Manifold learning techniques attempt to map a high-dimensional space onto a lower-dimensional one. From a mathematical point of view, a manifold is a topological Hausdorff space that is locally Euclidean. From Machine Learning point of view, we can interpret this embedded manifold as the underlying support of the data distribution. When dealing with high dimensional data sets, nonlinear dimensionality reduction methods can provide more faithful data representation than linear ones. However, the local geometrical distortion induced by the nonlinear mapping leads to a loss of information and affects interpretability, with a negative impact in the model visualization results.
This talk will discuss an approach which involves probabilistic nonlinear dimensionality reduction through Gaussian Process Latent Variables Models. The main focus is on the intrinsic geometry of the model itself as a tool to improve the exploration of the latent space and to recover information loss due to dimensionality reduction. We aim to analytically quantify and visualize the distortion due to dimensionality reduction in order to improve the performance of the model and to interpret data in a more faithful way.
In collaboration with: N.D. Lawrence (University of Sheffield), A. Vellido (UPC)