{"abstract":[{"text":"The traditional way to find a linear solution to the feature extraction problem is based on the maximization of the class-between scatter over the class-within scatter (Fisher mapping). For the multi-class problem this is, however, sub-optimal due to class conjunctions, even for the simple situation of normal distributed classes with identical covariance matrices. We propose a novel, equally fast method, based on nonlinear PCA. Although still sub-optimal, it may avoid the class conjunction. The proposed method is experimentally compared with Fisher mapping and with a neural network based approach to nonlinear PCA. It appears to outperform both methods, the first one even in a dramatic way.","lang":"eng"}],"publication":"International Conference on Pattern Recognition (ICPR 2000)","_id":"11758","year":"2000","main_file_link":[{"open_access":"1","url":"https://groups.uni-paderborn.de/nt/pubs/2000/DuLoHa2000paper.pdf"}],"citation":{"apa":"Duin, R. P. W., Loog, M., &#38; Haeb-Umbach, R. (2000). Multi-class Linear Feature Extraction by Nonlinear PCA. In <i>International Conference on Pattern Recognition (ICPR 2000)</i>.","ama":"Duin RPW, Loog M, Haeb-Umbach R. Multi-class Linear Feature Extraction by Nonlinear PCA. In: <i>International Conference on Pattern Recognition (ICPR 2000)</i>. ; 2000.","mla":"Duin, Robert P. W., et al. “Multi-Class Linear Feature Extraction by Nonlinear PCA.” <i>International Conference on Pattern Recognition (ICPR 2000)</i>, 2000.","ieee":"R. P. W. Duin, M. Loog, and R. Haeb-Umbach, “Multi-class Linear Feature Extraction by Nonlinear PCA,” in <i>International Conference on Pattern Recognition (ICPR 2000)</i>, 2000.","chicago":"Duin, Robert P.W., Marco Loog, and Reinhold Haeb-Umbach. “Multi-Class Linear Feature Extraction by Nonlinear PCA.” In <i>International Conference on Pattern Recognition (ICPR 2000)</i>, 2000.","short":"R.P.W. Duin, M. Loog, R. Haeb-Umbach, in: International Conference on Pattern Recognition (ICPR 2000), 2000.","bibtex":"@inproceedings{Duin_Loog_Haeb-Umbach_2000, title={Multi-class Linear Feature Extraction by Nonlinear PCA}, booktitle={International Conference on Pattern Recognition (ICPR 2000)}, author={Duin, Robert P.W. and Loog, Marco and Haeb-Umbach, Reinhold}, year={2000} }"},"oa":"1","language":[{"iso":"eng"}],"user_id":"44006","department":[{"_id":"54"}],"author":[{"last_name":"Duin","first_name":"Robert P.W.","full_name":"Duin, Robert P.W."},{"last_name":"Loog","full_name":"Loog, Marco","first_name":"Marco"},{"id":"242","full_name":"Haeb-Umbach, Reinhold","first_name":"Reinhold","last_name":"Haeb-Umbach"}],"title":"Multi-class Linear Feature Extraction by Nonlinear PCA","status":"public","date_updated":"2022-01-06T06:51:08Z","type":"conference","date_created":"2019-07-12T05:27:41Z"}