Incremental local outlier detection for data streams

Outlier detection has recently become an important problem in many industrial and financial applications. This problem is further complicated by the fact that in many cases, outliers have to be detected from data streams that arrive at an enormous pace. In this paper, an incremental LOF (Local Outlier Factor) algorithm, appropriate for detecting outliers in data streams, is proposed. The proposed incremental LOF algorithm provides equivalent detection performance as the iterated static LOF algorithm (applied after insertion of each data record), while requiring significantly less computational time. In addition, the incremental LOF algorithm also dynamically updates the profiles of data points. This is a very important property, since data profiles may change over time. The paper provides theoretical evidence that insertion of a new data point as well as deletion of an old data point influence only limited number of their closest neighbors and thus the number of updates per such insertion/deletion does not depend on the total number of points N in the data set. Our experiments performed on several simulated and real life data sets have demonstrated that the proposed incremental LOF algorithm is computationally efficient, while at the same time very successful in detecting outliers and changes of distributional behavior in various data stream applications.