Nonlinear dimensionality reduction viewed as information retrieval

Nonlinear dimensionality reduction methods are commonly used for two purposes: (i) as preprocessing methods to reduce the number of input variables or to represent the inputs in terms of more natural variables describing the embedded data manifold, or (ii) for making the data set more understandable, by making the similarity relationships between data points explicit through visualizations. The visualizations are commonly needed in exploratory data analysis, and in interfaces to high-dimensional data. In this abstract we will focus on the latter types of applications and call them information visualization, with the understanding that the goal is to visualize neighborhood or proximity relationships within a set of high-dimensional data samples. The introduced methods are expected to be useful for other kinds of dimensionality reduction tasks as well, however.