The Research Of Probabilistic Rank-one Discriminant Analysis

With the advent of the era of big data,the massive amount of high-dimensional data brings challenge for data analysis,and how to extract low-dimensional effective data from high-dimensional data is an important research in the field of machine learning.Linear discriminant analysis(LDA)is widely used in classification applications as a reduced-dimensional subspace learning method.Its probabilistic model,probabilistic linear discriminant analysis(PLDA)takes into account the uncertainty of data and individual-specific variations within a probabilistic framework,which enables PLDA to extract discriminant features that may be missed in traditional LDA algorithms.In the research area of 2D probabilistic LDA algorithms,the probabilistic rank one discriminant analysis algorithm(PRODA)retains the advantages of probabilistic models while being able to exploit the structural relationships of 2D data,and thus can be better applied to 2D information data.However,the PRODA model noise is assumed to obey the matrix normal distribution,which makes the PRODA algorithm sensitive to outliers.Therefore,in order to make the algorithm robust to outliers,in this paper,we combine the L1 parametrization with the PRODA model,propose the L1-PRODA algorithm,and use the variational Bayes EM algorithm(VBEM)to estimate the model parameters.Numerical examples based on the artificially generated data set,face database ORL,JAFFE,object image database COIL-20,ETH-80,image database MNIST for handwritten figures,and ballet movement database to demonstrates the advantages of L1-PRODA algorithm in the accuracy of parameter estimations,image recognition,and outlier detection.In this paper,we also propose an extension method based on the PRODA model by replacing individual parameters in the model with individual parameters of each class separately and introducing individual rank factor matrix of each class separately to construct an improved PRODA algorithm(I-PRODA).Compared with the traditional PRODA algorithm,the I-PRODA algorithm is more suitable for image recognition with large intra-class variance.Finally,it is shown by numerical examples based on the artificial data and real dataset JAFFE that the I-PRODA algorithm has better classification results and higher recognition rates on datasets with large intra-class variance.