Equivalence of Fisher Discriminant Analysis and Least Square

Linear Discriminant Analysis (LDA) is a well-known method for dimensionality reduction and classification. LDA in the binary-class case has been shown to be equivalent to linear regression with the class label as the output. This implies that LDA for binary class classification can be formulated as a least square problem. However many real-world applications involves multi-class classification, where a least square formulation for LDA is desirable.