  The Classification on high-dimension low-sample-size data (HDLSS) is a
challenging problem and it is common to have class-imbalanced data in most
application fields. We term this as Imbalanced HDLSS (IHDLSS). Recent
theoretical results reveal that the classification criterion and tolerance
similarity are crucial to HDLSS, which emphasizes the maximization of
within-class variance on the premise of class separability. Based on this idea,
a novel linear binary classifier, termed Population Structure-learned
Classifier (PSC), is proposed. The proposed PSC can obtain better
generalization performance on IHDLSS by maximizing the sum of inter-class
scatter matrix and intra-class scatter matrix on the premise of class
separability and assigning different intercept values to majority and minority
classes. The salient features of the proposed approach are: (1) It works well
on IHDLSS; (2) The inverse of high dimensional matrix can be solved in low
dimensional space; (3) It is self-adaptive in determining the intercept term
for each class; (4) It has the same computational complexity as the SVM. A
series of evaluations are conducted on one simulated data set and eight
real-world benchmark data sets on IHDLSS on gene analysis. Experimental results
demonstrate that the PSC is superior to the state-of-art methods in IHDLSS.
