Non-Parametric Pattern Recognition Part Ⅰ: The Locally Disjoint Case

摘要

The validity of the decision theoretic approach to pattern recognition depends primarily on the assumptions of the unknown under-lying probability distribution. Here a mathematically rigorous procedure is developed which transforms the underlying unknown probability structure and then partitions the space by non-parametric techniques. In particular, the procedure transforms the learned samples to the real line using a functional which is dependent on estimates obtained from the learned samples. Treating these transformed one-dimensional random variables in terms of cumulative distribution, the underlying probability space is then partitioned by the fact that the location of the extrema of the difference or cumulative functions will converge to the boundaries of the likelihood decision rule. The decision rule which essentially defines this procedure is dependent on the location of the extrema. Moreover, this decision will provide perfect discrimination between category j and k for some finite learning phase if j and k are locally separate or disjoint.