Related papers: Deep matrix factorizations
Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations. They aim to extract complex hierarchies of features within high-dimensional datasets. Most of the loss…
Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…
Data often comes in the form of an array or matrix. Matrix factorization techniques attempt to recover missing or corrupted entries by assuming that the matrix can be written as the product of two low-rank matrices. In other words, matrix…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
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 of nonnegative data vectors. We first illustrate this…
Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion. Nevertheless, they suffer from two drawbacks:…
Despite the outstanding performance of deep neural networks in different applications, they are still computationally extensive and require a great number of memories. This motivates more research on reducing the resources required for…
Semi-Non-negative Matrix Factorization is a technique that learns a low-dimensional representation of a dataset that lends itself to a clustering interpretation. It is possible that the mapping between this new representation and our…
Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image…
Supervised matrix factorization (SMF) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. Our goal is to use SMF to learn…
Deep Matrix Factorization (DMF) is an emerging approach to the problem of matrix completion. Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix.…
Learning sophisticated feature interactions behind user behaviors is critical in maximizing CTR for recommender systems. Despite great progress, existing methods seem to have a strong bias towards low- or high-order interactions, or require…
Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning. Deep learning, however, with its carefully designed hierarchical structure,…
Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity." We study the implicit…
Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…
It has been an important approach of using matrix completion to perform image restoration. Most previous works on matrix completion focus on the low-rank property by imposing explicit constraints on the recovered matrix, such as the…
Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…
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…