Linear separability and classification complexity

We study the relationship between linear separability and the level of complexity of classification data sets. Linearly separable classification problems are generally easier to solve than non linearly separable ones. This suggests a strong correlation between linear separability and classification complexity. We propose a novel and simple method for quantifying the complexity of the classification problem. The method, which is shown below, reduces any two class classification problem to a sequence of linearly separable steps. The number of such reduction steps could be viewed as measuring the degree of non-separability and hence the complexity of the problem. This quantification in turn can be used as a measure for the complexity of classification data sets. Results obtained using several benchmarks are provided.