Visualization and synthesis of data using manifold learning based on Locally Linear Embedding

In this paper we analyze high-dimensional data by means of the manifold learning algorithm Locally Linear Embedding. We employ this method to visually analyze both artificial and real-world datasets lying on nonlinear structures, comparing its transformations against the traditional feature extraction technique Principal Components Analysis. Moreover, we propose a data synthesis scheme based on manifold learning that allows to represent the observations in a low-dimensional space, and then we learn the underlying data structure to properly infer unknown samples. The synthesis results are compared against an interpolation technique that directly estimates unknown samples in the input space. According to the obtained results, the employed manifold learning method improves the data representability, suitably computing low-dimensional transformations of the observations, and properly synthesizing new samples with low relative errors.