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Axis-aligned subspace clustering generally entails searching through enormousnumbers of subspaces (feature combinations) and evaluation of cluster qualitywithin each subspace. In this paper, we tackle the problem of identifyingsubsets of features with the most significant contribution to the formation ofthe local neighborhood surrounding a given data point. For each point, therecently-proposed Local Intrinsic Dimension (LID) model is used in identifyingthe axis directions along which features have the greatest localdiscriminability, or equivalently, the fewest number of components of LID thatcapture the local complexity of the data. In this paper, we develop anestimator of LID along axis projections, and provide preliminary evidence thatthis LID decomposition can indicate axis-aligned data subspaces that supportthe formation of clusters.

Subspace Determination through Local Intrinsic Dimensional Decomposition: Theory and Experimentation