Artificial olfaction is a potential tool for noninvasive chemical monitoring. Application of "electronic noses" typically involves recognition of "pretrained" chemicals, while long-term operation and generalization of training to allow chemical classification of "unknown" analytes remain challenges. The latter analytical capability is critically important, as it is unfeasible to pre-expose the sensor to every analyte it might encounter. Here, we demonstrate a biologically inspired approach where the recognition and generalization problems are decoupled and resolved in a hierarchical fashion. Analyte composition is refined in a progression from general (e.g., target is a hydrocarbon) to precise (e.g., target is ethane), using highly optimized response features for each step. We validate this approach using a MEMS-based chemiresistive microsensor array. We show that this approach, a unique departure from existing methodologies in artificial olfaction, allows the recognition module to better mitigate sensor-aging effects and to better classify unknowns, enhancing the utility of chemical sensors for real-world applications.