Related papers: A majorization-minimization algorithm for nonnegat…
Binary data matrices can represent many types of data such as social networks, votes, or gene expression. In some cases, the analysis of binary matrices can be tackled with nonnegative matrix factorization (NMF), where the observed data…
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…
Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…
Matrix decomposition is ubiquitous and has applications in various fields like speech processing, data mining and image processing to name a few. Under matrix decomposition, nonnegative matrix factorization is used to decompose a…
This article introduces new multiplicative updates for nonnegative matrix factorization with the $\beta$-divergence and sparse regularization of one of the two factors (say, the activation matrix). It is well known that the norm of the…
This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF). The beta-divergence is a family of cost functions parametrized by a single shape parameter beta that takes the Euclidean…
A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson…
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…
The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the…
This paper is on improving the training of binary neural networks in which both activations and weights are binary. While prior methods for neural network binarization binarize each filter independently, we propose to instead parametrize…
Max-norm regularizer has been extensively studied in the last decade as it promotes an effective low-rank estimation for the underlying data. However, such max-norm regularized problems are typically formulated and solved in a batch manner,…
We introduce a Bayesian perspective for the structured matrix factorization problem. The proposed framework provides a probabilistic interpretation for existing geometric methods based on determinant minimization. We model input data…
The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from…
Clustering multivariate binary data is of interest in many scientific fields, including ecology, biomedicine, and social policy. Beyond heuristic clustering algorithms, such data can be modelled using multivariate Bernoulli mixture models.…
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. As opposed to binary matrix factorization which uses standard arithmetic, BMF uses the Boolean OR and Boolean AND…
This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis…
Bayesian matrix factorization (BMF) is a powerful tool for producing low-rank representations of matrices and for predicting missing values and providing confidence intervals. Scaling up the posterior inference for massive-scale matrices is…
Binary concepts are empirically used by humans to generalize efficiently. And they are based on Bernoulli distribution which is the building block of information. These concepts span both low-level and high-level features such as "large vs…
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…