Mathematic explanation needed for a univariate classification method based on solving a quadratic equation
$begingroup$
I read a piece of codes on classifying image hue values into three classes with derived thresholds. The thresholds are calculated by simply using a quadratic formula. The related documentations for the codes are as follows:
/*
* (v_B - v_A)x^2 + 2(m_B*v_A - m_A*v_B)x + (m_A^2*v_B - m_B^2*v_A) = 0
*
* v_A : variance of group A
* m_A : mean of group A
* v_B : variance of group B
* m_B : mean of group B
*
* Quadratic formula
* ax^2 + bx + c = 0
* a = v_B - v_A
* b = 2(m_B*v_A - m_A*v_B)
* c = (m_A^2*v_B - m_B^2*v_A)
*
* x1 = (-b+sqrt(b^2-4ac))/2a
* x2 = (-b-sqrt(b^2-4ac))/2a
*
*/
Here above is to find a threshold to delimit the class A and B, based on solving a quadratic equation involving the mean and variance of the two groups, and the threshold is one of the solutions (i.e., x1 and x2) depending on their signs.
I haven't seen such a quadratic equation based classification method before. Anyone know what formal name for the method? It, on the first sight, seems to me a simplified case of quadratic discriminant analysis, but not sure about that. I need a little bit mathematic background for the method. Educate me if you know that. Thanks!
classification
asked 10 hours ago
jingweimojingweimo
1012
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$begingroup$
I read a piece of codes on classifying image hue values into three classes with derived thresholds. The thresholds are calculated by simply using a quadratic formula. The related documentations for the codes are as follows:
/*
* (v_B - v_A)x^2 + 2(m_B*v_A - m_A*v_B)x + (m_A^2*v_B - m_B^2*v_A) = 0
*
* v_A : variance of group A
* m_A : mean of group A
* v_B : variance of group B
* m_B : mean of group B
*
* Quadratic formula
* ax^2 + bx + c = 0
* a = v_B - v_A
* b = 2(m_B*v_A - m_A*v_B)
* c = (m_A^2*v_B - m_B^2*v_A)
*
* x1 = (-b+sqrt(b^2-4ac))/2a
* x2 = (-b-sqrt(b^2-4ac))/2a
*
*/
Here above is to find a threshold to delimit the class A and B, based on solving a quadratic equation involving the mean and variance of the two groups, and the threshold is one of the solutions (i.e., x1 and x2) depending on their signs.
I haven't seen such a quadratic equation based classification method before. Anyone know what formal name for the method? It, on the first sight, seems to me a simplified case of quadratic discriminant analysis, but not sure about that. I need a little bit mathematic background for the method. Educate me if you know that. Thanks!
classification
asked 10 hours ago
jingweimojingweimo
1012
New contributor
jingweimo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment |
$begingroup$
I read a piece of codes on classifying image hue values into three classes with derived thresholds. The thresholds are calculated by simply using a quadratic formula. The related documentations for the codes are as follows:
/*
* (v_B - v_A)x^2 + 2(m_B*v_A - m_A*v_B)x + (m_A^2*v_B - m_B^2*v_A) = 0
*
* v_A : variance of group A
* m_A : mean of group A
* v_B : variance of group B
* m_B : mean of group B
*
* Quadratic formula
* ax^2 + bx + c = 0
* a = v_B - v_A
* b = 2(m_B*v_A - m_A*v_B)
* c = (m_A^2*v_B - m_B^2*v_A)
*
* x1 = (-b+sqrt(b^2-4ac))/2a
* x2 = (-b-sqrt(b^2-4ac))/2a
*
*/
Here above is to find a threshold to delimit the class A and B, based on solving a quadratic equation involving the mean and variance of the two groups, and the threshold is one of the solutions (i.e., x1 and x2) depending on their signs.
I haven't seen such a quadratic equation based classification method before. Anyone know what formal name for the method? It, on the first sight, seems to me a simplified case of quadratic discriminant analysis, but not sure about that. I need a little bit mathematic background for the method. Educate me if you know that. Thanks!
classification
asked 10 hours ago
jingweimojingweimo
1012
New contributor
jingweimo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I read a piece of codes on classifying image hue values into three classes with derived thresholds. The thresholds are calculated by simply using a quadratic formula. The related documentations for the codes are as follows:
/*
* (v_B - v_A)x^2 + 2(m_B*v_A - m_A*v_B)x + (m_A^2*v_B - m_B^2*v_A) = 0
*
* v_A : variance of group A
* m_A : mean of group A
* v_B : variance of group B
* m_B : mean of group B
*
* Quadratic formula
* ax^2 + bx + c = 0
* a = v_B - v_A
* b = 2(m_B*v_A - m_A*v_B)
* c = (m_A^2*v_B - m_B^2*v_A)
*
* x1 = (-b+sqrt(b^2-4ac))/2a
* x2 = (-b-sqrt(b^2-4ac))/2a
*
*/
Here above is to find a threshold to delimit the class A and B, based on solving a quadratic equation involving the mean and variance of the two groups, and the threshold is one of the solutions (i.e., x1 and x2) depending on their signs.
I haven't seen such a quadratic equation based classification method before. Anyone know what formal name for the method? It, on the first sight, seems to me a simplified case of quadratic discriminant analysis, but not sure about that. I need a little bit mathematic background for the method. Educate me if you know that. Thanks!
classification
classification
asked 10 hours ago
jingweimojingweimo
1012
New contributor
jingweimo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 hours ago
jingweimojingweimo
1012
New contributor
jingweimo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 8 hours ago
jingweimo
asked 10 hours ago
jingweimojingweimo
1012
New contributor
jingweimo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 10 hours ago
jingweimojingweimo
1012
asked 10 hours ago
jingweimojingweimo
1012
1012
New contributor
jingweimo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
jingweimo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
jingweimo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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