arXiv research

DeepMP improves non-negative sparse recovery performance.

Non-negative blind source separation (non-negative BSS), which is also referred to as non-negative matrix factorization (NMF), is a very active field in domains as different as astrophysics, audio processing or biomedical signal processing. In this context, the efficient retrieval of the sources requires the use of sig…

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the spars…

The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for such a system can exist, based on the theory of polytopes. Furthermore, we deve…

NCL improves interpretability of deep features by enforcing non-negativity.

Non-negative blind source separation (BSS) has raised interest in various fields of research, as testified by the wide literature on the topic of non-negative matrix factorization (NMF). In this context, it is fundamental that the sources to be estimated present some diversity in order to be efficiently retrieved. Spar…

We are interested in the decomposition of motion data into a sparse linear combination of base functions which enable efficient data processing. We combine two prominent frameworks: dynamic time warping (DTW), which offers particularly successful pairwise motion data comparison, and sparse coding (SC), which enables an…

Non-negative curvature affects Markov chains' mixing and expansion properties.

Efficient private matrix analysis algorithms for recent variants.

Unified framework for structured principal subspace estimation with bounds and rates.

We propose an algorithm for the non-negative factorization of an occurrence tensor built from heterogeneous networks. We use l0 norm to model sparse errors over discrete values (occurrences), and use decomposed factors to model the embedded groups of nodes. An efficient splitting method is developed to optimize the non…

Non-negative matrix factorization models based on a hierarchical Gamma-Poisson structure capture user and item behavior effectively in extremely sparse data sets, making them the ideal choice for collaborative filtering applications. Hierarchical Poisson factorization (HPF) in particular has proved successful for scala…

NSA-Flow optimizes matrix representations for interpretability in complex data.

Solution to sparse PCA tuning problem using Empirical Bayes.

Non-negative matrix factorization (NMF) approximates a non-negative matrix $X$ by a product of two non-negative low-rank factor matrices $W$ and $H$. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean distance between $X$ and $W^T H$ to model the Poisson noise or the Gaussian noise.…

We introduce a new algorithm, called adaptive sparse backfitting algorithm, for solving high dimensional Sparse Additive Model (SpAM) utilizing symmetric, non-negative definite smoothers. Unlike the previous sparse backfitting algorithm, our method is essentially a block coordinate descent algorithm that guarantees to …

This paper addresses the issue of building a part-based representation of a dataset of images. More precisely, we look for a non-negative, sparse decomposition of the images on a reduced set of atoms, in order to unveil a morphological and interpretable structure of the data. Additionally, we want this decomposition to…

Demixing problems in many areas such as hyperspectral imaging and differential optical absorption spectroscopy (DOAS) often require finding sparse nonnegative linear combinations of dictionary elements that match observed data. We show how aspects of these problems, such as misalignment of DOAS references and uncertain…

This work proposes a new algorithm for automated and simultaneous phenotyping of multiple co-occurring medical conditions, also referred as comorbidities, using clinical notes from the electronic health records (EHRs). A basic latent factor estimation technique of non-negative matrix factorization (NMF) is augmented wi…

Given a collection of data points, non-negative matrix factorization (NMF) suggests to express them as convex combinations of a small set of `archetypes' with non-negative entries. This decomposition is unique only if the true archetypes are non-negative and sufficiently sparse (or the weights are sufficiently sparse),…

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…

New method for inference on covariates in NMF with random effects.

AL$\ell_0$CORE tensor decomposition reduces computational cost for sparse count data.

BN^2MF identifies unknown exposure patterns in environmental mixtures.

Due to recent explosion of text data, researchers have been overwhelmed by ever-increasing volume of articles produced by different research communities. Various scholarly search websites, citation recommendation engines, and research databases have been created to simplify the text search tasks. However, it is still d…

Subspace sparse coding (SSC) algorithms have proven to be beneficial to clustering problems. They provide an alternative data representation in which the underlying structure of the clusters can be better captured. However, most of the research in this area is mainly focused on enhancing the sparse coding part of the p…

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

Brain networks in fMRI are typically identified using spatial independent component analysis (ICA), yet mathematical constraints such as sparse coding and positivity both provide alternate biologically-plausible frameworks for generating brain networks. Non-negative Matrix Factorization (NMF) would suppress negative BO…

Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and $ε$-neighborhood methods are among the most common methods used for neighborhood selection, due to their computational simplicity. However, the choice of param…

This paper proposes learning to jump for generative modeling of sparse, skewed, heavy-tailed data.

