Finding wombling boundaries in LHC data with Voronoi and Delaunay tessellations

Matchev, Konstantin T.; Roman, Alexander; Shyamsundar, Prasanth

doi:10.1007/jhep12(2020)137

Title: Finding wombling boundaries in LHC data with Voronoi and Delaunay tessellations

Abstract

We address the problem of finding a wombling boundary in point data generated by a general Poisson point process, a specific example of which is an LHC event sample distributed in the phase space of a final state signature, with the wombling boundary created by some new physics. We discuss the use of Voronoi and Delaunay tessellations of the point data for estimating the local gradients and investigate methods for sharpening the boundaries by reducing the statistical noise. The outcome from traditional wombling algorithms is a set of boundary cell candidates with relatively large gradients, whose spatial properties must then be scrutinized in order to construct the boundary and evaluate its significance. Here we propose an alternative approach where we simultaneously form and evaluate the significance of all possible boundaries in terms of the total gradient flux. We illustrate our method with several toy examples of both straight and curved boundaries with varying amounts of signal present in the data.

Authors:

Matchev, Konstantin T. ^[1]; Roman, Alexander ^[1];

^[1]

Univ. of Florida, Gainesville, FL (United States)

Publication Date:: Mon Dec 21 00:00:00 EST 2020

Research Org.:: Univ. of Florida, Gainesville, FL (United States)

Sponsoring Org.:: USDOE Office of Science (SC); LHC Physics Center; Charles Vincent and Heidi Cole McLaughlin Endowment

OSTI Identifier:: 1851347

Grant/Contract Number:: SC0010296

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 12; Journal ID: ISSN 1029-8479

Publisher:: Springer Nature

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; supersymmetry phenomenology

Citation Formats


                    Matchev, Konstantin T., Roman, Alexander, and Shyamsundar, Prasanth. Finding wombling boundaries in LHC data with Voronoi and Delaunay tessellations.  United States: N. p., 2020. 
Web.  doi:10.1007/jhep12(2020)137.

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                    Matchev, Konstantin T., Roman, Alexander, & Shyamsundar, Prasanth. Finding wombling boundaries in LHC data with Voronoi and Delaunay tessellations.  United States.  https://doi.org/10.1007/jhep12(2020)137

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                    Matchev, Konstantin T., Roman, Alexander, and Shyamsundar, Prasanth. Mon .  
"Finding wombling boundaries in LHC data with Voronoi and Delaunay tessellations".  United States.  https://doi.org/10.1007/jhep12(2020)137.  https://www.osti.gov/servlets/purl/1851347.

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@article{osti_1851347,

  title        = {Finding wombling boundaries in LHC data with Voronoi and Delaunay tessellations},

  author       = {Matchev, Konstantin T. and Roman, Alexander and Shyamsundar, Prasanth},

  abstractNote = {We address the problem of finding a wombling boundary in point data generated by a general Poisson point process, a specific example of which is an LHC event sample distributed in the phase space of a final state signature, with the wombling boundary created by some new physics. We discuss the use of Voronoi and Delaunay tessellations of the point data for estimating the local gradients and investigate methods for sharpening the boundaries by reducing the statistical noise. The outcome from traditional wombling algorithms is a set of boundary cell candidates with relatively large gradients, whose spatial properties must then be scrutinized in order to construct the boundary and evaluate its significance. Here we propose an alternative approach where we simultaneously form and evaluate the significance of all possible boundaries in terms of the total gradient flux. We illustrate our method with several toy examples of both straight and curved boundaries with varying amounts of signal present in the data.},

  doi          = {10.1007/jhep12(2020)137},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 12,

  volume       = 2020,

  place        = {United States},

  year         = {Mon Dec 21 00:00:00 EST 2020},

  month        = {Mon Dec 21 00:00:00 EST 2020}

}

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Title: Finding wombling boundaries in LHC data with Voronoi and Delaunay tessellations

Abstract

Citation Formats

Generalized Wombling journal, September 1994

A Supersymmetry Primer book, April 2010

QCD or what? journal, January 2019

Edge Detection Algorithms for Two-Dimensional Ecological Data journal, August 1993

Least squares quantization in PCM journal, March 1982

The map comparison problem: Tests for the overlap of geographic boundaries journal, November 1995

Differential Systematics journal, September 1951

Singular ways to search for the Higgs boson journal, June 2012

Adversarially-trained autoencoders for robust unsupervised new physics searches journal, October 2019

Singularity variables for missing energy event kinematics journal, April 2020

FastJet user manual: (for version 3.0.2) journal, March 2012

A generic anti-QCD jet tagger journal, November 2017

Categorical Wombling: Detecting Regions of Significant Change in Spatially Located Categorical Variables journal, October 1993

Uncovering latent jet substructure journal, September 2019

Anomaly detection with density estimation journal, April 2020

Systematic analysis of HEP collider data journal, November 2004

Extending the search for new resonances with machine learning journal, January 2019

