Change Detection in Learning Histograms from Data Streams

Abstract

In this paper we study the problem of constructing histograms from high-speed time-changing data streams. Learning in this context requires the ability to process examples once at the rate they arrive, maintaining a histogram consistent with the most recent data, and forgetting out-date data whenever a change in the distribution is detected. To construct histogram from high-speed data streams we use the two layer structure used in the Partition Incremental Discretization (PiD) algorithm. Our contribution is a new method to detect whenever a change in the distribution generating examples occurs. The base idea consists of monitoring distributions from two different time windows: the reference time window, that reflects the distribution observed in the past; and the current time window reflecting the distribution observed in the most recent data. We compare both distributions and signal a change whenever they are greater than a threshold value, using three different methods: the Entropy Absolute Difference, the Kullback-Leibler divergence and the Cosine Distance. The experimental results suggest that Kullback-Leibler divergence exhibit high probability in change detection, faster detection rates, with few false positives alarms.