Question:
For any binary classification dataset, let \(S_B\in \R^{d\times d}\) and \(S_W\in \R^{d\times d}\) be the between-class and within-class scatter (covariance) matrices, respectively. The Fisher linear discriminant is defined by \(u^* \in \R ^d\), that maximizes
\(J(u)=\frac{u^TS_Bu}{u^TS_Wu}\)
If λ = J(u*), SW is non-singular and SB ≠ 0, then (u*, λ) must satisfy which ONE of the following equations ?
Note : R denotes the set of real numbers.
For any binary classification dataset, let \(S_B\in \R^{d\times d}\) and \(S_W\in \R^{d\times d}\) be the between-class and within-class scatter (covariance) matrices, respectively. The Fisher linear discriminant is defined by \(u^* \in \R ^d\), that maximizes
\(J(u)=\frac{u^TS_Bu}{u^TS_Wu}\)
If λ = J(u*), SW is non-singular and SB ≠ 0, then (u*, λ) must satisfy which ONE of the following equations ?
Note : R denotes the set of real numbers.
\(J(u)=\frac{u^TS_Bu}{u^TS_Wu}\)
If λ = J(u*), SW is non-singular and SB ≠ 0, then (u*, λ) must satisfy which ONE of the following equations ?
Note : R denotes the set of real numbers.
Updated On: Jul 9, 2024
- \(S_W^{-1}S_Bu^*=\lambda u^*\)
- \(S_Wu^*=\lambda S_Bu^*\)
- \(S_BS_Wu^*=\lambda u^*\)
- \(u^{*T}u^*=\lambda^2\)
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The Correct Option is A
Solution and Explanation
The correct option is (A) : \(S_W^{-1}S_Bu^*=\lambda u^*\).
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