Subspace histograms for outlier detection in linear time

Outlier detection algorithms are often computationally intensive because of their need to score each point in the data. Even simple distance-based algorithms have quadratic complexity. High-dimensional outlier detection algorithms such as subspace methods are often even more computationally intensive because of their need to explore different subspaces of the data. In this paper, we propose an exceedingly simple subspace outlier detection algorithm, which can be implemented in a few lines of code, and whose complexity is linear in the size of the data set and the space requirement is constant. We show that this outlier detection algorithm is much faster than both conventional and high-dimensional algorithms and also provides more accurate results. The approach uses randomized hashing to score data points and has a neat subspace interpretation. We provide a visual representation of this interpretability in terms of outlier sensitivity histograms. Furthermore, the approach can be easily generalized to data streams, where it provides an efficient approach to discover outliers in real time. We present experimental results showing the effectiveness of the approach over other state-of-the-art methods.