A Multi-Strip Algorithm and Its Application to Gene Characterization Using DNA-Array Data

A fast adaptive multiscale algorithm has been devised to characterize a random set of points spanning a high dimensional Euclidean space, but concentrated around special lower dimensional subsets. It has been adapted to analyze gene expression data from microarray experiments. We present here the simplest version of this “multi-strip” algorithm applied to a set of points in R concentrated around a line. The algorithm characterizes this set by finding a strip around the principal axis of the set, so that it isolates deviating points from the main bulk of points enveloped by the strip. The algorithm generalizes to computing a strip around a best L d-plane, where 1 ≤ d < D, or even fitting a strip around a d-dimensional Lipschitz graph. We establish various estimates for its performance. When applied to gene-expression data, the algorithm can be thought of as estimating the local statistics (means, standard deviations, tail distributions, etc.) as a function of the entire expression range. Genes with abnormal differential expression values can be identified and given biological interpretations based on the local deviations in their statistics. By avoiding rigid local segmentations (as in segmental nearest neighbor normalization) or nonadaptive global estimates, the algorithm achieves a superior performance.