Partial classification: the benefit of deferred decision

It is shown that partial classification which allows for indecision in certain regions of the data space, can increase a benefit function, defined as the difference between the probabilities of correct and incorrect decisions, joint with the event that a decision is made. This is particularly true for small data samples, which may cause a large deviation of the estimated separation surface from the intersection surface between the corresponding probability density functions. Employing a particular density estimation method, an indecision domain is naturally defined by a single parameter whose optimal size, maximizing the benefit function, is derived from the data. The benefit function is shown to translate into profit in stock trading. Employing medical and economic data, it is shown that partial classification produces, on average, higher benefit values than full classification, assigning each new object to a class, and that the marginal benefit of partial classification reduces as the data size increases.