In biometrics field, usually feature vectors have major length and contain ineffective information. This problem is so called “curse of dimensionality‟. Hence, there is a need for efficient dimensionality reduction technique to remove the redundant features and reduce the size of feature vectors to get high accuracy rate with fast performance. In this paper a comprehensive study of commonly used dimensionality reduction techniques: Principle Component Analysis, Linear Discremenant Analysis, and Generalized Discremenant Analysis, have been handled. Theoretical background of these techniques is illustrated along with the methods used to calculate their projection spaces then; practical implementation is conducted to find out and adopt the best one for retina based biometric authentication system. From this extensive study, it has been concluded that PCA technique has a number of problems make it has a bad classification power. LDA technique has a number of problems make it impossible to implement in most cases of biometrics field, while GDA technique is more efficient than the PCA and LDA techniques for dimensionality reduction purpose. It has high classification power and consumes less computational time. Hence, GDA technique is adopted in the proposed authentication system.