In manufacturing and processing, it is of great significance to grasp the global information of process physical quantities for the overall machining of parts. However, the global information requires a large amount of data, and some machining physical quantities such as deformation, force and stiffness are difficult to measure. This paper proposes a model sparse representation strategy based on key points extraction, which can indirectly obtain the key points information of physical quantity through the determination of the greatest common divisor, so as to grasp the global distribution information. In the field of robotic machining deformation, considering the two factors that determine the machining deformation, the cutting force prediction model and the robotic end stiffness model based on PCA-GPR are developed. Then, through the clustering analysis and boundary line fitting of the force and stiffness distribution data, the key points extraction method of ridge line and ridge key value is proposed, and the key points is determined by the largest common divisor. The key points of deformation are obtained, and the global distribution information of deformation is obtained. Finally, the sparse representation error is calculated, which verifies the reliability of the sparse representation strategy.