Estimation of classification complexity

Classification problems vary on their level of complexity. Several methods have been proposed to calculate this level but it remains difficult to measure. Linearly separable classification problems are amongst the easiest problems to solve. There is a strong correlation between the degree of linear separability of a problem and its level of complexity. The more complex a problem is the more non-linear separable the data is. Here we propose a novel and simple method for quantifying, between 0 and 1, the complexity level of classification problems based on the degree of linear separability of the data set representing the problem. The method is based on the transformation of nonlinearly separable problems into linearly separable ones. Results obtained using several benchmarks are provided.