Locally linear embedding for nonlinear dimension reduction in classification problems: an application to gene expression data

Some real problems, such as image recognition or the analysis of gene expression data, involve the observation of a very large number of variables on a few units. In such a context conventional classification methods are difficult to employ both from analytical and interpretative points of view. In this paper we propose to deal with classification problems with high dimensional data, through a non linear dimension reduction technique, the so-called locally linear embedding. We consider a supervised version of the method in order to take into account of class information in the feature extraction phase. The proposed discriminant strategy is applied to the problem of cell classification using gene expression data.