# Discriminant

Also found in: Dictionary, Wikipedia.
Related to Discriminant: discriminant function

## discriminant

[di′skrim·ə·nənt]
(mathematics)
The quantity b 2- 4 ac, where a,b,c are coefficients of a given quadratic polynomial: ax 2+ bx + c.
More generally, for the polynomial equation a0 xn + a1 xn -1+···+ anx0= 0, a02 n-2times the product of the squares of all the differences of the roots of the equation, taken in pairs.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Discriminant

The discriminant of a polynomial

P(x) = a0xn + a1xn−1 + … + an

is the expression in which the product is distributed over all possible differences of the roots α1, β2, … , αn of the equation P (x) = 0. The discriminant vanishes if and only if there are equal roots among the roots of the polynomial. The discriminant can be expressed through the coefficients of the polynomial P(x) by representing it in the form of a determinant consisting of these coefficients. Thus, for the second-degree polynomial ax2 + bx + c, the discriminant is b2 − 4ac. For x3 + px + q, the discriminant is −4p3 −27q2. The discriminant differs only by a factor a0 from the resultant R(P, P′) of the polynomial P(x) and its derivative P′(x).

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Erimafa, Iduseri, and Edokpa, (2009) carried out a study to predict the class of degree obtained in university system by using discriminant analysis.
In this paper, we propose a semi-supervised multi-view manifold discriminant intact space learning (S[M.sup.2]DIS) approach.
Before implementing the canonical discriminant analysis, Pearson's correlation among the variables was conducted to identify the variables which were not important for study.
One of them is Generalized Singular Value Decomposition (GSVD)  which is generally applied by various discriminant analysis approaches [18, 19].
Next, discriminant analysis using MANOVA is done to factor out the variables that differentiate investors on the basis of age, income-group and the type of investors.
Although we extracted five discriminant functions, only the first one proved significant at the level of p<0.05.
The sources said the project is, therefore, aimed to identify discriminant sub-bands for efficient and robust face recognition.
These body parameters are also better assessed using multivariate principal component and discriminant analyses than the univariate approach (Yakubu et al., 2009; Malomane et al., 2014; Ribeiro et al., 2016; Dahloum et al., 2016).
Numerous scholars have carried out considerable research on water inrush source models and obtained great success in their practical application, However, present discriminant methods have not considered the complicated information superposition problem between hydrochemical data, a problem that results in misdiscrimination of the established model in the practical application process, and their discrimination accuracy still needs further improvement.
Discriminant functions are especially effective in the case of gulls (Laridae), allowing correct sexing from 90 to 100 % of individuals from different species (Mawhinney & Diamond 1999, Chochi et al.
Discriminant analysis is a multivariate statistical method that can distinguish newly acquired samples according to the quantitative characteristics of the existing observational sample.
The purpose of this paper is to design and develop a credit risk rating model for Indian state-owned banks based on multivariate discriminant analysis (MDA) using both financial and non-financial variables and find which category of variables had the strongest impact within the given samples.

Site: Follow: Share:
Open / Close