Using Nonlinear Dimensionality Reduction to Visualize Classifiers

Nonlinear dimensionality reduction (DR) techniques offer the possibility to visually inspect a given finite high-dimensional data set in two dimensions. In this contribution, we address the problem to visualize a trained classifier on top of these projections. We investigate the suitability of popular DR techniques for this purpose and we point out the benefit of integrating auxiliary information as provided by the classifier into the pipeline based on the Fisher information.

[1]  Geoffrey E. Hinton,et al.  Neighbourhood Components Analysis , 2004, NIPS.

[2]  Samuel Kaski,et al.  Improved learning of Riemannian metrics for exploratory analysis [Neural Networks 17 (8–9) 1087–1100] , 2005 .

[3]  Xiaoru Wang,et al.  SVMV - A Novel Algorithm for the Visualization of SVM Classification Results , 2006, ISNN.

[4]  Jacek M. Zurada,et al.  Advances in Neural Networks - ISNN 2006, Third International Symposium on Neural Networks, Chengdu, China, May 28 - June 1, 2006, Proceedings, Part I , 2006, International Symposium on Neural Networks.

[5]  Geoffrey E. Hinton,et al.  Visualizing Data using t-SNE , 2008 .

[6]  Hau-San Wong,et al.  Kernel clustering-based discriminant analysis , 2007, Pattern Recognit..

[7]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[8]  Barbara Hammer,et al.  How to visualize a classifier , 2012 .

[9]  Ivan Bratko,et al.  Nomograms for visualizing support vector machines , 2005, KDD '05.

[10]  Pak Chung Wong,et al.  Guest Editor's Introduction: Visual Data Mining , 1999, IEEE Computer Graphics and Applications.

[11]  Kilian Q. Weinberger,et al.  Unsupervised Learning of Image Manifolds by Semidefinite Programming , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[12]  Jorma Laaksonen,et al.  LVQ_PAK: The Learning Vector Quantization Program Package , 1996 .

[13]  Barbara Hammer,et al.  Out-of-sample kernel extensions for nonparametric dimensionality reduction , 2012, ESANN.

[14]  Michel Verleysen,et al.  Nonlinear Dimensionality Reduction , 2021, Computer Vision.

[15]  Matthew O. Ward,et al.  Interactive Data Visualization - Foundations, Techniques, and Applications , 2010 .

[16]  Barbara Hammer,et al.  Discriminative Dimensionality Reduction Mappings , 2012, IDA.

[17]  Jarkko Venna,et al.  Information Retrieval Perspective to Nonlinear Dimensionality Reduction for Data Visualization , 2010, J. Mach. Learn. Res..

[18]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[19]  G. Baudat,et al.  Generalized Discriminant Analysis Using a Kernel Approach , 2000, Neural Computation.

[20]  Vasant Honavar,et al.  Visual Methods for Examining SVM Classifiers , 2008, Visual Data Mining.

[21]  Thomas Villmann,et al.  Limited Rank Matrix Learning, discriminative dimension reduction and visualization , 2012, Neural Networks.

[22]  Paulo J. G. Lisboa,et al.  Making machine learning models interpretable , 2012, ESANN.

[23]  Michael Biehl,et al.  A General Framework for Dimensionality-Reducing Data Visualization Mapping , 2012, Neural Computation.

[24]  Peter A. Flach,et al.  Brier Curves: a New Cost-Based Visualisation of Classifier Performance , 2011, ICML.

[25]  David Cohn,et al.  Informed Projections , 2002, NIPS.