Distance-based classifier by data transformation for high-dimension, strongly spiked eigenvalue models
Author
Abstract
Suggested Citation
DOI: 10.1007/s10463-018-0655-z
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Peter Hall & J. S. Marron & Amnon Neeman, 2005. "Geometric representation of high dimension, low sample size data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 427-444, June.
- Marron, J.S. & Todd, Michael J. & Ahn, Jeongyoun, 2007. "Distance-Weighted Discrimination," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1267-1271, December.
- Yata, Kazuyoshi & Aoshima, Makoto, 2013. "PCA consistency for the power spiked model in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 334-354.
- Jeongyoun Ahn & J. S. Marron, 2010. "The maximal data piling direction for discrimination," Biometrika, Biometrika Trust, vol. 97(1), pages 254-259.
- Yata, Kazuyoshi & Aoshima, Makoto, 2012. "Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 193-215.
- Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
- Makoto Aoshima & Kazuyoshi Yata, 2014. "A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 983-1010, October.
- Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
- Watanabe, Hiroki & Hyodo, Masashi & Seo, Takashi & Pavlenko, Tatjana, 2015. "Asymptotic properties of the misclassification rates for Euclidean Distance Discriminant rule in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 234-244.
- Peter Hall & Yvonne Pittelkow & Malay Ghosh, 2008. "Theoretical measures of relative performance of classifiers for high dimensional data with small sample sizes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 159-173, February.
- Yata, Kazuyoshi & Aoshima, Makoto, 2010. "Effective PCA for high-dimension, low-sample-size data with singular value decomposition of cross data matrix," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2060-2077, October.
- Enrico Glaab & Jaume Bacardit & Jonathan M Garibaldi & Natalio Krasnogor, 2012. "Using Rule-Based Machine Learning for Candidate Disease Gene Prioritization and Sample Classification of Cancer Gene Expression Data," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-18, July.
- Yao-Ban Chan & Peter Hall, 2009. "Scale adjustments for classifiers in high-dimensional, low sample size settings," Biometrika, Biometrika Trust, vol. 96(2), pages 469-478.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Yugo Nakayama & Kazuyoshi Yata & Makoto Aoshima, 2020. "Bias-corrected support vector machine with Gaussian kernel in high-dimension, low-sample-size settings," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1257-1286, October.
- Liebscher, Eckhard & Okhrin, Ostap, 2023. "Semiparametric estimation of the high-dimensional elliptical distribution," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
- Ishii, Aki & Yata, Kazuyoshi & Aoshima, Makoto, 2022. "Geometric classifiers for high-dimensional noisy data," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
- Aki Ishii & Kazuyoshi Yata & Makoto Aoshima, 2021. "Hypothesis tests for high-dimensional covariance structures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 599-622, June.
- Nakagawa, Tomoyuki & Watanabe, Hiroki & Hyodo, Masashi, 2021. "Kick-one-out-based variable selection method for Euclidean distance-based classifier in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
- Nakayama, Yugo & Yata, Kazuyoshi & Aoshima, Makoto, 2021. "Clustering by principal component analysis with Gaussian kernel in high-dimension, low-sample-size settings," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Ishii, Aki & Yata, Kazuyoshi & Aoshima, Makoto, 2022. "Geometric classifiers for high-dimensional noisy data," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
- Makoto Aoshima & Kazuyoshi Yata, 2014. "A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 983-1010, October.
- Yugo Nakayama & Kazuyoshi Yata & Makoto Aoshima, 2020. "Bias-corrected support vector machine with Gaussian kernel in high-dimension, low-sample-size settings," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1257-1286, October.
- Kazuyoshi Yata & Makoto Aoshima, 2020. "Geometric consistency of principal component scores for high‐dimensional mixture models and its application," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 899-921, September.
- Makoto Aoshima & Kazuyoshi Yata, 2019. "High-Dimensional Quadratic Classifiers in Non-sparse Settings," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 663-682, September.
- Yata, Kazuyoshi & Aoshima, Makoto, 2013. "PCA consistency for the power spiked model in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 334-354.
- Rauf Ahmad, M. & Pavlenko, Tatjana, 2018. "A U-classifier for high-dimensional data under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 269-283.
- Yata, Kazuyoshi & Aoshima, Makoto, 2013. "Correlation tests for high-dimensional data using extended cross-data-matrix methodology," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 313-331.
- Wang, Shao-Hsuan & Huang, Su-Yun & Chen, Ting-Li, 2020. "On asymptotic normality of cross data matrix-based PCA in high dimension low sample size," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
- Jonathan Gillard & Emily O’Riordan & Anatoly Zhigljavsky, 2023. "Polynomial whitening for high-dimensional data," Computational Statistics, Springer, vol. 38(3), pages 1427-1461, September.
- Wang, Shao-Hsuan & Huang, Su-Yun, 2022. "Perturbation theory for cross data matrix-based PCA," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
- Marron, J.S., 2017. "Big Data in context and robustness against heterogeneity," Econometrics and Statistics, Elsevier, vol. 2(C), pages 73-80.
- Niladri Roy Chowdhury & Dianne Cook & Heike Hofmann & Mahbubul Majumder & Eun-Kyung Lee & Amy Toth, 2015. "Using visual statistical inference to better understand random class separations in high dimension, low sample size data," Computational Statistics, Springer, vol. 30(2), pages 293-316, June.
- Nakagawa, Tomoyuki & Watanabe, Hiroki & Hyodo, Masashi, 2021. "Kick-one-out-based variable selection method for Euclidean distance-based classifier in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
- Nakayama, Yugo & Yata, Kazuyoshi & Aoshima, Makoto, 2021. "Clustering by principal component analysis with Gaussian kernel in high-dimension, low-sample-size settings," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
- Anil K. Ghosh & Munmun Biswas, 2016. "Distribution-free high-dimensional two-sample tests based on discriminating hyperplanes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 525-547, September.
- Jung, Sungkyu, 2018. "Continuum directions for supervised dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 27-43.
- Bolivar-Cime, A. & Marron, J.S., 2013. "Comparison of binary discrimination methods for high dimension low sample size data," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 108-121.
- Aki Ishii & Kazuyoshi Yata & Makoto Aoshima, 2021. "Hypothesis tests for high-dimensional covariance structures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 599-622, June.
- Jung, Sungkyu & Sen, Arusharka & Marron, J.S., 2012. "Boundary behavior in High Dimension, Low Sample Size asymptotics of PCA," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 190-203.
More about this item
Keywords
Asymptotic normality; Data transformation; Discriminant analysis; Large p small n; Noise-reduction methodology; Spiked model;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:aistmt:v:71:y:2019:i:3:d:10.1007_s10463-018-0655-z. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.