Monitoring data streams in a distributed system is a challenging problem with profound applications. The task of feature selection (e.g., by monitoring the information gain of various features) is an example of an application that requires special techniques to avoid a very high communication overhead when performed using straightforward centralized algorithms. Motivated by recent contributions based on geometric ideas, we present an alternative approach that combines system theory techniques and clustering. The proposed approach enables monitoring values of an arbitrary threshold function over distributed data streams through a set of constraints applied independently on each stream and/or clusters of streams. The clusters are designed to adapt themselves to the data stream. A correct choice of clusters yields a reduction in communication load. Unlike many clustering algorithms that attempt to collect together similar data items, monitoring requires clusters with dissimilar vectors canceling each other as much as possible. In particular, sub-clusters of a good cluster do not have to be good. This novel type of clustering dictated by the problem at hand requires development of new algorithms, and the paper is a step in this direction. We report experiments on real-world data that detect instances where communication between nodes is required, and show that the clustering approach reduces communication load.