Researches On Non-negative Matrix Factorization Algorithms Based On Huber Loss In Clustering

Non-negative matrix factorization is a classic data analysis tool that is widely used in clustering tasks.It guarantees a good approximation of the original matrix,and finds a non-negative,linear matrix representation for the original data.Because the features extracted by this method are non-negative,they are consistent with the essential characteristics of real data,so they are used to process image data,spectral data,and gene expression data.In addition to application fields,non-negative matrix factorization has also received a lot of attention in the scientific research field,and now many research results have appeared in the field of vision.Based on the existing research methods and theories,this paper further analyzes the advantages and disadvantages of the algorithm and makes corresponding improvements.The main work of the thesis is as follows:(1)The traditional non-negative matrix factorization algorithm uses the mean square error function to measure the reconstruction error.The model's fitting effect is easily affected when processing data with large noise.The penalty performed by the Huber loss function for smaller residuals is the same as the mean squared error loss function.The penalty performed for larger residuals increases linearly,so Huber loss function has a stronger strength than the mean squared error loss function.The robustness of 2,1norm sparse regular terms has been proven to have feature selection in machine learning classification and clustering models.Combining the advantages of the two,this paper proposes a non-negative matrix factorization algorithm based on Huber loss function and incorporating the 2,1 norm regular term,and gives an optimization process based on the projection gradient update rule.The proposed algorithm is compared with various clustering algorithms,and the experimental results verify the effectiveness of the proposed algorithm.(2)The traditional non-negative matrix factorization algorithm uses a simple and intuitive linear representation model,and problems in the real world almost always involve data that does not meet the linear hypothesis,which leads to the linear model being unable to effectively express various real data sets.Existing algorithms have proposed solutions to this problem from multiple angles.This paper proposes a novel method to solve this problem.In the process of incorporating the "self-expressive" feature into the non-negative matrix factorization learning basis vector group,a non-linear non-negative matrix factorization algorithm is proposed.Matrix decomposition algorithms and the optimization process based on the projection gradient update rule are given.The proposed algorithm is compared with multiple clustering algorithms on multiple sets of data sets.Experimental results show that the proposed algorithm performs better than some algorithms with good convergence.The class-quality method proves the effectiveness of the proposed algorithm.