Visualizing multidimensional data based on Laplacian Eigenmaps projection

This paper describes a multidimensional projection technique based on Laplacian Eigenmaps, which is a commonly employed algorithm for nonlinear dimensionality reduction. The proposed visualization technique is characterized by a nonlinear mapping function, which transforms data from a high dimensional space to a two- or three-dimensional space. This mapping function consists on computing spectral decomposition of the Laplacian graph, which is obtained from the dissimilarities of the data instances. We performed some experiments for visualizing real-world and noisy multidimensional data sets, comparing the discriminability and the preservation of neighborhood relationships with related strategies in literature, such as Principal Component Analysis, Isometric Feature Mapping and Local Linear Embedding. The promising results showed that Laplacian Eigenmaps are appropriate choices in those situations, producing visualizations with good precision.