Estimating the intrinsic dimension of datasets by a minimal neighborhood information

Facco, Elena; D’Errico, M.; Rodríguez, Álex; Laio, Alessandro

doi:10.1038/s41598-017-11873-y

Cited by 225 publications

(314 citation statements)

References 22 publications

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“…On the other hand, the dynamics of typical biomolecular systems such as proteins evolves in a high-dimensional phase space with an effective dimension that has been estimated to be between 5 and 10 (given optimal collective coordinates x i that are usually not known). [44][45][46] Hence, even for appropriate dimensionality reduction and large data sets (N ∼ 10 7 ), the problem outlined in Fig. 1 is hard to avoid.…”

Section: Introductionmentioning

confidence: 99%

Dynamical coring of Markov state models

Nagel

Weber

Lickert

et al. 2019

The Journal of Chemical Physics

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The accurate definition of suitable metastable conformational states is fundamental for the construction of a Markov state model describing biomolecular dynamics. Following the dimensionality reduction of a molecular dynamics trajectory, these microstates can be generated by a recently proposed density-based geometrical clustering algorithm [J. Chem. Theory Comput. 12, 2426 (2016)], which by design cuts the resulting clusters at the energy barriers and allows for a data-based identification of all parameters. Nevertheless, projection artifacts due to the inevitable restriction to a low-dimensional space combined with insufficient sampling often leads to a misclassification of sampled points in the transition regions. This typically causes intrastate fluctuations to be mistaken as interstate transitions, which leads to artificially short life time of the metastable states. As a simple but effective remedy, dynamical coring requires that the trajectory spends a minimum time in the new state for the transition to be counted. Adopting molecular dynamics simulations of two well-established biomolecular systems (alanine dipeptide and villin headpiece), dynamical coring is shown to considerably improve the Markovianity of the resulting metastable states, which is demonstrated by Chapman-Kolmogorov tests and increased implied timescales of the Markov model. Providing high structural and temporal resolution, the combination of density-based clustering and dynamical coring is particularly suited to describe the complex structural dynamics of unfolded biomolecules.

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Section: Introductionmentioning

confidence: 99%

Dynamical coring of Markov state models

Nagel

Weber

Lickert

et al. 2019

The Journal of Chemical Physics

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“…We have 1 + δ 2 + (1 + δ 2 ) 2 − 1 ≥ 1 + √ 2δ, which leads to where we have used concavity of the log and the fact that 1 + √ 2 ≥ 2. It follows by combining (20), (21), (22) and (23), that Q : y → R( y 2 ) satisfies the claimed properties.…”

Section: Lemma 16mentioning

confidence: 77%

Data Analysis from Empirical Moments and the Christoffel Function

2020

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Spectral features of the empirical moment matrix constitute a resourceful tool for unveiling properties of a cloud of points, among which, density, support and latent structures. It is already well known that the empirical moment matrix encodes a great deal of subtle attributes of the underlying measure. Starting from this object as base of observations we combine ideas from statistics, real algebraic geometry, orthogonal polynomials and approximation theory for opening new insights relevant for Machine Learning (ML) problems with data supported on singular sets. Refined concepts and results from real algebraic geometry and approximation theory are empowering a simple tool (the empirical moment matrix) for the task of solving non-trivial questions in data analysis. We provide (1) theoretical support, (2) numerical experiments and, (3) connections to real world data as a validation of the stamina of the empirical moment matrix approach.

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“…where d is the intrinsic dimension (ID) of the dataset 46 , is the volume of the d-sphere with unitary radius and , is the distance of point i from its k-th nearest neighbor. In DPC it is the density rank which is relevant for the final cluster assignation.…”

Section: Block 4: Density Peak Clusteringmentioning

confidence: 99%

Unfolding and identification of membrane proteins in situ

Galvanetto

Maity

Ilieva

et al. 2019

Preprint

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Is the mechanical unfolding of proteins just a technological feat applicable only to synthetic preparations or is it applicable to real biological samples? Here, we describe a method providing all the necessary steps to deal with native membranes, from the isolation of the plasma membrane of single cells, to the characterization and identification of the embedded membrane proteins. We combined single-molecule force spectroscopy with an automatic pattern classification of the obtained Force-distance curves, and we provide a Bayesian identification of the unfolded proteins. The Bayesian identification is based on the crossmatching of Mass Spectrometry datasets with proteomic databases (Uniprot, PDB). We applied this method to four cell types where we classified the unfolding of 5-10% of their total content of membrane proteins. The ability to mechanically probe membrane proteins directly in their native membrane enables the phenotyping of different cell types with almost singlecell level of resolution.

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Estimating the intrinsic dimension of datasets by a minimal neighborhood information

Cited by 225 publications

References 22 publications

Dynamical coring of Markov state models

Dynamical coring of Markov state models

Data Analysis from Empirical Moments and the Christoffel Function

Unfolding and identification of membrane proteins in situ

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