Interval Discriminant Analysis : An Efficient Method to integrate Errors in Supervised Pattern Recognition

@inproceedings{nivlet:hal-04053616,
 abstract = {In a statistical pattern recognition context, probabilistic algorithms like parametric or nonparametric discriminant analysis are designed to classify objects into predefined classes. Because these methods require precise input data, they cannot propagate uncertainties in the classifying process. In real case studies, this could lead to drastic misinterpretations of objects. We have thus developed an extension of these methods to directly propagate imprecise interval-form data. The computations are based on interval arithmetic, which appears to be an efficient tool to handle intervals. They consist in calculating successively interval conditional probability density functions and interval posterior probabilities, whose definitions are closely associated with the imprecise probability theory. The algorithms eventually assign any object to a subset of classes, consistent with the data and its imprecision. The resulting classifying model is thus less precise, but much more realistic than the standard one. The efficiency of this algorithm is tested on a synthetic case study.},
 address = {Ithaca, United States},
 author = {Nivlet, Philippe and Fournier, Fr{\'e}d{\'e}rique and Royer, Jean-Jacques},
 booktitle = {{2nd International Symposium on Imprecise Probabilities and Their Applications}},
 hal_id = {hal-04053616},
 hal_version = {v1},
 keywords = {discriminant analysis ; interval arithmetic ; imprecise probabilities},
 title = {{Interval Discriminant Analysis : An Efficient Method to integrate Errors in Supervised Pattern Recognition}},
 url = {https://hal.univ-lorraine.fr/hal-04053616},
 year = {2001}
}