-sparse regularizers are motivated as a relaxation of the number of nonzero columns in a factorization of the matrix. These nonco…

Reverse annealing boosts quantum matrix factorization performance.

Efficiently factorizes coupled matrix tensor data for better accuracy and speed.

The paper studies the loss landscape of regularized deep matrix factorization, revealing unique and sharp minimizers.

We propose a privacy-enhanced matrix factorization recommender that exploits the fact that users can often be grouped together by interest. This allows a form of "hiding in the crowd" privacy. We introduce a novel matrix factorization approach suited to making recommendations in a shared group (or nym) setting and the …

Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity of matrix factorization methods. In this paper, we propose a new method for CP te…

Paper finds exact Hessian sharpness in deep matrix factorization.

Bayesian model infers factor dimensionality and sparse loading matrix adaptively.

A new NMF model for co-clustering and data approximation.

The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization. A multi-objective optimization problem finds conical combinations of templates …

The paper develops algorithms for Boolean matrix factorization using IP and heuristics.

We study the stability vis a vis adversarial noise of matrix factorization algorithm for matrix completion. In particular, our results include: (I) we bound the gap between the solution matrix of the factorization method and the ground truth in terms of root mean square error; (II) we treat the matrix factorization as …

Paper improves efficiency in matrix computations for Gaussian processes.

A new method STMF improves missing value prediction using tropical semiring.

New insights into how deep models generalize, focusing on matrix factorization.

This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but little was known for non-convex problems. We propose a novel analytical framework an…

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning, sparse component analysis, and non-negative matrix factorization. Our algorithm str…

Matrix factorization techniques have been widely used as a method for collaborative filtering for recommender systems. In recent times, different variants of deep learning algorithms have been explored in this setting to improve the task of making a personalized recommendation with user-item interaction data. The idea …

Motivated by an application in computational biology, we consider low-rank matrix factorization with $\{0,1\}$-constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared with other matrix factorization schemes, our problem is further complicated by a c…

Several complex tasks that arise in organizations can be simplified by mapping them into a matrix completion problem. In this paper, we address a key challenge faced by our company: predicting the efficiency of artists in rendering visual effects (VFX) in film shots. We tackle this challenge by using a two-fold approac…

Unweighted matrix factorization can match or outperform weighted methods in recommender systems.

A method learns matrix factorization from diverse matrices and applies the knowledge to unseen matrices.

We give a simple explicit algorithm for building multi-factor risk models. It dramatically reduces the number of or altogether eliminates the risk factors for which the factor covariance matrix needs to be computed. This is achieved via a nested "Russian-doll" embedding: the factor covariance matrix itself is modeled v…

A1GM method improves efficiency in reconstructing missing data using KL divergence.

Paper checks SSC for matrix factorizations using Gurobi.

Proposes Robust Matrix Factorization with Grouping Effect (GRMF) for better performance and robustness.