Macrostate data clustering

Korenblum, Daniel; Shalloway, David

doi:10.1103/physreve.67.056704

Cited by 10 publications

(26 citation statements)

References 23 publications

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“…The macrostate data clustering algorithm is an earlier formulation developed in [37,41]. Detailed comparisons between the two formulations are not included here because the previous methods required customized algorithm implementations that limited their practicality.…”

Section: Previous Formulationsmentioning

confidence: 99%

“…Another difference is that in [37,41] only unbounded inverse quadratic similarity measures and soft Gaussian thresholds that do not directly control sparsity were tested. Here, other choices of similarity/distance measures are tested and the use of hard thresholding is examined to directly control sparsity of the resulting Laplacian matrix used as the primary input into the algorithm.…”

Section: Previous Formulationsmentioning

confidence: 99%

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Laplacian mixture modeling for network analysis and unsupervised learning on graphs

Korenblum¹

2018

PLoS ONE

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Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.

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Section: Previous Formulationsmentioning

confidence: 99%

Section: Previous Formulationsmentioning

confidence: 99%

Laplacian mixture modeling for network analysis and unsupervised learning on graphs

Korenblum¹

2018

PLoS ONE

Self Cite

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“…A related approach was developed by Shalloway and his group. See Orešič and Shalloway [1994], Church et al [1996], Shalloway [1996], Ulitsky and Shalloway [1998], Korenblum and Shalloway [2003]. Church et al [1999] review these methods.…”

Section: Perron Cluster Cluster Analysismentioning

confidence: 99%

Computing Reaction Rates in Bio-molecular Systems Using Discrete Macro-states

Darve

Ryu²

2012

Innovations in Biomolecular Modeling and Simulations

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We discuss different techniques to calculate reaction rates in biomolecular systems. We first review historically the first approaches based on reactive flux, which make certain simplifying assumptions in order to derive relatively simple formulas to estimate rates. Then we discuss a series of methods that attempt to do a more direct calculation based on path sampling, and related techniques such as transition interface sampling, forward flux sampling, and milestoning. Another set of approaches is based on the concept of metastability and includes techniques like conformational dynamics and recently developed methods such as Markov state models that are based on these concepts. Some recent methods attempt to combine the macro-state division of space used in Markov state models with transition path sampling in order to deal with systems exhibiting long memory, for which Markovian models are not sufficiently accurate. Such methods include weighted ensemble Brownian dynamics and non-equilibrium umbrella sampling. Finally, we include a numerical analysis of Markov state models to understand systematic and statistical errors and their behavior, along with some numerical benchmarks to illustrate the results.

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“…The method is modified by incorporating pre-and post-smoothing steps as proposed in abstract operator notation in [5][6][7][8][9]. It is to be noted that this method is different from other methods such as hierarchical reduction [11], lumping [12,13] or aggregation into macrostates [14][15][16] as it does not require the states of the aggregation groups to preserve Markovian character or be kinetically related.…”

Section: Introductionmentioning

confidence: 99%

An iterative aggregation and disaggregation method for the steady state solution of large scale continuous systems

Biswas

2015

Computer Physics Communications

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Macrostate data clustering

Cited by 10 publications

References 23 publications

Laplacian mixture modeling for network analysis and unsupervised learning on graphs

Laplacian mixture modeling for network analysis and unsupervised learning on graphs

Computing Reaction Rates in Bio-molecular Systems Using Discrete Macro-states

An iterative aggregation and disaggregation method for the steady state solution of large scale continuous systems

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