Separability assessment of two-pattern multidimensional input spaces by inconsistent-case recognition

In pattern classification problems, if an input space is not completely separable, there will appear some ´inconsistent cases´ which lie in the regions occupied by other classes. The separability of the input space can be indicated by the ratio of the inconsistent cases. In this paper, a systematic method for recognizing the inconsistent cases is presented based on an extended nearest-neighbor classification concept. The regions occupied by the different classes can be found by defining a group of hyper-cubic neighboring regions around their samples. The inconsistent cases can be easily sorted out based on the defined hypercubic neighboring regions for separability assessment. The numerical results for a 2-dimensional input space show the effectiveness of the proposed method for separability assessment. As an application example, the proposed method is also applied to the transient-stability classification of power systems.