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Discriminants of the second class arise for problems depending on coefficients, when degenerate instances or singularities of the problem are characterized by the vanishing of a single polynomial in the coefficients. This is the case for the discriminant of a polynomial, which is zero when two roots collapse.
PCA, in contrast, does not take into account any difference in class, and factor analysis builds the feature combinations based on differences rather than similarities. Discriminant analysis is also different from factor analysis in that it is not an interdependence technique: a distinction between independent variables and dependent variables ...
Repeated discriminants: the discriminant of a quadratic field uniquely identifies it, but this is not true, in general, for higher-degree number fields. For example, there are two non-isomorphic cubic fields of discriminant 3969. They are obtained by adjoining a root of the polynomial x 3 − 21x + 28 or x 3 − 21x − 35, respectively. [7]
The extension to cases where there are more than two classes is relatively straightforward. [2] [6] [7] Let be the number of classes.Then multi-class KFD involves projecting the data into a ()-dimensional space using () discriminant functions
A result greater than 0.70, however, suggests that the two constructs overlap greatly and they are likely measuring the same thing, and therefore, discriminant validity between them cannot be claimed. [1] Consider researchers developing a new scale designed to measure narcissism.
The set of discriminants of quadratic fields is exactly the set of fundamental discriminants (apart from , which is a fundamental discriminant but not the discriminant of a quadratic field). Prime factorization into ideals
An extension L that is a splitting field for a set of polynomials p(X) over K is called a normal extension of K.. Given an algebraically closed field A containing K, there is a unique splitting field L of p between K and A, generated by the roots of p.
Discriminative models, also referred to as conditional models, are a class of models frequently used for classification.They are typically used to solve binary classification problems, i.e. assign labels, such as pass/fail, win/lose, alive/dead or healthy/sick, to existing datapoints.