Analysis of feature selection stability on high dimension and small sample data

Feature selection is an important step when building a classifier on high dimensional data. As the number of observations is small, the feature selection tends to be unstable. It is common that two feature subsets, obtained from different datasets but dealing with the same classification problem, do not overlap significantly. Although it is a crucial problem, few works have been done on the selection stability. The behavior of feature selection is analyzed in various conditions, not exclusively but with a focus on t-score based feature selection approaches and small sample data. The analysis is in three steps: the first one is theoretical using a simple mathematical model; the second one is empirical and based on artificial data; and the last one is based on real data. These three analyses lead to the same results and give a better understanding of the feature selection problem in high dimension data.