  Linear discriminant analysis (LDA) is a popular technique to learn the most
discriminative features for multi-class classification. A vast majority of
existing LDA algorithms are prone to be dominated by the class with very large
deviation from the others, i.e., edge class, which occurs frequently in
multi-class classification. First, the existence of edge classes often makes
the total mean biased in the calculation of between-class scatter matrix.
Second, the exploitation of l2-norm based between-class distance criterion
magnifies the extremely large distance corresponding to edge class. In this
regard, a novel self-weighted robust LDA with l21-norm based pairwise
between-class distance criterion, called SWRLDA, is proposed for multi-class
classification especially with edge classes. SWRLDA can automatically avoid the
optimal mean calculation and simultaneously learn adaptive weights for each
class pair without setting any additional parameter. An efficient re-weighted
algorithm is exploited to derive the global optimum of the challenging l21-norm
maximization problem. The proposed SWRLDA is easy to implement, and converges
fast in practice. Extensive experiments demonstrate that SWRLDA performs
favorably against other compared methods on both synthetic and real-world
datasets, while presenting superior computational efficiency in comparison with
other techniques.
