Characteristics Of Local Intrinsic Dimensionality (Lid) In Subspaces: Local Neighbourhood Analysis

The local intrinsic dimensionality (LID) model enables assessment of the complexity of the local neighbourhood around a specific query object of interest. In this paper, we study variations in the LID of a query, with respect to different subspaces and local neighbourhoods. We illustrate the surprising phenomenon of how the LID of a query can substantially decrease as further features are included in a dataset. We identify the role of two key feature properties in influencing the LID for feature combinations: correlation and dominance. Our investigation provides new insights into the impact of different feature combinations on local regions of the data.