Theoretical Research On Semi-supervised Preference Learning

Preference learning,which is widely used in data mining and machine learning,is to obtain potential features through matrix decomposition.For data sets without any negative terms,non-negative matrix factorization(NMF)multiplies two non-negative matrices to find low-rank approximations.In recent years,many regularized NMFs have been proposed,but there are still some problems.Firstly,due to noise and outliers in some data,the traditional method is easy to generate the objective function with large error.Second,when the graph regularization constraint is added,the neighbor relation of the similarity matrix is determined.Once the calculation error will lead to the low quality of the constructed graph,which will affect the performance of the results.Thirdly,the traditional methods do not make full use of label information to guide the construction of similarity matrix.Based on the above mentioned problems,a preference learning algorithm with l_2,1norm,l₁norm and adaptive graph regularization is proposed for clustering,and then semi-supervised information is added to guide the construction of similarity matrix.The specific work of this article is as follows:First of all,most of the data have noise and outliers,which contain errors when entering the objective function.Therefore,it is easy to have a few noise and outliers with large errors to control the objective function.In this article,a preference learning algorithm with Laplacian regularization is proposed.The low rank decomposition of matrix is used to obtain the potential preference features,so as to realize the preference learning.The graph regularization is added to improve the clustering accuracy,and the objective function is adjusted by l_2,1norm,so as to solve the outlier problem.The l₁norm is used to solve the sparse noise problem.Experiments on several commonly used clustering data sets show that the proposed method is superior to some classical clustering methods.Secondly,the graph-based clustering method divides the data samples into disjoint groups by using similar graphs that describe the data relationships.If similar graphs are constructed in advance,once errors occur,they cannot be changed,which will lead to low quality of the graphs constructed.In this article,a preference learning model with adaptive graph regularization is proposed.Since the l₁norm and l_2,1norm are introduced,the l₁norm can not only solve the sparse noise problem but also solve the outlier problem.More important,the adaptive graph regularization is introduced to improve the clustering performance based on the previous work.Experimental results on 14 datasets for four application scenarios,such as face image,handwriting recognition,UCI and biology,illustrate the superiority of the proposed method over seven existing classical clustering methods.Experimental results showed that better clustering performance was achieved in ACC and Purity.Finally,a semi-supervised preference learning algorithm based on Gaussian field and harmonic function is proposed to solve the problem that traditional clustering does not use label information to guide the construction of similarity matrix.On the basis of the previous work is insensitive to data noise and outliers and the addition of adaptive graph regularization improves the clustering performance,the proposed method uses Gaussian field and harmonic function method to introduce supervised information to construct similarity matrix to realize semi-supervised learning.In order to solve the optimization goal of clustering problem,an iterative updating algorithm called Aug-mented Lagrangian Method(ALM)was proposed to update the optimization variables respectively.The experimental results on 4 datasets show that the proposed method is superior to 7 classical clustering methods,and the clustering performance is better.In summary,the introduction of label information and adaptive graph regular-ization semi-supervised clustering is not only insensitive to noise and outliers,but also greatly improves the clustering results.Compared with the previous two algo-rithms based on graph Laplacian regularization and adaptive graph regularization,the semi-supervised clustering algorithm with label information and adaptive graph regularization is better.