We present the Interactive Classification System (ICS), a web-based application that supports the activity of manual text classification. The application uses machine learning to continuously fit automatic classification models that are in turn used to actively support its users with classification suggestions. The key requirement we have established for the development of ICS is to give its users total freedom of action: they can at any time modify any classification schema and any label assignment, possibly reusing any relevant information from previous activities. We investigate how this requirement challenges the typical scenarios faced in machine learning research, which instead give no active role to humans or place them into very constrained roles, e.g., on-demand labeling in active learning processes, and always assume some degree of batch processing of data. We satisfy the "total freedom" requirement by designing an unobtrusive machine learning model, i.e., the machine learning component of ICS as an unobtrusive observer of the users, that never interrupts them, continuously adapts and updates its models in response to their actions, and it is always available to perform automatic classifications. Our efficient implementation of the unobtrusive machine learning model combines various machine learning methods and technologies, such as hash-based feature mapping, random indexing, online learning, active learning, and asynchronous processing.