Deep Semisupervised Nonnegative Matrix Factorization Model And Its Applications

Nonnegative matrix factorization(NMF)is an unsupervised feature learning method,which does not depend on the label information of the data and can achieve nonlinear dimension reduction.NMF-based feature learning methods are widely used in the field of image processing and pattern recognition.However,the traditional NMF approach contains the following weaknesses: To begin with,NMF,as an unsupervised feature learning method,cannot make use of the label information of the data.Secondly,as a shallow model,the NMF model is susceptible to the influence of the initial values and is unable to mine the deep features hidden in the data.Thirdly,the NMF model ignores the geometric structure information of the data.Therefore,in order to solve the above weaknesses,two deep semisupervised nonnegative matrix factorization models are constructed in this paper.And the main work is summarized as follows:Firstly,a label consistency-based deep semisupervised nonnegative matrix factorization(LC-DNMF)model is proposed.The LC-DNMF model considers constructing a joint label matrix by using the label information of the labeled samples,which makes an explicit correspondence between the labeled samples and the base matrix,and obtains the discriminant codes of the labeled samples.By introducing label consistency regularization constructed with the joint label matrix,the LC-DNMF model enables data from the same class to have similar representations and discriminative features are learned.In addition,the LC-DNMF model considers introducing layer-by-layer pretraining and multilayer representation strategies of deep learning,which can effectively alleviate the problem of initial value sensitivity and mine the deep features hidden in the data so that the model is more robust.Then,the gradient descent method is used to solve the LC-DNMF model.Furthermore,for the solution algorithm of the model,the convergence theorem and its proof are given,and its complexity is analyzed in this paper.Secondly,a deep semisupervised nonnegative matrix factorization model with fused graph structure(FGLC-DNMF)is proposed.The FGLC-DNMF model further considers the geometric structure information between data based on the LC-DNMF model and introduces graph regularization that fuses discriminative information.The FGLC-DNMF model can promote samples of the same category to be as close as possible and samples of different categories to be as far away as possible,which further improves the feature learning ability of the LC-DNMF model.Similarly,the gradient descent method is used to solve the FGLC-DNMF model in this paper,and the convergence proof and complexity analysis of the solution algorithm are given.Finally,the LC-DNMF model and FGLC-DNMF model in this paper are combined with classifiers to formulate a tumor recognition algorithm,and it is applied to gene expression profile data for tumor recognition.By comparing it with different feature learning methods and classification methods,it is found that the feature learning model in this paper can learn more discriminative and compact features,which results in higher recognition accuracy of the tumor recognition algorithm.