Discriminant & TableOfReal: To ClassificationTable...

A command to use the selected Discriminant to classify each row from the selected TableOfReal. The newly created ClassificationTable will then contain the posterior probabilities of group membership.

## Settings

Pool covariance matrices
  when on, all group covariance matrices are pooled and distances will be determined on the basis of only this pooled covariance matrix (see below).

## Details

The posterior probabilities of group membership pj for a vector x are defined as:

pj = p(j|x) = exp (–dj2(x) / 2) / ∑k=1..numberOfGroups exp (–dk2(x) / 2),

where di2 is the generalized squared distance function:

di2(x) = ((x–μi)′ Σi-1 (x–μi) + ln determinant (Σi)) / 2 – ln aprioriProbabilityi

that depends on the individual covariance matrix Σi and the mean μi for group i.

When the covariances matrices are pooled, the squared distance function can be reduced to:

di2(x) = ((x–μi)′ Σ-1 (x–μi) – ln aprioriProbabilityi,

and Σ is now the pooled covariance matrix.

The a priori probabilities normally will have values that are related to the number of training vectors ni in each group:

aprioriProbabilityi = ni / Σk=1..numberOfGroups nk

### Links to this page

- Discriminant & PatternList: To Categories...
- Discriminant analysis