Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Metric Multidimensional Scaling-Based Nonlinear Manifold Learning Approach for Unsupervised Data Reduction | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2008 Article ID 862015 12 pages doi 2008 862015 Research Article A Metric Multidimensional Scaling-Based Nonlinear Manifold Learning Approach for Unsupervised Data Reduction M. Brucher 1 2 Ch. Heinrich 1 F. Heitz 1 and . Armspach2 1 Laboratoire des Sciences de l Image de l Informatique et de la Teledetection LSIIT UMR 7005 CNRS-Université Louis Pasteur Strasbourg 1 Boulevard S. Brant BP 10413 67412 Illkirch Cedex France 2Laboratoire d Imagerie et de Neurosciences Cognitives LINC UMR 7191 CNRS-Universite Louis Pasteur Strasbourg 1 LINC-IPB 4 rue Kirschleger 67085 Strasbourg Cedex France Correspondence should be addressed to M. Brucher brucher@ Received 30 September 2007 Revised 21 January 2008 Accepted 7 March 2008 Recommended by Olivier Lezoray Manifold learning may be seen as a procedure aiming at capturing the degrees of freedom and structure characterizing a set of high-dimensional data such as images or patterns. The usual goals are data understanding visualization classification and the computation of means. In a linear framework this problem is typically addressed by principal component analysis PCA . We propose here a nonlinear extension to PCA. Firstly the reduced variables are determined in the metric multidimensional scaling framework. Secondly regression of the original variables with respect to the reduced variables is achieved considering a piecewise linear model. Both steps parameterize the noisy manifold holding the original data. Finally we address the projection of data onto the manifold. The problem is cast in a Bayesian framework. Application of the proposed approach to standard data sets such as the COIL-20 database is presented. Copyright 2008 M. Brucher et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium .
