Locally linear embedding for classification

Locally linear embedding (LLE) is a recently proposed unsupervised procedure for mapping high-dimensional data nonlinearly to a lower- dimensional space. In this paper, a supervised variation on LLE is proposed. This mapping, when combined with simple classifiers such as the nearest mean classifier, is shown to yield remarkably good classification results in experiments. Furthermore, a number of algorithmic improvements are proposed which should ease application of both traditional and supervised LLE by eliminating the need for setting some of the parameters.