The problem of responses less than the reporting limit in unsupervised pattern recognition

The problem of the presence and of the treatment of values below the detection limit (or 'less than' values) is examined, for some real cases of unsupervised pattern recognition of samples. The experimental data refer to archaeological glass fragments of the seventh and eighth centuries AD and to ceramic shards of Roman epoch and of different provenances. Increasing amounts of less-thans are progressively introduced into the original data by a particular procedure and the less-thans treated each time with three different substitution methods (i.e. substitution with constant values, with randomly distributed values and with values obtained by principal component analysis). A subsequent multivariate classification of the samples by various techniques and an evaluation of the corresponding results, allows one to evaluate and to compare the effectiveness of the three methods of treatment of less-thans.