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Journal of Applied Mathematics
Volume 2014, Article ID 965602, 12 pages
Research Article

A Comparative Study: Globality versus Locality for Graph Construction in Discriminant Analysis

1College of Computer Science, Inner Mongolia University, Hohhot 010021, China
2Department of Computer Science and Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China

Received 23 April 2014; Accepted 27 June 2014; Published 21 July 2014

Academic Editor: Jong Hae Kim

Copyright © 2014 Bo Yang and Songcan Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Local graph based discriminant analysis (DA) algorithms recently have attracted increasing attention to mitigate the limitations of global (graph) DA algorithms. However, there are few particular concerns on the following important issues: whether the local construction is better than the global one for intraclass and interclass graphs, which (intraclass or interclass) graph should locally or globally be constructed? and, further how they should be effectively jointed for good discriminant performances. In this paper, pursuing our previous studies on the graph construction and DA, we firstly address the issues involved above, and then by jointly utilizing both the globality and the locality, we develop, respectively, a Globally marginal and Locally compact Discriminant Analysis (GmLcDA) algorithm based on so-introduced global interclass and local intraclass graphs and a Locally marginal and Globally compact Discriminant Analysis (LmGcDA) based on so-introduced local interclass and global intraclass graphs, the purpose of which is not to show how novel the algorithms are but to illustrate the analyses in theory. Further, by comprehensively comparing the Locally marginal and Locally compact DA (LmLcDA) based on locality alone, the Globally marginal and Globally compact Discriminant Analysis (GmGcDA) just based on globality alone, GmLcDA, and LmGcDA, we suggest that the joint of locally constructed intraclass and globally constructed interclass graphs is more discriminant.