Journal ArticleDOI
Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification
Susanna Röblitz,Marcus Weber +1 more
TLDR
It is demonstrated in this paper that PCCA+ always delivers an optimal fuzzy clustering for nearly uncoupled, not necessarily reversible, Markov chains with transition states.Abstract:
Given a row-stochastic matrix describing pairwise similarities between data objects, spectral clustering makes use of the eigenvectors of this matrix to perform dimensionality reduction for clustering in fewer dimensions. One example from this class of algorithms is the Robust Perron Cluster Analysis (PCCA+), which delivers a fuzzy clustering. Originally developed for clustering the state space of Markov chains, the method became popular as a versatile tool for general data classification problems. The robustness of PCCA+, however, cannot be explained by previous perturbation results, because the matrices in typical applications do not comply with the two main requirements: reversibility and nearly decomposability. We therefore demonstrate in this paper that PCCA+ always delivers an optimal fuzzy clustering for nearly uncoupled, not necessarily reversible, Markov chains with transition states.read more
Citations
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Improving Estimation of the Koopman Operator with Kolmogorov-Smirnov Indicator Functions
TL;DR: In this article , a simple and computationally efficient clustering procedure is proposed to infer surrogate observables that form a good basis for slow modes, which can significantly improve the estimation of the leading eigenvalues of the Koopman operators and correctly identify key states and transition timescales of stochastic systems.
Journal ArticleDOI
Is Posttranslational Folding More Efficient Than Refolding from a Denatured State: A Computational Study
TL;DR: The authors used coarse-grained molecular dynamics simulations to compare the mechanisms by which the proteins dihydrofolate reductase, type III chloramphenicol acetyltransferase, and d-alanine-dalanine ligase B fold during and after vectorial synthesis on the ribosome.
Posted ContentDOI
Macrophage phenotype transitions in a stochastic gene-regulatory network model
TL;DR: A stochastic modeling approach for the macrophage polarization process that allows for a probabilistic interpretation of macrophages phenotype transitions and biological inference on phenotype robustness and can easily be adapted to other systems where random state switches are known to occur.
Book ChapterDOI
A Graphical Approach for the Selection of the Number of Clusters in the Spectral Clustering Algorithm
TL;DR: In this paper , a multi-graphic method was proposed to select the optimal number of clusters in the spectral clustering algorithm, which takes into account geometric characteristics derived from the similarity matrix and from the Laplacian embedding among data.
Journal ArticleDOI
Structural and Dynamical Properties of Elastin-Like Peptides near Their Lower Critical Solution Temperature
TL;DR: In this article , the authors investigate the role of intra-and interpeptide interactions in the formation of dynamical aggregates with coil-like conformation, in which valine central residues play an important role.
References
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Normalized cuts and image segmentation
Jianbo Shi,Jitendra Malik +1 more
TL;DR: This work treats image segmentation as a graph partitioning problem and proposes a novel global criterion, the normalized cut, for segmenting the graph, which measures both the total dissimilarity between the different groups as well as the total similarity within the groups.
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A tutorial on spectral clustering
TL;DR: In this article, the authors present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches, and discuss the advantages and disadvantages of these algorithms.
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On Spectral Clustering: Analysis and an algorithm
TL;DR: A simple spectral clustering algorithm that can be implemented using a few lines of Matlab is presented, and tools from matrix perturbation theory are used to analyze the algorithm, and give conditions under which it can be expected to do well.
Journal ArticleDOI
Laplacian Eigenmaps for dimensionality reduction and data representation
Mikhail Belkin,Partha Niyogi +1 more
TL;DR: In this article, the authors proposed a geometrically motivated algorithm for representing high-dimensional data, based on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold and the connections to the heat equation.