Abstract：
This paper is concerned with the problem of feature screening for multi-class linear
discriminant analysis under ultrahigh dimensional setting. We allow the number of
classes to be relatively large. As a result, the total number of relevant features is
larger than usual. This makes the related classification problem much more
challenging than the conventional one, where the number of classes is small (very
often two). To solve the problem, we propose a novel pairwise sure independence
screening method for linear discriminant analysis with an ultrahigh dimensional
predictor. The proposed procedure is directly applicable to the situation with many
classes. We further prove that the proposed method is screening consistent.
Simulation studies are conducted to assess the finite sample performance of the new
procedure. We also demonstrate the proposed methodology via an empirical analysis
of a real life example on handwritten Chinese character recognition.
Keywords: Multi-class Linear Discriminant Analysis; Pairwise Sure Independence
Screening; Sure Independence Screening; Strong Screening Consistency. |