document: Mining distance-based outliers in near linear time with randomization and a simple pruning rule Defining outliers by their distance to neighboring examples is a popular approach to finding unusual examples in a data set . Recently , much work has been conducted with the goal of finding fast algorithms for this task . We show that a simple nested loop algorithm that in the worst case is quadratic can give near linear time performance when the data is in random order and a simple pruning rule is used . We test our algorithm on real high-dimensional data sets with millions of examples and show that the near linear scaling holds over several orders of magnitude . Our average case analysis suggests that much of the efficiency is because the time to process non-outliers , which are the majority of examples , does not depend on the size of the data set .
doc_bio_tags: O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O