Robust Dimensionality Reduction Methods On Image Data With Outliers

The current methods for image processing are almost vector representation for image data.However,this representation of image data not only destroys the internal structure information,but also may cause the dimension disaster because of the high dimension,and then increases the cost of storage and transmission,even more makes the efficiency of the algorithms dramatically decrease.Thus,how to reduce the dimension of image data and get more effective information has always been a concern.PLDA and LPP are two of famous dimensionality reduction methods,they use squared L2 norm when measuring the errors and get good results on image with Gaussian distribution noise.However,the noise in real-life image data is complex,in some cases the squared L2 norm will be abnormal.For example,when there is outlier in image,the squared L2 norm will extremely exaggerate the function of outlier,the trained projection direction is biased toward to outlier,which is not conducive to learn the correct projection matrix.In order to deal with the problem that squared L2 norm is sensitive to outliers,this paper improves the two algorithms form the following points: 1)L1 norm is more stable than L2 norm when processes outliers,so proposes the L1 norm PLDA mothed to avoid the outlier is enlarged by squared L2 norm and learn a robust projection matrix.2)In order to avoid the problem that data quantization destroys space structure,2DPLDA based on L1 norm is proposed.3)For the LPP method,F norm is more robust to outliers than squared L2 norm,we propose F norm LPP method and extend it to the two-dimensional data.Specifically,the main work of this paper includes the followings:(1)Aiming at dealing with the problem that dimensionality reduction method based on squared L2 norm is sensitive to outliers,we propose probabilistic linear discriminant analysis based on L1-norm method,termed as L1-PLDA.L1-PLDA is a linear probabilistic model,in which the input data is considered as random variable and generalized by latent variables and noise.In this model,we assume the noise following Laplacian distribution whose density function measured by L1 norm,which is robust to outliers.Due to the non-differentiable of L1 norm,we extend the Laplacian distribution into the summation of infinity Gaussian distribution and use variational EM algorithm to solve its variables and parameters.We do experiments about outlier detection,position detection of outliers and classification on several public databases and get good results.(2)Aiming at the problem that input data is vector representation,we extend L1-PLDA and propose two dimensional probabilistic linear discriminant analysis based on L1 norm,namely L1-2DPLDA.In the case of matrix variate,we give the assumption of variables and the solutions.L1-2DPLDA is a bilateral dimensionality reduction method to matrix variate data,which avoids destroying the structure information.In the training process,the parameters if projection matrix is reduced and the training speed improves due to taking use of the representation of matrix variate.Not only L1-PLDA model can use the information of structure,but also it is robust to outliers by using the L1 norm noise.We do reconstruction experiment and classification experiment to validate this model.(3)Aiming at nonlinear data robust dimensionality reduction,we propose locality preserving projection based on F norm,termed as F-LPP.LPP method is a linear approximation to the nonlinear data,which preserves the image's manifold information.In order to robust to outliers,we improve LPP and propose F-LPP.In order to solve the F norm objective function,we use alternative iterative method.To avoid destroying the space information,we extend the vector based F-LPP to matrix based method,F-2DLPP.We do robust detection experiments and classification experiment to test the F norm methods on public databases.