Proposal of a new stability concept to detect changes in unsupervised data streams

Learning from continuous streams of data has been receiving an increasingly attention in the last years. Among the many challenges related to mining data streams, change detection is one topic frequently addressed. Being able to determine whether or not data characteristics are changing along time is a major concern for data stream algorithms, be it on the supervised or unsupervised scenario. The unsupervised scenario is particularly relevant due to many practical applications do not provide target labeling information. In this scenario, most of the strategies induce consecutive models over time and compare them in order to detect data changes. In this situation, model changes are assumed to be a consequence of data modifications. However, there is no guarantee this assumption is true, since those algorithms do not rely on any theoretical background to ensure that model divergences truly indicate data changes. The need for such theoretical framework has motivated this paper to propose a new stability concept to establish bounds on the learning abilities of unsupervised algorithms designed to detect changes on data streams. This stability concept, based on the surrogate data strategy from time series analysis, provides learning guarantees for online unsupervised algorithms even in case of time dependency among observations. Furthermore, we propose a new change detection algorithm that meets the requirements of this stability concept. Experimental results on different synthetical scenarios illustrate how the stability concept proposed in this paper is applied to detect changes in unsupervised data streams.