On distance computation in space of mixed-type variables in medical data mining

In the next study we consider two distance metrics that were presented in the machine leaming literature for mixed-type variables. We show that they are not really metrics, but pseudometrics. The problem arose from missing values. The metrics can be redefined to satisfy the metricity definition. Distance computation can then be performed reliably without a possibility that a distance between exactly similar patient cases would not be zero. We experimented with both procedures and so-called ignore mode using two medical data sets and observed that the redefined procedure was as good as the original approach as measured with the classification ability of one-nearest neighbour searching. It is noticeable that the described problem caused by missing values can be with any distance measure if its missing values are treated in the pessimistic manner as in the original version of these distance measures.