  Various approaches to gene selection for cancer classification based on
microarray data can be found in the literature and they may be grouped into two
categories: univariate methods and multivariate methods. Univariate methods
look at each gene in the data in isolation from others. They measure the
contribution of a particular gene to the classification without considering the
presence of the other genes. In contrast, multivariate methods measure the
relative contribution of a gene to the classification by taking the other genes
in the data into consideration. Multivariate methods select fewer genes in
general. However, the selection process of multivariate methods may be
sensitive to the presence of irrelevant genes, noises in the expression and
outliers in the training data. At the same time, the computational cost of
multivariate methods is high. To overcome the disadvantages of the two types of
approaches, we propose a hybrid method to obtain gene sets that are small and
highly discriminative.
  We devise our hybrid method from the univariate Maximum Likelihood method
(LIK) and the multivariate Recursive Feature Elimination method (RFE). We
analyze the properties of these methods and systematically test the
effectiveness of our proposed method on two cancer microarray datasets. Our
experiments on a leukemia dataset and a small, round blue cell tumors dataset
demonstrate the effectiveness of our hybrid method. It is able to discover sets
consisting of fewer genes than those reported in the literature and at the same
time achieve the same or better prediction accuracy.
