One of the biggest challenges in Big Data is to exploit value from large volumes of variable and changing data. For this, one must focus on analyzing the data in these Big Data sources and classify the data items according to a domain model (e.g. an ontology). To automatically classify unstructured text documents according to an ontology, a hierarchical multi-label classification process called Semantic HMC was proposed. This process uses ontologies to describe the classification model. To prevent cold start and user overload, the classification process automatically learns the ontology-described classification model from a very large set of unstructured text documents. However, data is always being generated and its statistical properties can change over time. In order to learn in such environment, the classification processes must handle streams of non-stationary data to adapt the classification model. This paper proposes a new adaptive learning process to consistently adapt the ontology-described classification model according to a non-stationary stream of unstructured text data in Big Data context. The adaptive process is then instantiated for the specific case of of the previously proposed Semantic HMC.