744
Views
23
CrossRef citations to date
0
Altmetric
Articles: Classification

Functional Robust Support Vector Machines for Sparse and Irregular Longitudinal Data

&
Pages 379-395 | Received 01 Dec 2010, Published online: 30 May 2013

REFERENCES

  • An , L. T. H. and Tao , P. D. 1997 . “Solving a Class of Linearly Constrained Indefinite Quadratic Problems by D.C. Algorithms,” . Journal of Global Optimization , 11 : 253 – 285 .
  • Bartlett , P. , Jordan , M. and McAuliffe , J. 2006 . “Convexity, Classification, and Risk Bounds,” . Journal of the American Statistical Association , 101 : 138 – 156 .
  • Borggaard , C. and Thodberg , H. H. 1992 . “Optimal Minimal Neural Interpretation of Spectra,” . Analytical Chemistry , 64 : 545 – 551 .
  • Bredensteiner , E. and Bennett , K. 1999 . “Multicategory Classification by Support Vector Machines,” . Computational Optimizations and Applications , 12 : 53 – 79 .
  • Brown , M. P. S. , Grundy , W. N. , Lin , D. , Cristianini , N. , Sugnet , C. W. , Furey , T. S. , Ares , M. and Haussler , D. 2000 . “Knowledge-Based Analysis of Microarray Gene Expression Data by Using Support Vector Machines,” . Proceedings of the National Academy of Sciences , 97 : 262 – 267 .
  • Canu , S. , Mary , X. and Rakotomamonjy , A. 2002 . “Functional Learning Through Kernel,” . In Advances in Learning Theory: Methods, Models and Applications , Edited by: Suykens , J. , Horvath , G. , Basu , S. , Micchelli , C. and Vandewalle , J. 89 – 110 . Amsterdam : IOS Press .
  • Crammer , K. and Singer , Y. 2001 . “On the Algorithmic Implementation of Multiclass Kernel-Based Vector Machines,” . Journal of Machine Learning Research , 2 : 265 – 292 .
  • Cristianini , N. and Shawe-Taylor , J. 2000 . An Introduction to Support Vector Machines , Cambridge : Cambridge University Press .
  • Diggle , P. , Heagerty , P. , Liang , K. and Zeger , S. 2002 . Analysis of Longitudinal Data(2nd ed.) , New York : Oxford University Press .
  • Hall , P. , Poskitt , D. S. and Presnell , B. 2001 . “A Functional Data-Analytic Approach to Signal Discrimination,” . Technometrics , 43 : 1 – 9 .
  • Hastie , T. , Tibshirani , R. and Friedman , J. H. 2009 . The Elements of Statistical Learning: Data Mining, Inference, and Prediction(2nd ed.) , New York : Springer-Verlag .
  • James , G. M. and Hastie , T. J. 2001 . “Functional Linear Discriminant Analysis for Irregularly Sampled Curves,” . Journal of Royal Statistical Society, Series B , 63 : 533 – 550 .
  • Kimeldorf , G. and Wahba , G. 1971 . “Some Results on Tchebycheffian Spline Functions,” . Journal of Mathematical Analysis and Applications , 33 : 82 – 95 .
  • Lee , H. 2004 . “Functional Data Analysis: Classification and Regression,” . Ph.D. dissertation, Department of Statistics, A&M University, Texas
  • Lee , Y. , Lin , Y. and Wahba , G. 2004 . “Multicategory Support Vector Machines: Theory, and Application to the Classification of Microarray Data and Satellite Radiance Data,” . Journal of the American Statistical Association , 99 : 67 – 81 .
  • Leng , X. and Müller , H.-G. 2006 . “Classification Using Functional Data Analysis for Temporal Gene Expression Data,” . Bioinformatics , 22 : 68 – 76 .
  • Li , B. and Yu , Q. 2008 . “Classification of Functional Data: A Segmentation Approach,” . Computational Statistics and Data Analysis , 52 : 4790 – 4800 .
  • Lin , Y. 2004 . “A Note on Margin-Based Loss Functions in Classification,” . Statistics and Probability Letters , 68 : 73 – 82 .
  • Liu , Y. 2007 . “Fisher Consistency of Multicategory Support Vector Machines,” . In Proceedings of the Eleventh International Workshop on Artificial Intelligence and Statistics 289 – 296 .
  • Liu , Y. and Shen , X. 2006 . “Multicategory ψ-Learning,” . Journal of the American Statistical Association , 101 : 500 – 509 .
  • Liu , Y. and Yuan , M. 2011 . “Reinforced Multicategory Support Vector Machines,” . Journal of Computational and Graphical Statistics , 20 : 901 – 919 .
  • Müller , H.-G. and Stadtmüller , U. 2005 . “Generalized Functional Linear Models,” . The Annals of Statistics , 33 : 774 – 805 .
  • Müller , H. G. and Yao , F. 2008 . “Functional Additive Models,” . Journal of the American Statistical Association , 103 : 1534 – 1544 .
  • Preda , C. 2007 . “Regression Models for Functional Data by Reproducing Kernel Hilbert Spaces Methods,” . Journal of Statistical Planning and Inference , 137 : 829 – 840 .
  • Rossi , F. and Villa , N. 2006 . “Support Vector Machine for Functional Data Classification,” . Neurocomputing , 69 : 730 – 742 .
  • Shen , X. , Tseng , G. , Zhang , X. and Wong , W. 2003 . “On ψ-Learning,” . Journal of the American Statistical Association , 98 : 724 – 734 .
  • Wahba , G. 1990 . Spline Models for Observational Data , Philadelphia, , PA : Society for Industrial and Applied Mathematics .
  • Wang , J. , Shen , X. and Liu , Y. 2008 . “Probability Estimation for Large Margin Classifiers,” . Biometrika , 95 : 149 – 167 .
  • Weston , J. and Watkins , C. 1999 . “Support Vector Machines for Multi-Class Pattern Recognition,” . In Proceedings of the 7th European Symposium on Artificial Neural Networks (ESANN-99) 219 – 224 .
  • Wu , Y. and Liu , Y. 2007 . “Robust Truncated-Hinge-Loss Support Vector Machines,” . Journal of the American Statistical Association , 102 : 974 – 983 .
  • Wu , Y. , Zhang , H. H. and Liu , Y. 2010 . “Robust Model-Free Multiclass Probability Estimation,” . Journal of the American Statistical Association , 105 : 424 – 436 .
  • Yao , F. and Müller , H.-G. 2010 . “Functional Qudratic Regression,” . Biometrika , 97 : 49 – 64 .
  • Yao , F. , Müller , H.-G. and Wang , J.-L. 2005a . “Functional Data Analysis for Sparse Longitudinal Data,” . Journal of the American Statistical Association , 100 : 577 – 590 .
  • Yao , F. , Müller , H.-G. and Wang , J.-L. 2005b . “Functional Linear Regression Analysis for Longitudinal Data,” . The Annals of Statistics , 33 : 2873 – 2903 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.