Study On Nonnegative Matrix Factorization With Sparse Constraint And Its Application

In the Internet plus era,data continues to the explosive growth,and the dimension of data is getting bigger and bigger.How to deal with the massive and high dimension information becomes one of the hot issues in current scientific research.The nonnegative matrix factorization method with sparse constraint not only inherits the nonnegative property of matrix factorization,which has the intuitionistic physical meaning of the decomposition result,but also generates the sparse representation of data,which is convenient for discovering the pattern or feature behind the data and is also convenient for the storage and analysis of data.The sparse nonnegative matrix factorization method has been widely used in these fields such as computer vision,speech recognition,text clustering,network security,biomedical engineering and so on.Especially,it has important theoretical significance and application value in large-scale data processing tasks.This thesis mainly focuses on nonnegative matrix factorization with sparse constraint.The major works are as follows.(1)Convolutive nonnegative matrix factorization based on L1/2 sparse constraintTaking advantages of the L_q norm constraint,a novel convolutive nonnegative matrix factorization algorithm based on L1/n sparse constraint is proposed,where a multiplicative iteration rules is presented to optimizing the solution of the proposed algorithm and the convergence is also analyzed.The proposed method adopts the Euclidean distance as the objective function,combing with the L1/2 sparse constraint.Based on the afore mentioned convolutive nonnegative matrix factorization with L1/2 sparse constraint,a single-channel speech enhancement model is presented,which has obvious advantage in characterizing the correlation of inter-frame and obtaining the sparser representation of the speech signal.In this model,the prior information of noise bases is firstly obtained by decomposing the noise with non-negative matrix factorization.Then,the speech base is separated from noisy speech by the proposed non-negative matrix factorization with L1/2 sparse constraint,which combining with the noise base priori known.The enhanced speech is reconstructed by the speech base and its corresponding coefficient.The experimental results show that,compared with conventional speech enhancement algorithms,the proposed method may obtain the speech base with less noise,and the speech intelligibility of the reconstructed speech is improved.(2)Orthogonal projection nonnegative matrix factorization using alternating direction method of multipliersThis thesis proposed an orthogonal projection nonnegative matrix factorization using alternating direction multipliers.An orthogonal projection nonnegative matrix factorization is that the base matrix is constrained with the orthogonality and projection.The orthogonal projection constraint can decrease correlation between column vectors of base matrices,and obtain sparser bases in the decomposition of data.However,the conventional multiplicative updating rules algorithm has very slow convergence rates.To tackle this issue,we proposed an optimization method based on alternating direction method of multipliers,which has faster and more reliable convergence.Simulation results show that alternating direction method of multipliers outperforms 'the conventional multiplicative updating rule in the aspect of convergence accuracy as well as convergence speed.The performance improves obviously especially in large-scale data processing context.Meanwhile,the experimental results of object tracking show that the frame processing speed improves significantly,and the obtained sparse object templates also deal with the residual noise effectively.