Search results
Results from the WOW.Com Content Network
Quadratic_discriminants_presentation.pdf (754 × 566 pixels, file size: 331 KB, MIME type: application/pdf, 5 pages) This is a file from the Wikimedia Commons . Information from its description page there is shown below.
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or ...
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 ...
The discriminant of a quadratic form, concretely the class of the determinant of a representing matrix in K / (K ×) 2 (up to non-zero squares) can also be defined, and for a real quadratic form is a cruder invariant than signature, taking values of only "positive, zero, or negative".
Gauss conjectures that there are infinitely many real quadratic fields with class number one. The original Gauss class number problem for imaginary quadratic fields is significantly different and easier than the modern statement: he restricted to even discriminants, and allowed non-fundamental discriminants.
The discriminant of a quadratic form is invariant under linear changes of variables (that is a change of basis of the vector space on which the quadratic form is defined) in the following sense: a linear change of variables is defined by a nonsingular matrix S, changes the matrix A into , and thus multiplies the discriminant by the square of ...
Mahalanobis distance is widely used in cluster analysis and classification techniques. It is closely related to Hotelling's T-square distribution used for multivariate statistical testing and Fisher's linear discriminant analysis that is used for supervised classification .
For quadratic equations with rational coefficients, if the discriminant is a square number, then the roots are rational—in other cases they may be quadratic irrationals. If the discriminant is zero, then there is exactly one real root − b 2 a , {\displaystyle -{\frac {b}{2a}},} sometimes called a repeated or double root or two equal roots.