The Classification Problem
Statistical classification considers a set of vectors of observations x of an object or event, each of which has a known type y. This set is referred to as the training set. The problem is then to determine for a given new observation vector, what the best class should be. For a quadratic classifier, the correct solution is assumed to be quadratic in the measurements, so y will be decided based on
In the special case where each observation consists of two measurements, this means that the surfaces separating the classes will be conic sections (i.e. either a line, a circle or ellipse, a parabola or a hyperbola). In this sense we can state that a quadratic model is a generalization of the linear model, and its use is justified by the desire to extend the classifier's ability to represent more complex separating surfaces.
Read more about this topic: Quadratic Classifier
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“It is commonplace that a problem stated is well on its way to solution, for statement of the nature of a problem signifies that the underlying quality is being transformed into determinate distinctions of terms and relations or has become an object of articulate thought.”
—John Dewey (1859–1952)