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The null linear discriminant analysis method is a competitive approach fordimensionality reduction. The implementation of this method, however, iscomputationally expensive. Recently, a fast implementation of null lineardiscriminant analysis method using random matrix multiplication with scattermatrices was proposed. However, if the random matrix is chosen arbitrarily, theorientation matrix may be rank deficient, and some useful discriminantinformation will be lost. In this paper, we investigate how to choose therandom matrix properly, such that the two criteria of the null LDA method aresatisfied theoretically. We give a necessary and sufficient condition toguarantee full column rank of the orientation matrix. Moreover, the geometriccharacterization of the condition is also described.

A theoretical contribution to the fast implementation of null linear  discriminant analysis method using random matrix multiplication with scatter  matrices