Learning from experience and adapting to changing stimuli are fundamental capabilities for artificial cognitive systems. This calls for on-line learning methods able to achieve high accuracy while at the same time using limited computer power. Research on autonomous agents has been actively investigating these issues, mostly using probabilistic frameworks and within the context of navigation and learning by imitation. Still, recent results on robot localization have clearly pointed out the potential of discriminative classifiers for cognitive systems. In this paper we follow this approach and propose an on-line version of the Support Vector Machine (SVM) algorithm. Our method, that we call On-line Independent SVM, builds a solution on-line, achieving an excellent accuracy vs.~compactness trade-off. In particular the size of the obtained solution is always bounded, implying a bounded testing time. At the same time, the algorithm converges to the optimal solution at each incremental step, as opposed to similar approaches where optimality is achieved in the limit of infinite number of training data. These statements are supported by experiments on standard benchmark databases as well as on two real-world applications, namely $(a)$ place recognition by a mobile robot in an indoor environment, and $(b)$ human grasping posture classification.