Comparación de métodos de reducción de dimensión basados en análisis por localidades

Abstract

In this paper, a comparison of methods for nonlinear dimensionality reduction is proposed in order to determine which technique preserves better the local properties, without losing the overall structure of the original data. We seek to establish which of these methods is the most appropriate for visualization tasks. The embeddings obtained with each technique are evaluated by two criteria Preservation Neighborhood Error and Preserved Neighbors Average. The methodologies were tested on artificial and real-world data sets which allow us to visually confirm the quality of the embedding. The results obtained show that Maximum variance unfolding computes high quality embeddings, because the optimization problem pretends to preserve exactly the local pair-wise distance between neighbors and conserve the global manifold structure.