Geometric insights into support vector machine behavior using the KKT conditions

The support vector machine (SVM) is a powerful and widely used classification algorithm. This paper uses the Karush-Kuhn-Tucker conditions to provide rigorous mathematical proof for new insights into behavior of SVM. These perhaps unexpected relationships between SVM two other linear classifiers: mean difference maximal data piling direction. For example, we show that in many cases can be viewed as cropped version these classifiers. By carefully exploring connections how tuning affected by characteristics including: balanced vs. unbalanced classes, low high dimension, separable non-separable data. results further via cross-validation explaining observed pathological motivating improved methodology. Finally, also on geometry complete directions dimensional space.