Pattern recognition is becoming an increasingly important tool for making inferences from the massive amounts of data produced in fusion experiments. In this work, we present an integrated framework for (real-time) pattern recognition for fusion data. The main starting point is the inherent probabilistic nature of measurements of plasma quantities. Since pattern recognition is essentially based on geometric concepts such as the notion of distance, this necessitates a geometric formalism for probability distributions. To this end, we apply information geometry for calculating geodesic distances on probabilistic manifolds. This provides a natural and theoretically motivated similarity measure between data points for use in pattern recognition techniques. We apply this formalism to classification for the automated identification of plasma confinement regimes in an international database and the prediction of plasma disruptions at JET. We show the distinct advantage in terms of classification performance that is obtained by considering the measurement uncertainty and its geometry. We hence advocate the essential role played by measurement uncertainty for data interpretation in fusion experiments. Finally, we discuss future applications such as the establishment of scaling laws.