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    Deconvolution When Classifying Noisy Data Involving Transformations

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    Type
    Article
    Authors
    Carroll, Raymond
    Delaigle, Aurore
    Hall, Peter
    Date
    2012-10-08
    Online Publication Date
    2012-10-08
    Print Publication Date
    2012-09
    Permanent link to this record
    http://hdl.handle.net/10754/597922
    
    Metadata
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    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.
    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.
    Publisher
    Informa UK Limited
    Journal
    Journal of the American Statistical Association
    DOI
    10.1080/01621459.2012.699793
    PubMed ID
    23606778
    PubMed Central ID
    PMC3630802
    ae974a485f413a2113503eed53cd6c53
    10.1080/01621459.2012.699793
    Scopus Count
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