Related papers: Minimum description length as an objective functio…
Non-negative Matrix Factorization (NMF) is a useful method to extract features from multivariate data, but an important and sometimes neglected concern is that NMF can result in non-unique solutions. Often, there exist a Set of Feasible…
Nonnegative matrix factorization (NMF) is a prominent technique for data dimensionality reduction that has been widely used for text mining, computer vision, pattern discovery, and bioinformatics. In this paper, a framework called ARkNLS…
State-of-the-art neural networks can be trained to become remarkable solutions to many problems. But while these architectures can express symbolic, perfect solutions, trained models often arrive at approximations instead. We show that the…
The Minimum Description Length (MDL) principle states that the optimal model for a given data set is that which compresses it best. Due to practial limitations the model can be restricted to a class such as linear regression models, which…
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…
Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases and other information retrieval and clustering applications. In this report, we define an exact version of NMF. Then…
The recovery of the underlying low-rank structure of clean data corrupted with sparse noise/outliers is attracting increasing interest. However, in many low-level vision problems, the exact target rank of the underlying structure and the…
This paper considers nonlinear dynamic models where the main parameter of interest is a nonnegative matrix characterizing the network (contagion) effects. This network matrix is usually constrained either by assuming a limited number of…
Nonnegative matrix factorization (NMF) factorizes a non-negative matrix into product of two non-negative matrices, namely a signal matrix and a mixing matrix. NMF suffers from the scale and ordering ambiguities. Often, the source signals…
Nonnegative matrix factorization (NMF) has been widely used to dimensionality reduction in machine learning. However, the traditional NMF does not properly handle outliers, so that it is sensitive to noise. In order to improve the…
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…
This article introduces quaternion non-negative matrix factorization (QNMF), which generalizes the usual non-negative matrix factorization (NMF) to the case of polarized signals. Polarization information is represented by Stokes parameters,…
Given a matrix $M$ (not necessarily nonnegative) and a factorization rank $r$, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix $U$ with $r$ columns and a nonnegative matrix $V$ with $r$ rows such that $UV$ is the best…
A fundamental problem associated with the task of network reconstruction from dynamical or behavioral data consists in determining the most appropriate model complexity in a manner that prevents overfitting, and produces an inferred network…
Matrix factorization techniques, especially Nonnegative Matrix Factorization (NMF), have been widely used for dimensionality reduction and interpretable data representation. However, existing NMF-based methods are inherently single-scale…
Low dimensional nonlinear structure abounds in datasets across computer vision and machine learning. Kernelized matrix factorization techniques have recently been proposed to learn these nonlinear structures for denoising, classification,…
We introduce a new method based on nonnegative matrix factorization, Neural NMF, for detecting latent hierarchical structure in data. Datasets with hierarchical structure arise in a wide variety of fields, such as document classification,…
This is about the Minimum Description Length (MDL) principle applied to pattern mining. The length of this description is kept to the minimum. Mining patterns is a core task in data analysis and, beyond issues of efficient enumeration, the…
This is an up-to-date introduction to and overview of the Minimum Description Length (MDL) Principle, a theory of inductive inference that can be applied to general problems in statistics, machine learning and pattern recognition. While MDL…
Nonnegative Matrix Factorization (NMF) with Kullback-Leibler Divergence (NMF-KL) is one of the most significant NMF problems and equivalent to Probabilistic Latent Semantic Indexing (PLSI), which has been successfully applied in many…