Many bioinformatics problems deal with chemical concentrations that should be non-negative. Non-negative matrix factorization (NMF) is an approach to take advantage of non-negativity in data. We have recently developed sparse NMF algorithms via alternating nonnegativity-constrained least squares in order to obtain sparser basis vectors or sparser mixing coefficients for each sample, which lead ...

| This paper is concerned with regression under a \sum" of partial order constraints. Examples include locally monotonic, piecewise monotonic, runlength constrained, and uni-and oligo-modal regression. These are of interest in nonlinear ltering, but also in density estimation and chromatographic analysis. It is shown that, under a least absolute error criterion, these problems can be transforme...

The uncertainty involved in the gradient constraint for optical ow detection is often modeled as constant Gaussian noise added to the time-derivative of the image intensity. In this paper, we examine this modeling closely and investigate the error behavior by doing simulation. Our result indicates that the error depends on both the spatial derivatives and the image motion. We propose alternativ...

The inscribed square conjecture, also known as Toeplitz’ conjecture or the square peg problem, asserts that every Jordan curve in the Euclidean plane admits an inscribed square. Although there exists no proof of the general conjecture, there are affirmative proofs of the conjecture subject to additional local smoothness conditions. The weakest of these local smoothness conditions include the sp...

A FORTRAN IV computer program is presented which fits up to three exponential terms and a constant to experimental data according to a least-squares criterion. Initial estimates are necessary. but no specific kind of spacing is required. The program was tried out on artificially generated three-exponential curves with added white noise. The parameters required could be determined with satisfact...

The GDE criterion is based on the estimation of the Gerschgorin disks’ radii where the disks are separated in two distinct sets : one associated to the signal sources, the other related to the noise. We aim at modifying that criterion into a new one called SGDE by using the sum of the disks’ radii. Besides, the SGDE criterion is modified with a simple deflation on the sum of the Gerschgorin rad...

The Within-Cluster Sum of Squares (WCSS) is the most used criterion in cluster analysis. Optimizing this criterion is proved to be NP-Hard and has been studied by different communities. On the other hand, Constrained Clustering allowing to integrate previous user knowledge in the clustering process has received much attention this last decade. As far as we know, there is a single approach that ...

The goal of phylogenetic inference is the reconstruction of the evolutionary history of various biological entities (taxa) such as genes, proteins, viruses or species. Phylogenetic inference is of major importance in computational biology and has numerous applications ranging from the study of biodiversity to sequence analysis. Given a matrix of pairwise distances between taxa, the minimum evol...

We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the quadratic objective function (cost approximation), or in terms of some distance measure between the approximate minimizer and the true minimizer (solution approx...

Attenuation of photons in single-photon emission tomography (SPECT) makes three-dimensional reconstruction of unknown radioactivity distributions a mathematically intractable problem. Approaches to approximate SPECT reconstruction range from ignoring the effect of photon attenuation to incorporating assumed attenuation coefficients into an iterative reconstruction procedure. We have developed a...