相关论文: Online Matrix Factorization via Broyden Updates

We present a novel game-theoretic formulation of Non-Negative Matrix Factorization (NNMF), a popular data-analysis method with many scientific and engineering applications. The game-theoretic formulation is shown to have favorable scaling…

We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

We consider sequential maximization of performance metrics that are general functions of a confusion matrix of a classifier (such as precision, F-measure, or G-mean). Such metrics are, in general, non-decomposable over individual instances,…

Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices and has been widely used for unsupervised learning tasks such as product recommendation based on a rating matrix. However, although…

Nonnegative matrix factorization (NMF) was popularized as a tool for data mining by Lee and Seung in 1999. NMF attempts to approximate a matrix with nonnegative entries by a product of two low-rank matrices, also with nonnegative entries.…

Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization,…

Nonnegative Matrix Factorization (NMF) is a widely used technique for data representation. Inspired by the expressive power of deep learning, several NMF variants equipped with deep architectures have been proposed. However, these methods…

In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…

We develop and analyze a broad family of stochastic/randomized algorithms for inverting a matrix. We also develop specialized variants maintaining symmetry or positive definiteness of the iterates. All methods in the family converge…

Matrix factorization (MF) is a simple collaborative filtering technique that achieves superior recommendation accuracy by decomposing the user-item interaction matrix into user and item latent matrices. Because the model typically learns…

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…

Nonnegative matrix factorization (NMF) is now a common tool for audio source separation. When learning NMF on large audio databases, one major drawback is that the complexity in time is O(FKN) when updating the dictionary (where (F;N) is…

Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. They usually suffer from the major drawback that the solution is biased towards one of the optimization…

Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of…

Amid historically low response rates, survey researchers seek ways to reduce respondent burden while measuring desired concepts with precision. We propose to ask fewer questions of respondents and impute missing responses via probabilistic…

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…

Non-negative matrix factorization (NMF) is a common method for generating topic models from text data. NMF is widely accepted for producing good results despite its relative simplicity of implementation and ease of computation. One…

Matrix factorization (MF) has become a common approach to collaborative filtering, due to ease of implementation and scalability to large data sets. Two existing drawbacks of the basic model is that it does not incorporate side information…

Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being…