Extended local tangent space alignment for classification

The local tangent space alignment (LTSA) has demonstrated promising results in finding meaningful low-dimensional structures hidden in high-dimensional data. However, LTSA may have a limited effectiveness on the data which are organized in multiple classes or contain noisy points. In this paper, the distances between the samples and their neighbors are rescaled by using the reconstruction weights to overcome the limitation. An extension of LTSA is proposed based on the local rescaled distance matrix. Numerical experiments on both synthetic and real-world data sets are used to show the improvement of our extension for classification and the robustness to noisy data.