  Outlying Aspect Mining (OAM) aims to find the subspaces (a.k.a. aspects) in
which a given query is an outlier with respect to a given dataset. Existing OAM
algorithms use traditional distance/density-based outlier scores to rank
subspaces. Because these distance/density-based scores depend on the
dimensionality of subspaces, they cannot be compared directly between subspaces
of different dimensionality. $Z$-score normalisation has been used to make them
comparable. It requires to compute outlier scores of all instances in each
subspace. This adds significant computational overhead on top of already
expensive density estimation---making OAM algorithms infeasible to run in large
and/or high-dimensional datasets. We also discover that $Z$-score normalisation
is inappropriate for OAM in some cases. In this paper, we introduce a new score
called SiNNE, which is independent of the dimensionality of subspaces. This
enables the scores in subspaces with different dimensionalities to be compared
directly without any additional normalisation. Our experimental results
revealed that SiNNE produces better or at least the same results as existing
scores; and it significantly improves the runtime of an existing OAM algorithm
based on beam search.
