Why direct LDA is not equivalent to LDA

In this paper, we present counterarguments against the direct LDA algorithm (D-LDA), which was previously claimed to be equivalent to Linear Discriminant Analysis (LDA). We show from Bayesian decision theory that D-LDA is actually a special case of LDA by directly taking the linear space of class means as the LDA solution. The pooled covariance estimate is completely ignored. Furthermore, we demonstrate that D-LDA is not equivalent to traditional subspace-based LDA in dealing with the Small Sample Size problem. As a result, D-LDA may impose a significant performance limitation in general applications. 2005 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.