Provided are methods of classifying biological samples based on high dimensional data obtained from the samples. The methods are especially useful for prediction of a class to which the sample belongs under circumstances in which the data are statistically under-determined. The advent of microarray technologies which provide the ability to measure en masse many different variables (such as gene expression) at once has resulted in the generation of high dimensional data sets, the analysis of which benefits from the methods of the present invention. High dimensional data is data in which the number of variables, p, exceeds the number of independent observations (e.g. samples), N, made. The invention relies on a dimension reduction step followed by a logistic determination step. The methods of the invention are applicable for binary (i.e. univariate) classification and multi-class (i.e. multivariate) classifications. Also provided are data selection techniques that can be used in accordance with the methods of the invention.