3,492 research outputs found
Application of Non-negative Matrix Factorization to LC/MS data
International audienceLiquid Chromatography-Mass Spectrometry (LC/MS) provides large datasets from which one needs to extract the relevant information. Since these data are made of non-negative mixtures of non-negative mass spectra, non-negative matrix factorization (NMF) is well suited for its processing, but it has barely been used in LC/MS. Also, these data are very difficult to deal with since they are usually contaminated with non-Gaussian noise and the intensities vary on several orders of magnitude. In this article, we show the feasibility of the NMF approach on these data. We also propose an adaptation of one of the algorithms aiming at specifically dealing with LC/MS data. We finally perform experiments and compare standard NMF algorithms on both simulated data and an annotated LC/MS dataset. This lets us evaluate the influence of the noise model and the data model on the recovery of the sources
QCD Technology: Light-Cone Quantization and Commensurate Scale Relations
I discuss several theoretical tools which are useful for analyzing
perturbative and non-perturbative problems in quantum chromodynamics, including
(a) the light-cone Fock expansion, (b) the effective charge , (c)
conformal symmetry, and (d) commensurate scale relations. Light-cone Fock-state
wavefunctions encode the properties of a hadron in terms of its fundamental
quark and gluon degrees of freedom. Given the proton's light-cone
wavefunctions, one can compute not only the quark and gluon distributions
measured in deep inelastic lepton-proton scattering, but also the multi-parton
correlations which control the distribution of particles in the proton
fragmentation region and dynamical higher twist effects. Light-cone
wavefunctions also provide a systematic framework for evaluating exclusive
hadronic matrix elements, including timelike heavy hadron decay amplitudes and
form factors. The coupling, defined from the QCD heavy quark
potential, provides a physical expansion parameter for perturbative QCD with an
analytic dependence on the fermion masses which is now known to two-loop order.
Conformal symmetry provides a template for QCD predictions, including relations
between observables which are present even in a theory which is not scale
invariant. Commensurate scale relations are perturbative QCD predictions based
on conformal symmetry relating observable to observable at fixed relative
scale. Such relations have no renormalization scale or scheme ambiguity.Comment: Lectures presented at the 12th Nuclear Physics Summer School and
Symposium (NuSS'99) and 11th International Light-Cone School and Workshop,
May 26-June 18, 1999, APCTP, Seoul, Kore
Compressive PCA for Low-Rank Matrices on Graphs
We introduce a novel framework for an approxi- mate recovery of data matrices
which are low-rank on graphs, from sampled measurements. The rows and columns
of such matrices belong to the span of the first few eigenvectors of the graphs
constructed between their rows and columns. We leverage this property to
recover the non-linear low-rank structures efficiently from sampled data
measurements, with a low cost (linear in n). First, a Resrtricted Isometry
Property (RIP) condition is introduced for efficient uniform sampling of the
rows and columns of such matrices based on the cumulative coherence of graph
eigenvectors. Secondly, a state-of-the-art fast low-rank recovery method is
suggested for the sampled data. Finally, several efficient, parallel and
parameter-free decoders are presented along with their theoretical analysis for
decoding the low-rank and cluster indicators for the full data matrix. Thus, we
overcome the computational limitations of the standard linear low-rank recovery
methods for big datasets. Our method can also be seen as a major step towards
efficient recovery of non- linear low-rank structures. For a matrix of size n X
p, on a single core machine, our method gains a speed up of over Robust
Principal Component Analysis (RPCA), where k << p is the subspace dimension.
Numerically, we can recover a low-rank matrix of size 10304 X 1000, 100 times
faster than Robust PCA
Non-Negative Blind Source Separation Algorithm Based on Minimum Aperture Simplicial Cone
International audienceWe address the problem of Blind Source Separation (BSS) when the hidden sources are Nonnegative (N-BSS). In this case, the scatter plot of the mixed data is contained within the simplicial cone generated by the columns of the mixing matrix. The proposed method, termed SCSA-UNS for Simplicial Cone Shrinking Algorithm for Unmixing Non-negative Sources, aims at estimating the mixing matrix and the sources by fitting a Minimum Aperture Simplicial Cone (MASC) to the cloud of mixed data points. SCSA-UNS is evaluated on both independent and correlated synthetic data and compared to other N-BSS methods. Simulations are also performed on real Liquid Chromatography-Mass Spectrum (LC-MS) data for the metabolomic analysis of a chemical sample, and on real dynamic Positron Emission Tomography (PET) images, in order to study the pharmacokinetics of the [18F]-FDG (FluoroDeoxyGlucose) tracer in the brain
Summing threshold logs in a parton shower
When parton distributions are falling steeply as the momentum fractions of
the partons increases, there are effects that occur at each order in
that combine to affect hard scattering cross sections and need to be summed. We
show how to accomplish this in a leading approximation in the context of a
parton shower Monte Carlo event generator.Comment: 83 pages, 8 figure
Interpretable Low-Rank Document Representations with Label-Dependent Sparsity Patterns
In context of document classification, where in a corpus of documents their
label tags are readily known, an opportunity lies in utilizing label
information to learn document representation spaces with better discriminative
properties. To this end, in this paper application of a Variational Bayesian
Supervised Nonnegative Matrix Factorization (supervised vbNMF) with
label-driven sparsity structure of coefficients is proposed for learning of
discriminative nonsubtractive latent semantic components occuring in TF-IDF
document representations. Constraints are such that the components pursued are
made to be frequently occuring in a small set of labels only, making it
possible to yield document representations with distinctive label-specific
sparse activation patterns. A simple measure of quality of this kind of
sparsity structure, dubbed inter-label sparsity, is introduced and
experimentally brought into tight connection with classification performance.
Representing a great practical convenience, inter-label sparsity is shown to be
easily controlled in supervised vbNMF by a single parameter
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