In this work, discriminant analysis is used as the main approach for building a physics based automated classifier for the discrimination of the edge-localized mode (ELM) plasma instability. The classifier is then applied for distinguishing type I and type III ELMs from a set of carbon-wall plasmas at JET. This provides a fast, standardized classification of ELM types which is expected to significantly reduce the effort of ELM experts in identifying ELM types. Further, the classifier yields a separation hyperplane in terms of global plasma parameters, which provides an insight into the range of conditions under which specific ELM behaviors occur.