Using Separable Nonnegative Matrix Factorization Techniques for the Analysis of Time-Resolved Raman Spectra

Luce, Robert; Hildebrandt, Peter; Kuhlmann, Uwe; Liesen, Jörg

doi:10.1177/0003702816662600

Cited by 26 publications

(48 citation statements)

References 24 publications

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“…There are several applications to solving near-separable NMF, e.g., blind hyperspectral unmixing [5,26], topic modeling and document classification [22,2], video summarization and image classification [11], and blind source separation [8,9,25].…”

Section: Introductionmentioning

confidence: 99%

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

Gillis

Luce

2018

IEEE Trans. on Image Process.

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A nonnegative matrix factorization (NMF) can be computed efficiently under the , which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably most robust methods to identify these are based on nonnegative sparse regression and self-dictionaries, and require the solution of large-scale convex optimization problems. In this paper, we study a particular nonnegative sparse regression model with self-dictionary. As opposed to previously proposed models, this model yields a smooth optimization problem, where the sparsity is enforced through linear constraints. We show that the Euclidean projection on the polyhedron defined by these constraints can be computed efficiently, and propose a fast gradient method to solve our model. We compare our algorithm with several state-of-the-art methods on synthetic data sets and real-world hyperspectral images.A nonnegative matrix factorization (NMF) can be computed efficiently under the , which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably most robust methods to identify these are based on nonnegative sparse regression and self-dictionaries, and require the solution of large-scale convex optimization problems. In this paper, we study a particular nonnegative sparse regression model with self-dictionary. As opposed to previously proposed models, this model yields a smooth optimization problem, where the sparsity is enforced through linear constraints. We show that the Euclidean projection on the polyhedron defined by these constraints can be computed efficiently, and propose a fast gradient method to solve our model. We compare our algorithm with several state-of-the-art methods on synthetic data sets and real-world hyperspectral images.

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Section: Introductionmentioning

confidence: 99%

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

Gillis

Luce

2018

IEEE Trans. on Image Process.

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“…, v n ∈ R d . Depending on the ratio (concentration) of components of the mixture in each of the n states, the weights of this convex combination are changing over time [46]. The time-dependent measured signal is:…”

Section: Sequential Spectroscopymentioning

confidence: 99%

Implications of PCCA+ in Molecular Simulation

Weber

2018

Computation

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Upon ligand binding or during chemical reactions the state of a molecular system changes in time. Usually we consider a finite set of (macro-) states of the system (e.g., 'bound' vs. 'unbound'), although the process itself takes place in a continuous space. In this context, the formula χ = XA connects the micro-dynamics of the molecular system to its macro-dynamics. χ can be understood as a clustering of micro-states of a molecular system into a few macro-states. X is a basis of an invariant subspace of a transfer operator describing the micro-dynamics of the system. The formula claims that there is an unknown linear relation A between these two objects. With the aid of this formula we can understand rebinding effects, the electron flux in pericyclic reactions, and systematic changes of binding rates in kinetic ITC experiments. We can also analyze sequential spectroscopy experiments and rare event systems more easily. This article provides an explanation of the formula and an overview of some of its consequences.Keywords: Robust Perron Cluster Analysis; membership function; invariant subspace. MSC: 60J22 The Foundation of PCCA+Molecular simulation is used as a tool to estimate thermodynamical properties. Moreover, it could be used for investigation of molecular processes and their time scales. In computational drug design, e.g., binding affinities of ligand-receptor systems are estimated. In this case, trajectories in a 3N-dimensional space Ω of molecular conformations (N is the number of atoms) are generated. They will be denoted as micro-states x ∈ Ω in the following. After simulation the micro-states are classified as "bound" or "unbound". This classification can be achieved by projecting the state space Ω onto a low number n of macro-states of the system. Spectral clustering algorithms are one possible method in this context. Robust Perron Cluster Analysis (PCCA+) turned out to be a commonly used practical tool for this algorithmic step [1].Conformation Dynamics has been established in the late 1990s. From molecular simulations [2] transition matrices P ∈ R m×m were derived. The entries of P represent conditional transition probabilities between pre-defined m subsets of the state space Ω of a molecular process. Today P would be denoted as Markov State Model. According to the transfer operator theory and PCCA [3] the eigenvectors of these matrices were studied in the early 2000s leading to an empirical observation [4] and Figure 1: Given a matrix X ∈ R m×n of the n m leading eigenvectors of the m × m-transition matrix P, the m rows of X -plotted as n-dimensional points -seem to always form an (n − 1)-simplex. Some of those m points are located at the vertices of the simplices, other points are located on the edges. The points which are located at the n vertices of these simplices represent the thermodynamically stable conformations of the molecular systems. Whereas, the points which are located on the edges of the simplices represent transition regions. In order to transform the (n − 1)-simplex σ 1 ...

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“…2, we give an overview of NMF approaches and algorithms known so far. In particular we present the separable NMF method, which found application in the approach for spectral analysis in [5]. Our new NMF approach, as well as the algorithmic details of the corresponding computational method, are introduced in Sect.…”

Section: Introductionmentioning

confidence: 99%

Analyzing Raman spectral data without separabiliy assumption

et al. 2021

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Raman spectroscopy is a well established tool for the analysis of vibration spectra, which then allow for the determination of individual substances in a chemical sample, or for their phase transitions. In the time-resolved-Raman-sprectroscopy the vibration spectra of a chemical sample are recorded sequentially over a time interval, such that conclusions for intermediate products (transients) can be drawn within a chemical process. The observed data-matrix M from a Raman spectroscopy can be regarded as a matrix product of two unknown matrices W and H, where the first is representing the contribution of the spectra and the latter represents the chemical spectra. One approach for obtaining W and H is the non-negative matrix factorization. We propose a novel approach, which does not need the commonly used separability assumption. The performance of this approach is shown on a real world chemical example.

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Using Separable Nonnegative Matrix Factorization Techniques for the Analysis of Time-Resolved Raman Spectra

Cited by 26 publications

References 24 publications

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

Implications of PCCA+ in Molecular Simulation

Analyzing Raman spectral data without separabiliy assumption

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