Linear discriminant analysis (LDA) is a powerful supervised dimensionality reduction method for analysing high-dimensional data. However, LDA cannot use locality information in data, which makes LDA degrade dramatically in performance on multimodal data. A number of LDA variants have been proposed to exploit locality information in data, including subclass-based LDAs. We discover a problem with these variants, which is that subclasses are selected on a within-class basis without considering other classes. This causes the loss of important information at class boundaries. In this paper, we present a novel variant of subclass-based LDA, Global Subclass Discriminant Analysis (GSDA). Unlike other subclass-based LDAs, GSDA selects subclasses from global clusters that may cross class boundaries, thus utilising within-class information and between-class information. More specifically, GSDA applies an effective clustering algorithm to the whole data to construct global clusters. It then utilises the local structure refining strategy on these global clusters to construct subclasses. Finally, GSDA learns a representative data subspace by maximising inter-subclass distance and minimising intra-subclass distance simultaneously. GSDA is extensively evaluated on a wide range of public datasets through comparison with the state-of-the-art LDA algorithms. Experimental results demonstrate its superiority in terms of accuracy and run times.
Bibliographical noteFunding Information:
The work is supported by the National Natural Science Foundation of China under Grant No. 62106090 and 62106093 , and the Jiangxi Urgent Need for Overseas Talents project under Grant No. 20223BCJ25026 and 20223BCJ25040 .
Bryan W. Scotney received the B.Sc. degree in mathematics from Durham University, UK in 1980 and the Ph.D. degree in mathematics from the University of Reading, UK in 1985. He is Professor of Informatics at Ulster University, UK, and was Director of Ulster University’s Computer Science Research Institute since its formation in 2005 until May 2015. He has over 300 publications, spanning a range of research interests in mathematical computation, especially in digital image processing and computer vision, pattern recognition and classification, statistical databases, reasoning under uncertainty, and applications to healthcare informatics, official statistics, biomedical and vision sciences, and telecommunications network management. He has collaborated widely with academic, government and commercial partners, and much of his work has been supported by funding from the European Union Framework Programmes and the UK Research Councils. Prof. Scotney was President of the Irish Pattern Recognition and Classification Society 2007–2014, and a member of the Governing Board of the International Association for Pattern Recognition (IAPR), 2007–2014. He is currently Guest Professor at Keio University, Tokyo.
© 2023 The Authors
- Supervised discriminant reduction
- Linear discriminant analysis
- Local structure
- Subclass discriminant analysis
- Global subclass discriminant analysis
- Face recognition
- Pattern recognition
- Machine learning