This paper deals with finding outliers (exceptions) in large, multidimensional datasets. The identification of outliers can lead to the discovery of truly unexpected knowledge in areas such as electronic commerce, credit card fraud, and even the analysis of performance statistics of professional athletes. Existing methods that we have seen for finding outliers can only deal efficiently with two dimensions/attributes of a dataset. In this paper, we study the notion of DB (distance-based) outliers. Specifically, we show that (i) outlier detection can be done efficiently for large datasets, and for k-dimensional datasets with large values of k (e.g., $k ge 5$); and (ii), outlier detection is a meaningful and important knowledge discovery task.First, we present two simple algorithms, both having a complexity of $O(k : N^2)$, k being the dimensionality and N being the number of objects in the dataset. These algorithms readily support datasets with many more than two attributes. Second, we present an optimized cell-based algorithm that has a complexity that is linear with respect to N, but exponential with respect to k. We provide experimental results indicating that this algorithm significantly outperforms the two simple algorithms for $k leq 4$. Third, for datasets that are mainly disk-resident, we present another version of the cell-based algorithm that guarantees at most three passes over a dataset. Again, experimental results show that this algorithm is by far the best for $k leq 4$. Finally, we discuss our work on three real-life applications, including one on spatio-temporal data (e.g., a video surveillance application), in order to confirm the relevance and broad applicability of DB outliers.
