On the Visualization of Outliers via Self-Organizing Maps

References

• Atkinson , A. C. 1994 . “Fast Very Robust Methods for the Detection of Multiple Outliers” . Journal of the American Statistical Association , 89 : 1329 – 1339 .
   Web of Science ®Google Scholar
• Balakrishnan , P. V. , Cooper , M. C. , Jacob , V. S. and Lewis , P. A. 1994 . “A Study of the Classification Abilities of Neural Networks Using Unsupervised Learning: A Comparison With k-Means Clustering” . Psychometrika , 59 : 509 – 525 .
   Web of Science ®Google Scholar
• Barnett , V. and Lewis , T. 1994 . Outliers in Statistical Data, , 3rd ed. , New York : John Wiley .
   Google Scholar
• Bauer , H. U. and Pawelzik , K. R. 1992 . “Quantifying the Neighborhood Preservation of Self-Organizing Feature Maps” . IEEE Transactions on Neural Networks , 3 : 570 – 579 .
   PubMed Web of Science ®Google Scholar
• Bouton , C. and Pagès , G. 1993 . “Self-Organization of the One-Dimensional Kohonen Algorithm With Non-uniformly Distributed Stimuli” . Stochastic Processes and their Applications , 47 : 249 – 274 .
   Web of Science ®Google Scholar
• Cheng , B. and Titterington , D. M. 1994 . “Neural Networks: A Review From a Statistical Perspective” . Statistical Science , 9 : 2 – 54 .
   Web of Science ®Google Scholar
• Colosimo , A. 1994 . “Connectionist Systems in the Study of Proteins’ Structures” . In Statistical Tools in Human Biology , Edited by: Di Bacco , M. , Pacciani , E. and Borgognini , S. 16 – 30 . Singapore : World Scientific .
   Google Scholar
• Cottrell , M. , Fort , J. C. and Pagès , G. 1994 . “Two or Three Things that We Know About the Kohonen Algorithm” , Paris , , France : Universite Paris 1 . technical report
   Google Scholar
• Dawkins , B. P. 1995 . “Investigating the Geometry of a p-Dimensional Data Set” . Journal of the American Statistical Association , 90 : 350 – 359 .
   Web of Science ®Google Scholar
• Everitt , B. 1979 . Graphical Techniques for Multivariate Data , New York : North-Holland .
   Google Scholar
• Finkel , L. H. and Edelman , G. M. 1990 . “Models of Somatotopic Map Organization” . In SFI Lectures in Complex Systems , Edited by: Nadel , L. and Stein , D. 269 – 284 . Reading , MA : Addison-Wesley .
   Google Scholar
• Jain , A. K. and Mao , J. “Artificial Neural Network for Nonlinear Projection of Multivariate Data” . Proceedings of the IEEE International Joint Conference on Neural Networks . vol. 3 , pp. 335 – 340 . Baltimore , MD : IEEE .
   Google Scholar
• Kohonen , T. 1982 . “Self-Organized Formation of Topologically Correct Feature Maps” . Biological Cybernetics , 43 : 59 – 69 .
   Web of Science ®Google Scholar
• Kohonen , T. 1991 . “Self-Organizing Maps: Optimization Approaches” . In Artificial Neural Networks , Edited by: Kohonen , T. , Makisara , K. , Simula , O. and Kangas , J. 981 – 990 . Amsterdam : North Holland .
   Google Scholar
• Kohonen , T. 1995 . Self-Organizing Maps , Heidelberg , , Germany : Springer Verlag .
   Google Scholar
• Kohonen , T. , Hynninen , J. , Kangas , J. and Laaksonen , J. 1995 . “SOM_PAK: The Self-Organizing Map Program Package” , Helsinki University of Technology, Laboratory of Computer and Information Science . technical report, Available via anonymous ftp at: cochlea.hut.fi/pub/som_pak (130.233.168.48)
   Google Scholar
• Kraaijveld , M. A. , Mao , J. and Jain , A. K. 1995 . “A Nonlinear Projection Method Based on Kohonen's Topology Preserving Maps” . IEEE Transactions on Neural Networks , 6 : 548 – 559 .
