Application Of FCM-based Non-negative Matrix Factorization In Image Clustering

Image clustering is a process of dividing a group of data into clusters so that the data within the cluster are similar to each other but the data between the clusters are not similar.As an effective dimensionality reduction method,non-negative matrix factorization(NMF)can well mine the potential structural features of the data and reduce the data dimension.Due to the strong interpretability of NMF,it becomes an effective algorithm for clustering tasks.However,traditional NMF still has some shortcomings.We are required to preserve the structure of the original data information for complex high-dimensional data,which makes its convergence speed and clustering accuracy need to be further improved.In addition,NMF is essentially a dimensionality reduction technique and cannot be directly used for clustering.Fuzzy C-means(FCM)is a very classical clustering algorithm,but the sensitivity of FCM for the complex structure of high-dimensional data,initial value and noise all lead to the decline of its clustering effect.Based on NMF and FCM,this paper proposes three new image clustering algorithms.First,in view of the problem that the traditional FCM algorithm will generate a large amount of computation when dealing with high-dimensional data sets with complex structures.The large amount of computation will lead to the decline of the clustering effect,a new clustering algorithm-based non-negative matrix factorization on modified Fuzzy Clustering Algorithm(MFCM-NMF)is proposed.The algorithm uses non-negative matrix decomposition for dimensionality reduction,and extracts the essential features of the data as the cluster centers of fuzzy clustering.Combining NMF and MSFCM,a new objective function is proposed and solved by an alternate iterative algorithm.In the iterative process,those samples that do not change their nearest cluster centers in the next iteration are filtered out based on the triangular inequality method.A new membership update formula is used for the filtered samples to reduce the amount of computation and improve the clustering performance.Second,generally,the initial value of FCM is randomly assigned,which has a great impact on the clustering of FCM.Therefore,a modified fuzzy clustering algorithm based on local constrained non-negative matrix factorization(MFCM-LCNMF)is proposed.The method is to use the non-negative matrix decomposition to reduce the dimension of the data to obtain a low-dimensional representation of the data,and use the low-dimensional representation of the data as the original data of the FCM to reduce the influence of the initial value.However,the non-negative matrix decomposition will lose Some information inevitably,in order to better preserve the local geometry,we add local linear constraints to the objective function.Third,the sensitivity of FCM to noise inevitably leads to the decline of the clustering effect.In order to improve the clustering effect,the2,1L NMF with noise residual estimation is combined with the improved FCM,the robustness of2,1L NMF and the noise constraint term are used to weaken the influence of noise on data clustering.In addition,since the low-dimensional representation of NMF is the hub connecting2,1L NMF and FCM,in order to obtain a more accurate low-dimensional representation,we construct a new local constraint term with the new metric.Based on this,Robust denoising FCM clustering via2,1L NMF and local constraint(RFCM-NMF)is proposed.For the above three methods,the iterative update formula is given by solving the optimization model,and the effectiveness of these methods is verified by experiments to improve the clustering effect.