  Axis-aligned subspace clustering generally entails searching through enormous
numbers of subspaces (feature combinations) and evaluation of cluster quality
within each subspace. In this paper, we tackle the problem of identifying
subsets of features with the most significant contribution to the formation of
the local neighborhood surrounding a given data point. For each point, the
recently-proposed Local Intrinsic Dimension (LID) model is used in identifying
the axis directions along which features have the greatest local
discriminability, or equivalently, the fewest number of components of LID that
capture the local complexity of the data. In this paper, we develop an
estimator of LID along axis projections, and provide preliminary evidence that
this LID decomposition can indicate axis-aligned data subspaces that support
the formation of clusters.
