In dimensionality reduction techniques an important step is to construct optimal similarity graph to achieve effective classiffcation results. The graph construction process in many existing algorithms is manual and thus severely affects the classiffcation performance, if the neighborhood parameter is not optimal. Moreover, existing methods that are based on Collaborative representation lack the between-class information in the embedding process. In this paper, we addressed the problem of automatic Graph construction which is datum adaptive and incorporates within-class and between-class information into the linear representation to learn optimal projection for dimensionality reduction using the Collaborative representation technique. To optimize graph construction, the proposed method used the L₂ norm graph and log-Euclidean distance. The resultant graph shows local properties by Collaborative representation and global discriminate information is represented by a Maximum Margin classiffer (MMC). The MMC maximizes “between-class scatter” and minimizes “within-class scatter”, without locality information. Further for effective and accurate performance for image classiffcation real databases will be incorporated. The experimental results have demonstrated that the proposed methods achieved competitive results with compared methods.