A New Nonparametric Discriminant Analysis Algorithm Accounting for Bounded Data Errors

In a statistical pattern recognition context, discriminant analysis is designed to classify, when possible, objects into predefined categories. Because this method requires precise input data, uncertainties cannot be propagated in the classifying process. In real case studies, this could lead to drastic misinterpretations of objects. A new nonparametric algorithm based on interval arithmetic has thus been developed to propagate interval-form data. They consist in calculating interval conditional probability density functions and interval posterior probabilities. Objects are eventually assigned to a subset of classes, consistent with the data and their uncertainties. The classifying model is thus less precise, but more realistic than the standard one, which we prove on a real case study.