Deconvolution When Classifying Noisy Data Involving Transformations

Handle URI:
http://hdl.handle.net/10754/597922
Title:
Deconvolution When Classifying Noisy Data Involving Transformations
Authors:
Carroll, Raymond; Delaigle, Aurore; Hall, Peter
Abstract:
In the present study, we consider the problem of classifying spatial data distorted by a linear transformation or convolution and contaminated by additive random noise. In this setting, we show that classifier performance can be improved if we carefully invert the data before the classifier is applied. However, the inverse transformation is not constructed so as to recover the original signal, and in fact, we show that taking the latter approach is generally inadvisable. We introduce a fully data-driven procedure based on cross-validation, and use several classifiers to illustrate numerical properties of our approach. Theoretical arguments are given in support of our claims. Our procedure is applied to data generated by light detection and ranging (Lidar) technology, where we improve on earlier approaches to classifying aerosols. This article has supplementary materials online.
Citation:
Carroll R, Delaigle A, Hall P (2012) Deconvolution When Classifying Noisy Data Involving Transformations. Journal of the American Statistical Association 107: 1166–1177. Available: http://dx.doi.org/10.1080/01621459.2012.699793.
Publisher:
Informa UK Limited
Journal:
Journal of the American Statistical Association
Issue Date:
Sep-2012
DOI:
10.1080/01621459.2012.699793
PubMed ID:
23606778
PubMed Central ID:
PMC3630802
Type:
Article
ISSN:
0162-1459; 1537-274X
Sponsors:
Raymond Carroll is Head, Department of Statistics, Texas A&M University, College Station, TX 77843-3143 (E-mail: carroll@stat.tamu.edu). Aurore Delaigle is Associate Professor (E-mail: a.delaigle@ms.unimelb.edu.au) and Peter Hall is Professor (E-mail: halpstat@ms.unimelb.edu.au), Department of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia. Carroll's research was supported by a grant from the National Cancer Institute (R37-CA057030) and in part by award number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST) and by the National Science Foundation (DMS-0914951). Delaigle's research was supported by grants and a Queen Elizabeth II Fellowship from the Australian Research Council, and Hall's research was supported by a Federation Fellowship, a Laureate Fellowship, and grants from the Australian Research Council.
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Full metadata record

DC FieldValue Language
dc.contributor.authorCarroll, Raymonden
dc.contributor.authorDelaigle, Auroreen
dc.contributor.authorHall, Peteren
dc.date.accessioned2016-02-25T12:58:56Zen
dc.date.available2016-02-25T12:58:56Zen
dc.date.issued2012-09en
dc.identifier.citationCarroll R, Delaigle A, Hall P (2012) Deconvolution When Classifying Noisy Data Involving Transformations. Journal of the American Statistical Association 107: 1166–1177. Available: http://dx.doi.org/10.1080/01621459.2012.699793.en
dc.identifier.issn0162-1459en
dc.identifier.issn1537-274Xen
dc.identifier.pmid23606778en
dc.identifier.doi10.1080/01621459.2012.699793en
dc.identifier.urihttp://hdl.handle.net/10754/597922en
dc.description.abstractIn the present study, we consider the problem of classifying spatial data distorted by a linear transformation or convolution and contaminated by additive random noise. In this setting, we show that classifier performance can be improved if we carefully invert the data before the classifier is applied. However, the inverse transformation is not constructed so as to recover the original signal, and in fact, we show that taking the latter approach is generally inadvisable. We introduce a fully data-driven procedure based on cross-validation, and use several classifiers to illustrate numerical properties of our approach. Theoretical arguments are given in support of our claims. Our procedure is applied to data generated by light detection and ranging (Lidar) technology, where we improve on earlier approaches to classifying aerosols. This article has supplementary materials online.en
dc.description.sponsorshipRaymond Carroll is Head, Department of Statistics, Texas A&M University, College Station, TX 77843-3143 (E-mail: carroll@stat.tamu.edu). Aurore Delaigle is Associate Professor (E-mail: a.delaigle@ms.unimelb.edu.au) and Peter Hall is Professor (E-mail: halpstat@ms.unimelb.edu.au), Department of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia. Carroll's research was supported by a grant from the National Cancer Institute (R37-CA057030) and in part by award number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST) and by the National Science Foundation (DMS-0914951). Delaigle's research was supported by grants and a Queen Elizabeth II Fellowship from the Australian Research Council, and Hall's research was supported by a Federation Fellowship, a Laureate Fellowship, and grants from the Australian Research Council.en
dc.publisherInforma UK Limiteden
dc.subjectFourier transformen
dc.subjectcross-validationen
dc.subjectSpatial Dataen
dc.subjectCentroid Classifieren
dc.subjectInverse Transformen
dc.titleDeconvolution When Classifying Noisy Data Involving Transformationsen
dc.typeArticleen
dc.identifier.journalJournal of the American Statistical Associationen
dc.identifier.pmcidPMC3630802en
dc.contributor.institutionDepartment of Statistics, Texas A&M University, College Station, TX 77843-3143.en
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