Related papers: Validation of non-negative matrix factorization fo…
We discuss the statistical properties of parton distributions within the framework of the NNPDF methodology. We present various tests of statistical consistency, in particular that the distribution of results does not depend on the…
Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being…
Non-negative Matrix Factorization (NMF) is an intensively used technique for obtaining parts-based, lower dimensional and non-negative representation. Researchers in biology, medicine, pharmacy and other fields often prefer NMF over other…
We present a determination of the parton distribution functions (PDFs) of the proton from HERA data using a PDF parametrization inspired by a quantum statistical model of the proton dynamics. This parametrization is characterised by a very…
As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…
Using nonnegative/binary matrix factorization (NBMF), a matrix can be decomposed into a nonnegative matrix and a binary matrix. Our analysis of facial images, based on NBMF and using the Fujitsu Digital Annealer, leads to successful image…
Kernel principal component analysis (KPCA) provides a concise set of basis vectors which capture non-linear structures within large data sets, and is a central tool in data analysis and learning. To allow for non-linear relations, typically…
Non-negative matrix factorization (NMF) is a common method for generating topic models from text data. NMF is widely accepted for producing good results despite its relative simplicity of implementation and ease of computation. One…
Non-negative matrix factorization (NMF) is an important technique for obtaining low dimensional representations of datasets. However, classical NMF does not take into account data that is collected at different times or in different…
Nonnegative matrix factorization (NMF) is an emerging technique with a wide spectrum of potential applications in data analysis. Mathematically, NMF can be formulated as a minimization problem with nonnegative constraints. This problem is…
A "meta-analysis" is a method for comparison and combination of nonperturbative parton distribution functions (PDFs) in a nucleon obtained with heterogeneous procedures and assumptions. Each input parton distribution set is converted into a…
It is NP-complete to find non-negative factors $W$ and $H$ with fixed rank $r$ from a non-negative matrix $X$ by minimizing $\|X-WH^\top\|_F^2$. Although the separability assumption (all data points are in the conical hull of the extreme…
We discuss a test of the generalization power of the methodology used in the determination of parton distribution functions (PDFs). The "future test" checks whether the uncertainty on PDFs, in regions in which they are not constrained by…
The xPDFsuite software program is described. It is for processing and analyzing atomic pair distribution functions (PDF) from X-ray powder diffraction data. It provides a convenient GUI for SrXplanr and PDFgetX3, allowing the users to…
Beyond leading-order, perturbative QCD requires a choice of factorisation scheme to define the parton distribution functions (PDFs) and hard-process cross-section. The modified minimal-subtraction ($\overline{\mathrm{MS}}$) scheme has long…
Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…
We critically assess the robustness of uncertainties on parton distribution functions (PDFs) determined using neural networks from global sets of experimental data collected from multiple experiments. We view the determination of PDFs as an…
Calculations of the parton distribution function (PDF) and distribution amplitude (DA) are highly relevant to core experimental programs as they provide non-perturbative inputs to inclusive and exclusive processes, respectively. Direct…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides…