Multimedia Analysis Based On Manifold Learning

In recent years,multimedia analysis has attracted considerable interests.Multimedia data is often very high dimensional,which has brought many challenges.A common way to solve these problems is to adopt dimensionality reduction methods.So far,an enormous volume of literature has been devoted to investigate various data-dependent dimensionality reduction methods.Manifold learning has received sufficient attention in the field of dimen-sionality reduction.Locality Preserving Projections(LPP)and Neighborhood Preserving Embedding(NPE)are two classical manifold learning algorithms.They have been widely obtained in many fields.This paper aims to do a further research and discussion.The main contents are as follows:(1)We notice that in LPP the low-dimensional representation F is constrained to be in the linear subspace spanned by the matrix X(i.e.,F=W~TX).But,this type of constraint may lead to overfitting and unstability.LPP uses local structure information of the data to reduce the dimension and insufficiently considers the global information of the data.To solve these problems,Ratio Trace based Flexible LPP(RT-FLPP)is proposed in this paper.In RT-FLPP,a flexible regularizerW~TX-F_F~2which models the regression residual is introduced into the reformulated objective function.RT-FLPP also considers the global information of the data.Finally,the effectiveness of the RT-FLPP algorithm was verified through simulation experiments on seven multimedia databases.(2)NPE is another classic algorithm that uses the local structure information of data to reduce dimension.NPE limits the low-dimensional representation(i.e.,F)to the linear sub-space spanned by the matrix X by using a hard constraint(i.e.,F=W~TX),which may lead to overfitting and unstability.Inspired by RT-FLPP,We introduce a flexible regulariza-tion term(i.e.,W~TX-F_F~2)into the reformulated objective function and propose Ratio Trace based Flexible NPE(RT-FNPE)in the paper?Finally,the experimental results of sev-en databases verify the effectiveness of the RT-FNPE.