> For the complete documentation index, see [llms.txt](https://statduck.gitbook.io/statduck/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://statduck.gitbook.io/statduck/esl/ch4.-linear-methods-for-classification/rda.md).

# RDA

### ✏️ Definition

RDA(Regularized Discriminant Analysis) is the combinational model between LDA and QDA.

$$
\hat{\Sigma}\_k(\alpha)=\alpha\hat{\Sigma}\_k+(1-\alpha)\hat{\Sigma}, \quad \alpha \in\[0,1]
$$

Vector internal division. This is most common in combinational model. $$\hat{\Sigma}$$is a pooled covariance matrix from LDA.  If we replace $$\hat{\Sigma}$$as $$\hat{\Sigma}(\gamma)$$,  this also can be changed into  $$\hat{\Sigma}(\alpha,\gamma)$$. For generalization, parameter is just added.

$$
\hat{\Sigma}(\gamma)=\gamma\hat{\Sigma}+(1-\gamma)\hat{\sigma}^2I, \quad \gamma \in\[0,1]
$$

$$\hat{\sigma}^2I$$ also can be changed into $$diag(\hat{\Sigma}), \hat{\Sigma}/p,...$$ 

![](https://1943863620-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MZyJM_SVjd9SJ3tuTbA%2F-MbnpJfqnHSCcWIFZZpH%2F-MboDmnIW_lBGA4uF2JX%2Fimage.png?alt=media\&token=3f0459f4-1271-446c-942a-55ef62867fa4)