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Continuing from where we left of in [[Discriminant Functions For The Normal(Gaussian) Density|Part 1]], after establishing the basic format of a discriminant function, we will now look at the multiple cases for a multivariate normal distribution. | Continuing from where we left of in [[Discriminant Functions For The Normal(Gaussian) Density|Part 1]], after establishing the basic format of a discriminant function, we will now look at the multiple cases for a multivariate normal distribution. | ||
| − | '''Case 1: &Sigma<sub>i</sub> = &sigma<sup>2</sup>I''' | + | '''Case 1: Σ<sub>i</sub> = σ<sup>2</sup>I''' |
| − | This is the simplest case and it occurs when the features are statistically independent and each feature has the same variance, &sigma<sup>2</sup> | + | This is the simplest case and it occurs when the features are statistically independent and each feature has the same variance, σ<sup>2</sup>. Here, the covariance matrix is diagonal since its simply σ<sup>2</sup> times the identity matrix '''I'''. |
Revision as of 05:22, 13 April 2013
Discriminant Functions For The Normal Density - Part 1
Continuing from where we left of in Part 1, after establishing the basic format of a discriminant function, we will now look at the multiple cases for a multivariate normal distribution.
Case 1: Σi = σ2I
This is the simplest case and it occurs when the features are statistically independent and each feature has the same variance, σ2. Here, the covariance matrix is diagonal since its simply σ2 times the identity matrix I.