   PubMed Web of Science ®Google Scholar
• Mao , J. and Jain , A. K. 1995 . “Artificial Neural Networks for Feature Extraction and Multivariate Data Projection” . IEEE Transactions on Neural Networks , 6 : 296 – 317 .
   PubMed Web of Science ®Google Scholar
• Maronna , R. and Yohai , V. 1995 . “The Behavior of the Stahel-Donoho Robust Multivariate Estimator” . Journal of the American Statistical Association , 90 : 330 – 341 .
   Web of Science ®Google Scholar
• Martinetz , T. , Ritter , H. and Schulten , K. 1989 . “Kohonen's Self-Organizing Map for Modelling the Formation of the Auditory Cortex of a Bat” . In Connectionism in Perspective , Edited by: Pfeifer , R. , Schreter , Z. , Fogelman , F.-Soulie. and Steels , L. 403 – 412 . San Diego , CA : Elsevier (North-Holland) .
   Google Scholar
• Mulier , F. and Cherkassky , V. 1995 . “Self-Organization as an Iterative Kernel Smoothing Process” . Neural Computation , 7 : 1165 – 1177 .
   PubMed Web of Science ®Google Scholar
• Muñoz , A. and Muruzábal , J. “Outlier Detection via Self-Organizing Maps” . Proceedings of the 1995 Seminar on New Techniques and Technologies for Statistics . Bonn , Germany.
   Google Scholar
• Murtagh , F. 1994 . “Neural Networks and Related ‘Massively Parallel’ Networks for Statistics: A Short Overview” . International Statistical Review , 62 : 275 – 288 .
   Web of Science ®Google Scholar
• Muruzábal , J. “Topology-Based Genetic Search for the Stahel-Donoho Estimator” . Proceedings of the 2nd IEEE Conference on Evolutionary Computation . Edited by: Fogel , D. pp. 138 – 142 . Piscataway , NJ : IEEE Press .
   Google Scholar
• Oja , E. 1989 . “Neural Networks, Principal Components and Subspaces” . International Journal of Neural Systems , 1 : 61 – 68 .
   Google Scholar
• Peña , D. and Yohai , V. 1995 . “The Detection of Influential Subsets in Linear Regression by Using an Influence Matrix” . Journal of the Royal Statistical Society , 57 : 145 – 156 . Ser. B
   Google Scholar
• Ritter , H. and Schulten , K. 1986 . “On the Stationary State of Kohonen's Self-Organizing Sensory Mapping” . Biological Cybernetics , 54 : 99 – 106 .
   Web of Science ®Google Scholar
• Rohlf , F. J. 1975 . “Generalization of the Gap Test for the Detection of Multivariate Outliers” . Biometrics , 31 : 93 – 101 .
   Web of Science ®Google Scholar
• Sammon , J. W. 1969 . “A Nonlinear Mapping for Data Structure Analysis” . IEEE Transactions on Computers , 18 : 401 – 409 .
   Web of Science ®Google Scholar
• Seber , G. A.F. 1984 . Multivariate Observations , New York : John Wiley .
   Google Scholar
• Tierney , L. 1990 . LISP-STAT. An Object-Oriented Environment for Statistical Computing and Dynamic Graphics , New York : John Wiley .
   Google Scholar
• Woodruff , D. L. and Rocke , D. M. 1993 . “Heuristic Search Algorithms for the Minimum Volume Ellipsoid” . Journal of Computational and Graphical Statistics , 2 : 69 – 95 .
   Google Scholar
• Zheng , Y. and Greenleaf , J. F. 1996 . “The Effect of Concave and Convex Weight Adjustments on Self-Organizing Maps” . IEEE Transactions on Neural Networks , 7 : 87 – 96 .
   PubMed Web of Science ®Google Scholar