Theoretical Analysis of a Soft Cut Discretization

Crisp discretization is widely-used and easy to implement, but it cannot work well on some situations, for example, when there is no clear boundary between attribute values or the attribute values are close to a cut point and possibly affected by random noise. A discretization method named Softcut was proposed to accommodate such situations and has been applied to face recognition. Softcut introduced a parameter τ that defined a symmetrical interval (0.5-τ, 0.5+τ) named uncertain interval. The attribute values in (0.5-τ, 0.5+τ) were undiscretizable. However, because the performance of Softcut may deteriorate in some situations, an extension named eSoftcut was proposed, in which the uncertain interval was defined by two parameters, (τj1, τj2). In this article, the theoretical aspects of eSoftcut including its definition, algorithm, and properties are introduced.