ABID: Angle Based Intrinsic Dimensionality
This work provides a novel approach to intrinsic dimensionality estimation, which could enhance understanding and spur new research in data analysis, though it appears incremental as it builds on existing concepts.
The authors tackled the problem of estimating local intrinsic dimensionality by introducing a new method based on the distribution of angles between neighbor points, rather than distances, and experimentally verified that it behaves similarly but complementarily to existing measures.
The intrinsic dimensionality refers to the ``true'' dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower than the number of variables. Local intrinsic dimensionality refers to the observation that this property can vary for different parts of the data set; and intrinsic dimensionality can serve as a proxy for the local difficulty of the data set. Most popular methods for estimating the local intrinsic dimensionality are based on distances, and the rate at which the distances to the nearest neighbors increase, a concept known as ``expansion dimension''. In this paper we introduce an orthogonal concept, which does not use any distances: we use the distribution of angles between neighbor points. We derive the theoretical distribution of angles and use this to construct an estimator for intrinsic dimensionality. Experimentally, we verify that this measure behaves similarly, but complementarily, to existing measures of intrinsic dimensionality. By introducing a new idea of intrinsic dimensionality to the research community, we hope to contribute to a better understanding of intrinsic dimensionality and to spur new research in this direction.