Detecting human activity independent of intensity is essential in many applications, primarily in calculating metabolic equivalent rates (MET) and extracting human context awareness from on-body inertial sensors. Many classifiers that train on an activity at a subset of intensity levels fail to classify the same activity at other intensity levels. This demonstrates weakness in the underlying activity model. 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 application where the class labels exhibit large variability, the data is 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 for each dataset using two clustering techniques, K-Means and Gaussian Mixture Models. The Stochastic Approximation algorithm consistently outperforms other well-known classification schemes which validates the use of our proposed clustered data representation.