Study On The Theory And Application Of Graphical Lasso And The Related Methods

The feature dimension is often greater than the number of samples in practical applications, the traditional methods can not calculate the inverse of covariance matrix of data. For high-dimensional data, even if the covariance matrix is not a singular matrix, using the traditional methods to estimate the inverse of covariance matrix will be a very complex calculation. Meanwhile, we estimate the undirected graph model to the high-dimensional data meaningfully only when the inverse of covariance matrix is sparse, otherwise we will not be able to analyze a complex model. Graphical lasso can estimate the inverse of covariance matrix fast, the penalty parameter can control the sparsity of the inverse of the covariance matrix, the computing speed is also fast to high-dimensional data.Firstly, this paper expounds the basic principle and procedure of graphical lasso and introduces the theory of graphical lasso applied to the quadratic discriminant analysis, we verify the performance of graphical lasso through the simulation experiments and apply the graphical lasso to estimate the undirected graph model of flow cytometry data and analyze the experimental results, we also apply the graphical lasso quadratic discriminant analysis to the Semeion handwritten digital data set and the accuracy can achieve 92.2%.Secondly, this paper expounds the basic idea of joint graphical lasso and introduces the specific process of using the alternating direction multiplier method to solve the joint graphical lasso problem, including the solving process of two kinds of penalty function, and we apply the joint graphical lasso to the quadratic discriminant analysis, we apply the quadratic discriminant analysis based on graphical lasso and joint graphical lasso to PAMAP2 body activity monitoring data set and the experimental results show that the joint graphical lasso method based on the fusion lasso achieve a better result.Finally, this paper simply introduces the sparse gaussian graphical mixture model and introduces the specific process of the graphical lasso expectation maximization algorithm, we analyze and discuss the performance of sparse gaussian graphical mixture model based on graphical lasso through the simulation, and we apply the sparse gaussian graphical mixture model to the flow cytometry data and analyze and discuss to the experimental results.