This work explores non-negative low-rank matrix factorization based on regularized Poisson models (PF or "Poisson factorization" for short) for recommender systems with implicit-feedback data. The properties of Poisson likelihood allow a shortcut for very fast computations over zero-valued inputs, and oftentimes result…

In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares (S-NNLS) problem. We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R- GSM) to model the sparsity enforcing prior distribution for the solution. The R-GSM…

It has recently been observed that certain extremely simple feature encoding techniques are able to achieve state of the art performance on several standard image classification benchmarks including deep belief networks, convolutional nets, factored RBMs, mcRBMs, convolutional RBMs, sparse autoencoders and several othe…

Super-resolution is a classical problem in image processing, with numerous applications to remote sensing image enhancement. Here, we address the super-resolution of irregularly-sampled remote sensing images. Using an optimal interpolation as the low-resolution reconstruction, we explore locally-adapted multimodal conv…

New method for ordinal data improves recommendation systems.

Non-negative matrix factorization (NMF) is a dimensionality reduction technique which tends to produce a sparse representation of data. Commonly, the error between the actual and recreated matrices is used as an objective function, but this method may not produce the type of representation we desire as it allows for th…

This paper presents a Bayesian nonparametric latent feature model specially suitable for exploratory analysis of high-dimensional count data. We perform a non-negative doubly sparse matrix factorization that has two main advantages: not only we are able to better approximate the row input distributions, but the inferre…

Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a paradigm according to which sparsity-promoting regularization is regarded as a n…

Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set, adapting it to specific data. V…

We present a method based on the orthogonal symmetric non-negative matrix tri-factorization of the normalized Laplacian matrix for community detection in complex networks. While the exact factorization of a given order may not exist and is NP hard to compute, we obtain an approximate factorization by solving an optimiz…

In this letter, we address sparse signal recovery using spike and slab priors. In particular, we focus on a Bayesian framework where sparsity is enforced on reconstruction coefficients via probabilistic priors. The optimization resulting from spike and slab prior maximization is known to be a hard non-convex problem, a…

We consider a problem of clustering a sequence of multinomial observations by way of a model selection criterion. We propose a form of a penalty term for the model selection procedure. Our approach subsumes both the conventional AIC and BIC criteria but also extends the conventional criteria in a way that it can be app…

A collaborative convex framework for factoring a data matrix $X$ into a non-negative product $AS$, with a sparse coefficient matrix $S$, is proposed. We restrict the columns of the dictionary matrix $A$ to coincide with certain columns of the data matrix $X$, thereby guaranteeing a physically meaningful dictionary and …

Non-negative matrix factorization is a problem of dimensionality reduction and source separation of data that has been widely used in many fields since it was studied in depth in 1999 by Lee and Seung, including in compression of data, document clustering, processing of audio spectrograms and astronomy. In this work we…

Emergency Department (ED) crowding is a worldwide issue that affects the efficiency of hospital management and the quality of patient care. This occurs when the request for an admit ward-bed to receive a patient is delayed until an admission decision is made by a doctor. To reduce the overcrowding and waiting time of E…

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors $W$ and $H$, for the given input matrix $A$, such that $A \approx W H$. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, …

Gaussian process (GP) audio source separation is a time-domain approach that circumvents the inherent phase approximation issue of spectrogram based methods. Furthermore, through its kernel, GPs elegantly incorporate prior knowledge about the sources into the separation model. Despite these compelling advantages, the c…

Topic models have become popular tools for dimension reduction and exploratory analysis of text data which consists in observed frequencies of a vocabulary of $p$ words in $n$ documents, stored in a $p\times n$ matrix. The main premise is that the mean of this data matrix can be factorized into a product of two non-neg…