Classification Method Performance in High Dimensions

We discuss standard classification methods for high-dimensional data and a small number of observations. By means of designed simulations illustrating the practical relevance of theoretical results we show that in the 2-class case the following rules of thumb should be followed in such a situation to avoid the worst error rate, namely the probability $\pi$$_{1}$ of the smaller class: Avoid “complicated” classifiers: The independence rule (ir) might be adequate, the support vector machine (svm) should only be considered as an expensive alternative, which is additionally sensitive to noise factors. From the outset, look for stochastically independent dimensions and balanced classes. Only take into account features which influence class separation sufficiently. Variable selection might help, though filters might be too rough. Compare your result with the result of the data independent rule “Always predict the larger class”.