Research On P-Laplacian Algorithms For Image Recognition

With the rapid development of Internet technology and smart devices,billions of images or videos are uploaded and downloaded to social media platform such as You Tube,Facebook and Instagram everyday.These multimedia data help developing innovative machine learning algorithms.However,because annotating images is costly and time consuming,a small number of labeled samples are available in practical applications whereas a lot of unlabeled samples are easy to collect.Semi-supervised learning(SSL)which can make use of labeled and unlabeled data has been investigated to solve this problem.One successful work is manifold regularization(MR),which has attracted considerable attention because it successfully explores and exploits the local structure of data distribution.Although there are many representative works in MRSSL,including Laplacian regularization(Lap R)and Hessian regularization(Hes R),how to explore and exploit the local geometry of data manifold is still a challenging problem.Based on the in-depth study of the MR algorithm,the main contribution of this paper are as follows:1.A p-Laplcian regularized method(p Lap R)is proposed.As a nonlinear generalization of graph Laplacian,the p-Laplacian provides convincing theoretical evidence to better preserve the local structure.In this paper,we introduce a fully efficient approximation algorithm of graph p-Laplacian,and apply p Lap R to support vector machines(SVM)and kernel least squares(KLS).Extensive experiments on the Scene 67 dataset,Scene 15 dataset,and UC-Merced dataset validate the effectiveness of p Lap R in comparison to the conventional manifold regularization methods including Lap R and Hes R.2.A Hypergraph p-Laplcian regularized method(Hp Lap R)is proposed.In particular,Hypergraph is a generalization of a standard graph while p-Laplacian is a nonlinear generalization of the standard graph Laplacian.The hypergraph and p-Laplacian both show advantages in local structure preserving.The proposed Hp Lap R shows great potential to exploit the local structures than p Lap R.Applying Hp Lap R to logistic regression for remote sensing image recognition,the experiments demonstrate that the proposed Hp Lap R has superior performance in image recognition.3.An ensemble p-Laplcian regularized method(Ep Lap R)is proposed.In practical,it is difficult to determine the fitting graph p-Lapalcian i.e.the parameter which is a critical factor for the performance of graph p-Laplacian.Unfortunately,it cannot define an objective function to choose graph hyperparameters for intrinsic manifold estimation.Ep Lap R incorporates multiple graphs into a regularization term in order to sufficiently explore the complementation of graph p-Laplacian.Extensive experiments on UC-Merced data set demonstrate the effectiveness and efficiency of the proposed method.4.A multiview p-Laplacian regularized method(mpLapR)is proposed.Images usually can be represented by multiple views,such as shape,color and texture.In this paper,multiview p-Laplacian regularization is proposed to obtain the complete representation of the local geometry of the data distribution.Especially,mpLapR optimally combines multiple graph p-Laplacian,each of which is obtained from a particular view of instances.Extensive experiments validate the effectiveness of mpLapR in image recognition.