Image Clustering Algorithm Based On Conjugate Tikhonov Regularization L_r,c Non-Negative Matrix Factorization

The development of computer technology has produced a large number of complex high-dimensional data,which are often computationally complex and ambiguous in expressing information.Therefore,how to reduce the dimensionality of data through appropriate dimensionality reduction technology,and extract feature information that is beneficial to practical problems is particularly critical.Non-negative matrix factorization is a classical dimensionality reduction technique,which has become one of the mainstream algorithms because it considers non-negative constraints,the whole can be represented by local sparseness,and has good interpretability.It has been widely used in text mining,facial recognition,and image clustering.In the image clustering task,the grayscale image with size r×c is usually rearranged into a sample vector by column,and then multiple sample vectors are stored in the sample data matrix,which often changes the original spatial structure of the image data,while the objective function of traditional NMF,LL_2,1NMF and other algorithms directly measures the error between the sample vector and the reconstructed vector will further ignore the similarity between the original image and the reconstructed image column,resulting in the base matrix can not extract more feature information.In addition,for data carrying Gaussian noise,traditional NMF measures the error in terms of the Frobenius norm of the matrix,and this objective function is consistent with the Gaussian model of noise obeying the 0 mean,resulting in the numerical stability of the algorithm being easily affected by noise.Therefore,in order to consider the change of the spatial structure of the original image data and reduce the influence of the algorithm by noise or outliers,a new loss function,theL_r,cfunction of the vector is proposed,which can measure the error between the original image data and the reconstructed image data by column,and based on this function,we propose aL_r,cNMF model and design a numerical algorithm for the model.At the same time,theL_r,cNMF and theL_2,1NMF algorithm are subject to the0-mean Laplace model,are not susceptible to noise and outliers,inherit the robustness of theL_2,1NMF algorithm,in addition,the experimental results show that compared with theL_2,1NMF and NMF algorithm,the basis matrix learned by theL_r,cNMF algorithm has richer feature information.In order to prevent the algorithm from overfitting,on the basis of theL_r,cNMF algorithm,the Tikhonov regularization term is also considered,and the TL_r,cNMF algorithm and the CTL_r,cNMF algorithm are proposed.Experimental results show the effectiveness and rationality of the proposed algorithm.