Research On Manifold Learning Algorithm Based On Tensor Analysis

With the development of machine learning,manifold learning has become a hot topic.Manifold learning is machine learning directed to a dataset,each data point of the dataset can have multiple attribute values,each data point can be seen as a vector.Previous studies indicate that the data in a dataset can be considered as a point in Euclidean space,and for the study of high-dimensional space,there is a certain degree of difficulty of theoretical and computational complexity,so we need to analyze the data after a manipulate of dimensionality reduction of the high dimensional data.Most of the existing research methods have matrixed high-dimensional data and performed corresponding operations such as singular value decomposition on the matrix.Then use the common dimensionality reduction and classification algorithms such as principal component analysis(PCA)and linear discriminant analysis(LDA)to extract and classify them.However,due to the high data dimension and large scale,matrixing of the original data often leads to a large increasing in computational complexity,which affects the execution efficiency of the algorithm.In addition,matrixing of the original data destroys the internal structure of the original data and loses a lot of data information.In recent years,the research on high-dimensional data as tensor has been gradually increased.The tensor type data can well preserve the structural information in the original data,and does not need to directly operate the high-dimensional matrix after the matrixing of the original data.This greatly reduces the amount of calculation,reduces the complexity of the algorithm,and improves the efficiency of the algorithm.Classical tensor-based algorithms include multilinear principal component analysis(MPCA),multilinear discriminant analysis(MDA),and generalized tensor discriminant analysis(GTDA).Inspired by the idea of combining the characteristics of PCA and LDA in the vector algorithm for data feature extraction and classification,this paper uses the tensor analysis method to combine the multilinear versions of the two algorithms,considering that the MDA algorithm does not have good convergence.Therefore,this paper studies the feature extraction and classification methods of fused MPCA and GTDA.The method first maximizes the variance of each mode expansion matrix of the tensor data to achieve the purpose of feature extraction using MPCA,and then maximizes the total scatter of each mode expansion matrix to achieve the purpose of classification by GTDA.Firstly,the principle and flow of the algorithm are studied,and then the initial conditions,termination conditions and convergence of the algorithm are analyzed.