Detecting human activity independent of intensity is essential in many applications, primarily in calculating metabolic equivalent rates and extracting human context awareness. Many classifiers that train on an activity at a subset of intensity levels fail to recognize the same activity at other intensity levels. This demonstrates weakness in the underlying classification method. Training a classifier for an activity at every intensity level is also not practical. In this paper, we tackle a novel intensity-independent activity recognition problem where the class labels exhibit large variability, the data are of high dimensionality, and clustering algorithms are necessary. We propose a new robust stochastic approximation framework for enhanced classification of such data. Experiments are reported using two clustering techniques, K-Means and Gaussian Mixture Models. The stochastic approximation algorithm consistently outperforms other well-known classification schemes which validate the use of our proposed clustered data representation. We verify the motivation of our framework in two applications that benefit from intensity-independent activity recognition. The first application shows how our framework can be used to enhance energy expenditure calculations. The second application is a novel exergaming environment aimed at using games to reward physical activity performed throughout the day, to encourage a healthy lifestyle.