Discoveries far from the lamppost with matrix elements and ranking journal, April 2015

Supersymmetric particle mass measurement with invariant mass correlations journal, April 2009

Delineation of Ecological Boundaries: Comparison of Approaches and Significance Tests journal, April 1995

Novelty detection meets collider physics journal, April 2020

Improved mass measurement using the boundary of many-body phase space journal, January 2014

From fields to objects: A review of geographic boundary analysis journal, September 2000

Algebraic Singularity Method for Mass Measurements with Missing Energy journal, February 2010

Effects of data types on vegetation boundary delineation journal, November 1997

Two Dimensional Interpolation from Random Data journal, May 1976

Classification without labels: learning from mixed samples in high energy physics journal, October 2017

Variational autoencoders for new physics mining at the Large Hadron Collider journal, May 2019

Anomaly Detection for Resonant New Physics with Machine Learning journal, December 2018

Identifying phase-space boundaries with Voronoi tessellations journal, November 2016

Guiding new physics searches with unsupervised learning journal, March 2019

Searching for new physics with deep autoencoders journal, April 2020

Distribution of Cell Area in Bounded Poisson Voronoi Tessellations with Application to Secure Local Connectivity journal, June 2019

Edge detecting new physics the Voronoi way journal, May 2016

Bayesian wombling: finding rapid change in spatial maps: Bayesian wombling journal, August 2015

Measuring the W-Boson mass at a hadron collider: a study of phase-space singularity methods journal, August 2011

Bayesian Wombling: Curvilinear Gradient Assessment Under Spatial Process Models journal, December 2006

Machine Learning in High Energy Physics Community White Paper journal, September 2018

Multidimensional phase space methods for mass measurements and decay topology determination journal, January 2017

From Graphs to Spatial Graphs journal, December 2010

Estimation of gradients from scattered data journal, March 1984

Singular ways to search for the Higgs boson text, January 2012

Generalized Wombling
journal, September 1994

A Supersymmetry Primer
book, April 2010

QCD or what?
journal, January 2019

Edge Detection Algorithms for Two-Dimensional Ecological Data
journal, August 1993

Least squares quantization in PCM
journal, March 1982

The map comparison problem: Tests for the overlap of geographic boundaries
journal, November 1995

Differential Systematics
journal, September 1951

Singular ways to search for the Higgs boson
journal, June 2012

Adversarially-trained autoencoders for robust unsupervised new physics searches
journal, October 2019

Singularity variables for missing energy event kinematics
journal, April 2020

FastJet user manual: (for version 3.0.2)
journal, March 2012

A generic anti-QCD jet tagger
journal, November 2017

Categorical Wombling: Detecting Regions of Significant Change in Spatially Located Categorical Variables
journal, October 1993

Uncovering latent jet substructure
journal, September 2019

Anomaly detection with density estimation
journal, April 2020

Systematic analysis of HEP collider data
journal, November 2004

Extending the search for new resonances with machine learning
journal, January 2019

Discoveries far from the lamppost with matrix elements and ranking
journal, April 2015

Supersymmetric particle mass measurement with invariant mass correlations
journal, April 2009

Delineation of Ecological Boundaries: Comparison of Approaches and Significance Tests
journal, April 1995

Novelty detection meets collider physics
journal, April 2020

Improved mass measurement using the boundary of many-body phase space
journal, January 2014

From fields to objects: A review of geographic boundary analysis
journal, September 2000

Algebraic Singularity Method for Mass Measurements with Missing Energy
journal, February 2010

Effects of data types on vegetation boundary delineation
journal, November 1997

Two Dimensional Interpolation from Random Data
journal, May 1976

Classification without labels: learning from mixed samples in high energy physics
journal, October 2017

Variational autoencoders for new physics mining at the Large Hadron Collider
journal, May 2019

Anomaly Detection for Resonant New Physics with Machine Learning
journal, December 2018

Identifying phase-space boundaries with Voronoi tessellations
journal, November 2016

Guiding new physics searches with unsupervised learning
journal, March 2019

Searching for new physics with deep autoencoders
journal, April 2020

Distribution of Cell Area in Bounded Poisson Voronoi Tessellations with Application to Secure Local Connectivity
journal, June 2019

Edge detecting new physics the Voronoi way
journal, May 2016

Bayesian wombling: finding rapid change in spatial maps: Bayesian wombling
journal, August 2015

Measuring the W-Boson mass at a hadron collider: a study of phase-space singularity methods
journal, August 2011

Bayesian Wombling: Curvilinear Gradient Assessment Under Spatial Process Models
journal, December 2006

Machine Learning in High Energy Physics Community White Paper
journal, September 2018

Multidimensional phase space methods for mass measurements and decay topology determination
journal, January 2017

From Graphs to Spatial Graphs
journal, December 2010

Estimation of gradients from scattered data
journal, March 1984

Singular ways to search for the Higgs boson
text, January 2012