Local Intrinsic Dimensionality III: Density and Similarity.

In artificial intelligence, machine learning, and other areas in which statistical estimation and modeling is common, distributions are typically assumed to admit a representation in terms of a probability density function (pdf). However, in many situations, such as mixture modeling and subspace methods, the distributions in question are not always describable in terms of a single pdf. In this paper, we present a theoretical foundation for the modeling of density ratios in terms of the local intrinsic dimensionality (LID) model, in a way that avoids the use of traditional probability density functions. These formulations provide greater flexibility when modeling data under the assumption of local variation in intrinsic dimensionality, in that no explicit dependence on a fixed-dimensional data representation is required.