Extraction of discriminant features in post-cardiosurgical intensive care units

A linear transformation, based on the Karhunen-Loève expansion, is applied to 13 physiological variables, measured in 200 surgical patients, in order to extract a limited number of features well representative of the differences between normal and high-risk classes of subjects. This transformation may be considered as a mapping from the primitive 13-dimensional space to a lower dimensional one, without severely reducing class separability. The efficacy of both transformed and primitive variables in the separation of normal and high-risk subjects is compared using the error probability, i.e. the probability that a patient is assigned to the wrong class. In particular, its upper bound is evaluated through the Kullback divergence and its estimate is computed, from the available samples, by applying a quadratic classifier. The results obtained show that only two transformed variables are able to present a divergence better than the most effective set of eight primitive variables. In agreement with the divergence criterion, the classifier provides a recognition error lower than 5% and greater than 13% when using the two best transformed and the two best primitive variables, respectively. Even though the new variables do not have a direct physiological meaning, this limitation has been partially overcome by calculating the correlation matrix between transformed and primitive variables. The results presented show that the first two transformed variables are strongly related to the most discriminant primitive ones (i.e. cardiac index, oxygen delivery and arterio-venous oxygen difference). In conclusion, the transformation of variables proposed appears to be extremely attractive for practical applications, since it allows recognition systems to be designed which exhibit both high performance and great simplicity.