Activities performed in the same location in a smart home share common features and thus become difficult to classify. We propose an activity recognition approach that identifies key features from the information obtained using the sensors deployed in multiple locations and objects. Key features increase the separability between the classes, making the approach suitable for overlapping activities. For fewer number of activity instances in a class, we apply an oversampling approach for data balancing. The classification is performed using a learning method Evidence Theoretic K-Nearest Neighbors (ET-KNN), which performs better in uncertain conditions. Evaluation of the proposed approach using three publicly available smart home datasets demonstrates better recognition performance compared to the existing methods.