Research On Robust Feature Extraction Algorithm Based On Joint Norm

With the rapid development of science and technology,image recognition technology is widely used in face recognition,scene recognition,shape recognition and other application scenarios.The so-called image recognition is to extract the pattern features of images and classify them,and the most critical step is feature extraction.Principal Component Analysis(PCA)is one of the classical feature extraction methods,which is widely used in the field of image recognition.In the process of image acquisition and storage,it is often affected by image acquisition equipment,light intensity,image background and image storage mode,which is easy to cause image samples to be polluted by noise.This requires that the algorithm can reduce the influence of noise on the whole sample data during feature extraction of the sample data containing noise,that is,the algorithm has robustness.In order to realize the robustness of the algorithm,this paper deeply studies the robust feature extraction algorithm based on joint norm from the perspective of maximum PCA projection variance.The main contents of this paper are as follows:(1)Two-dimensional PCA(2DPCA)and Sequential Row-Column 2DPCA(RC2DPCA)use Euclidean distance squared to measure distance.The robustness of the algorithm is low.2DPCA-L₁ algorithm uses L₁ norm to measure distance,and its robustness is improved,but its objective function does not optimize the reconstruction error.Angle-2DPCA algorithm uses F-norm as the distance measurement of the objective function in the row direction,and its robustness is further improved,but it ignores the data structure information in the column direction.In view of the above related problems,this paper takes the F-norm as the distance measurement method,and simultaneously considers the optimization projection variance and the reconstruction error.a bidirectional two-dimensional principal component analysis algorithm Based on F-norm(B2DPCA-F)is proposed.The reconstruction error and projection variance are integrated into the objective function and solved by non-greedy iterative method.Experiments results on ORL,Yale face datasets and self-built weld dataset show that the average classification rate performance and the average reconstruction error performance of B2DPCA-F algorithm are better than 2DPCA,RC2DPCA,2DPCA-L₁and Angle-2DPCA,and have better robustness.(2)B2DPCA-F algorithm uses F norm as distance measure when constructing objective function,but it is still sensitive to noise.Considering that distance measurement using L₁ norm can weaken the influence of noise,a two-dimensional principal component analysis algorithm based on L₁-F joint norm(2DPCA based on L₁-F joint norm,2DPCA-L₁-F)is proposed in this paper.The algorithm integrates the reconstruction error,the projection variance and image samples into the objective function,constrains the original image samples with L₁ norm,constrains the reconstruction error and the projection variance with F norm,and solves them in a non-greedy way.The experimental results show that the average classification rate performance of 2DPCA-L₁-F algorithm is equivalent to that of 2DPCA,RC2DPCA,2DPCA-L₁and Angle-2DPCA algorithms,and the average reconstruction error performance of 2DPCA-L₁-F algorithm is slightly lower than that of 2DPCA,RC2DPCA,2DPCA-L₁ and Angle-2DPCA algorithms.It may be that both the reconstruction error and the projection variance use F-norm,which is equivalent to using square F-norm for distance measurement.As a result,the distance measurement based on L₁ norm does not weaken the noise and reduce the robustness of the algorithm.(3)Aiming at the problems in 2DPCA-L₁-F algorithm,considering the special case that L₁ norm is L_P norm,a two-dimensional principal component analysis algorithm based on L₂-Lp joint norm(2DPCA based on L₂-Lp joint norm,2DPCA-L₂-Lp)is proposed.The algorithm integrates the projection variance and image samples into the objective function,constrains the image samples with F norm and constrains the projection variance with L_p,and solves it in a greedy way.The experimental results show that the average classification rate performance and the average reconstruction error performance of 2DPCA-L₂-Lp algorithm are higher than those of the above comparison algorithms,and have better robustness.