Research And Application Of Locality Preserving Projections Algorithm Based On Maximum Marginal Criterion

In the context of today's big data era,massive amounts of data information are generated every day.However,most of these data are invalid redundant information.To extract effective information from the cluttered high-dimensional data and analyze the rules of the development of things,data reduction is a necessary and effective method.And manifold learning is a commonly used and effective data dimensionality reduction method in recent years.Classical manifold learning methods include Laplace feature mapping(LE)and local preserving projection(LPP).However,these linearized manifold learning algorithms generally have a small sample problem(SSS),that is,the dimension of the sample is much larger than the number of samples.Recently,another method to solve the problem of small samples is to linearize the matrix exponential dating algorithm.However,the main limitation of the matrix index method is that the time complexity of the algorithm is too large,because the computational complexity of the matrix index function is huge.On the one hand,for the LPP method,it is necessary to first construct a local topology graph,and it is difficult to determine an appropriate local neighborhood size.So,when the neighborhood size changes,the performance variable of the LPP method.In this paper,based on the results of the ELPP method,this paper can approximate the LPP method to a simple standard eigenvalue problem through matrix transformation and approximate replacement of the matrix index.In order to solve the small sample problem of LPP,this paper combines the idea of the maximum marginal criterion(MMC)algorithm and uses the characteristics of the maximum marginal criterion and matrix index to avoid the existence of a singular matrix when solving the characteristic equation,thereby solving the small sample problem.And then we called the new method as Locality Preserving Projections under Approximate Maximum Marginal Criterion(LPPMMC).In order to verify the performance of the algorithm,a detailed and rigorous comparative experiment is set up in this paper.The experiments are performed on the three public face databases: ORL,Georgia Tech and FERET.The results show that the performance of LPPMMC method is better than that of the existing methods for solving the Small sample problem of LPP,and the performance of LPPMMC method is stable when the neighborhood size parameter k varies.Compared with the state-of-the-art approaches to address the Small sample problem of LPP,LPPMMC has no the Small sample problem,and insensitive to the neighborhood parameter k,in addition,the algorithm is robust and has a high recognition rate.Finally,based on the maximum marginal criterion local maintenance projection algorithm proposed in this paper,a set of face comparison and recognition system is designed.This system is suitable for face comparison and recognition of small-scale sample data such as laboratory access control and company attendance.