Abstract – An increasing number of real-world applications are associated with streaming data drawn from drifting and nonstationary distributions that change over time. These applications demand new algorithms that can learn and adapt to such changes, also known as concept drift. Proper characterization of such data with existing approaches typically requires substantial amount of labeled instances, which may be difficult, expensive or even impractical to obtain. In this contribution, we introduce COMPOSE, a computational geometry based framework to learn from nonstationary streaming data, where labels are unavailable (or presented very sporadically) after initialization. We introduce the algorithm in detail, and discuss its results and performances on several synthetic and real-world datasets, which demonstrate the ability of the algorithm to learn under several different scenarios of initially labeled streaming environments (ILSE). On carefully designed synthetic datasets, we compare the performance of COMPOSE against the optimal Bayes classifier, as well as the APT algorithm, which addresses a similar environment referred to as extreme verification latency. Furthermore, using the real-world NOAA Weather Dataset, we demonstrate that COMPOSE is competitive even with a well-established, fully supervised, nonstationary learning algorithm that receives labeled data in every batch.