Distance geometry and data science

Liberti, Leo

doi:10.1007/s11750-020-00563-0

Cited by 25 publications

(8 citation statements)

References 142 publications

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“…In addition to the rich mathematical theory of DG, it has diverse applications which includes astronomy, biochemistry, data science, nanotechnology, robotics, and telecommunications 20–24 . Recent surveys on DG highlighting the theory and applications can be found in References 15, 25, and 26.…”

Section: A Dg Approachmentioning

confidence: 99%

Distance geometry and protein loop modeling

Labiak

Souza

2021

J Comput Chem

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Due to the role of loops in protein function, loop modeling is an important problem in computational biology. We present a new approach to loop modeling based on a combinatorial version of distance geometry, where the search space of the associated problem is represented by a binary tree and a branch‐and‐prune method is defined to explore it, following an atomic ordering previously given. This ordering is used to calculate the coordinates of atoms from the positions of its predecessors. In addition to the theoretical development, computational results are presented to illustrate the advantage of the proposed method, compared with another approach of the literature. Our algorithm is freely available at https://github.com/michaelsouza/bpl.

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Section: A Dg Approachmentioning

confidence: 99%

Distance geometry and protein loop modeling

Labiak

Souza

2021

J Comput Chem

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“…( 2018 ), Gambella et al. ( 2020 ), Liberti ( 2020 ) for surveys reviewing the use of Mathematical Optimization in Machine Learning, and Carrizosa and Romero Morales ( 2013 ), Duarte Silva ( 2017 ), Palagi ( 2019 ), and Piccialli and Sciandrone ( 2018 ) for surveys focusing on specific methodologies.…”

Section: Introductionmentioning

confidence: 99%

Mathematical optimization in classification and regression trees

Carrizosa

Molero-Río

Morales

2021

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Classification and regression trees, as well as their variants, are off-the-shelf methods in Machine Learning. In this paper, we review recent contributions within the Continuous Optimization and the Mixed-Integer Linear Optimization paradigms to develop novel formulations in this research area. We compare those in terms of the nature of the decision variables and the constraints required, as well as the optimization algorithms proposed. We illustrate how these powerful formulations enhance the flexibility of tree models, being better suited to incorporate desirable properties such as cost-sensitivity, explainability, and fairness, and to deal with complex data, such as functional data.

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“…There are many applications of Distance Geometry, mainly related to K ∈ {1, 2, 3} [3,4,27]. An application to Data Science can be found in [16], and a very recent survey on this subject is [15]. An important class of the DGP arises in the context of 3D protein structure calculations (K = 3), with distance information provided by Nuclear Magnetic Resonance (NMR) experiments [6,24,31].…”

Section: Introductionmentioning

confidence: 99%

A New Algorithm for the $$^K$$DMDGP Subclass of Distance Geometry Problems with Exact Distances

2021

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The fundamental inverse problem in distance geometry is the one of finding positions from inter-point distances. The Discretizable Molecular Distance Geometry Problem (DMDGP) is a subclass of the Distance Geometry Problem (DGP) whose search space can be discretized and represented by a binary tree, which can be explored by a Branch-and-Prune (BP) algorithm. It turns out that this combinatorial search space possesses many interesting symmetry properties that were studied in the last decade. In this paper, we present a new algorithm for this subclass of the DGP, which exploits DMDGP symmetries more effectively than its predecessors. Computational results show that the speedup, with respect to the classic BP algorithm, is considerable for sparse DMDGP instances related to protein conformation.

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Distance geometry and data science

Cited by 25 publications

References 142 publications

Distance geometry and protein loop modeling

Distance geometry and protein loop modeling

Mathematical optimization in classification and regression trees

A New Algorithm for the $$^K$$DMDGP Subclass of Distance Geometry Problems with Exact Distances

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