Abstract:
This paper considers the linear-discriminant analysis (LDA) problem in the undersampled situation, in which the number of features is very large and the number of observa...Show MoreMetadata
Abstract:
This paper considers the linear-discriminant analysis (LDA) problem in the undersampled situation, in which the number of features is very large and the number of observations is limited. Sparsity is often incorporated in the solution of LDA to make a well interpretation of the results. However, most of the existing sparse LDA algorithms pursue sparsity by means of the ℓ1-norm. In this paper, we give elaborate analysis for nonconvex penalties, including the ℓ0-based and the sorted ℓ1-based LDA methods. The latter one can be regarded as a bridge between the ℓ0 and ℓ1 penalties. These nonconvex penalty-based LDA algorithms are evaluated on the gene expression array and face database, showing high classification accuracy on realworld problems.
Published in: IEEE Transactions on Neural Networks and Learning Systems ( Volume: 29, Issue: 10, October 2018)
Funding Agency:
School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou, China
Jia Cai received the Ph.D. degree from the Department of Mathematics, City University of Hong Kong, Hong Kong, in 2009.
He is currently an Associate Professor with the School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou, China. His current research interests include statistical learning theory, machine learning, and data mining.
Jia Cai received the Ph.D. degree from the Department of Mathematics, City University of Hong Kong, Hong Kong, in 2009.
He is currently an Associate Professor with the School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou, China. His current research interests include statistical learning theory, machine learning, and data mining.View more
Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, Shanghai, China
Xiaolin Huang (S’10–M’12) received the B.S. degrees in contr ol science and engineering, and applied mathematics from Xi’an Jiaotong University, Xi’an, China, in 2006, and the Ph.D. degree in control science and engineering from Tsinghua University, Beijing, China, in 2012.
He was a Post-Doctoral Researcher with ESAT-STADIUS, KU Leuven, Leuven, Belgium, from 2012 to 2015. After that, he was selected as an Alexander von Hum...Show More
Xiaolin Huang (S’10–M’12) received the B.S. degrees in contr ol science and engineering, and applied mathematics from Xi’an Jiaotong University, Xi’an, China, in 2006, and the Ph.D. degree in control science and engineering from Tsinghua University, Beijing, China, in 2012.
He was a Post-Doctoral Researcher with ESAT-STADIUS, KU Leuven, Leuven, Belgium, from 2012 to 2015. After that, he was selected as an Alexander von Hum...View more
Contents School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou, China
Jia Cai received the Ph.D. degree from the Department of Mathematics, City University of Hong Kong, Hong Kong, in 2009.
He is currently an Associate Professor with the School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou, China. His current research interests include statistical learning theory, machine learning, and data mining.
Jia Cai received the Ph.D. degree from the Department of Mathematics, City University of Hong Kong, Hong Kong, in 2009.
He is currently an Associate Professor with the School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou, China. His current research interests include statistical learning theory, machine learning, and data mining.View more
Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, Shanghai, China
Xiaolin Huang (S’10–M’12) received the B.S. degrees in contr ol science and engineering, and applied mathematics from Xi’an Jiaotong University, Xi’an, China, in 2006, and the Ph.D. degree in control science and engineering from Tsinghua University, Beijing, China, in 2012.
He was a Post-Doctoral Researcher with ESAT-STADIUS, KU Leuven, Leuven, Belgium, from 2012 to 2015. After that, he was selected as an Alexander von Humboldt Fellow with the Pattern Recognition Laboratory, Friedrich-Alexander-Universität Erlangen–Nürnberg, Erlangen, Germany, where he was appointed as a Group Head in 2015. He is currently an Associate Professor with the School of Electronics, Information, and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China. His current research interests include machine learning, optimization, and their applications.
Dr. Huang was awarded as “1000-Talent” (Young Program).
Xiaolin Huang (S’10–M’12) received the B.S. degrees in contr ol science and engineering, and applied mathematics from Xi’an Jiaotong University, Xi’an, China, in 2006, and the Ph.D. degree in control science and engineering from Tsinghua University, Beijing, China, in 2012.
He was a Post-Doctoral Researcher with ESAT-STADIUS, KU Leuven, Leuven, Belgium, from 2012 to 2015. After that, he was selected as an Alexander von Humboldt Fellow with the Pattern Recognition Laboratory, Friedrich-Alexander-Universität Erlangen–Nürnberg, Erlangen, Germany, where he was appointed as a Group Head in 2015. He is currently an Associate Professor with the School of Electronics, Information, and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China. His current research interests include machine learning, optimization, and their applications.
Dr. Huang was awarded as “1000-Talent” (Young Program).View more
