  Rare data in a large-scale database are called outliers that reveal
significant information in the real world. The subspace-based outlier detection
is regarded as a feasible approach in very high dimensional space. However, the
outliers found in subspaces are only part of the true outliers in high
dimensional space, indeed. The outliers hidden in normal-clustered points are
sometimes neglected in the projected dimensional subspace. In this paper, we
propose a robust subspace method for detecting such inner outliers in a given
dataset, which uses two dimensional-projections: detecting outliers in
subspaces with local density ratio in the first projected dimensions; finding
outliers by comparing neighbor's positions in the second projected dimensions.
Each point's weight is calculated by summing up all related values got in the
two steps projected dimensions, and then the points scoring the largest weight
values are taken as outliers. By taking a series of experiments with the number
of dimensions from 10 to 10000, the results show that our proposed method
achieves high precision in the case of extremely high dimensional space, and
works well in low dimensional space.
