Out of samples extensions for SC-LLE, new nonlinear dimensionality reduction algorithm

In a previous paper a new version of nonlinear dimensionality reduction algorithm was proposed, the SC-LLE approach. This approach combines a supervised method, linear discriminant analysis (LDA, a simple but widely used algorithm in pattern recognition) with an unsupervised method, local linear embedding (LLE, manifold learning). SC-LLE method can generalize any linear classifier (like LDA) to nonlinear by transforming data into some low-dimensional feature space. This new concept (SC-LLE) applied to nonlinear data projection seems to be promising, and we show in this new paper that semi-supervised learning (SSL) is another interesting property of SC-LLE. Applications on 3D data show the interest of this method.