The Research On Gaussian Bayesian Classification Algorithm For Shrinking Estimate Covariance Matrix

Genes,texts,etc.belong to high-dimensional data sets,and data attributes are often associated with each other.It is more difficult to classify such data.Naive Bayes is a classic classification algorithm,but it is based on the theoretical assumption of "data attribute independence".It cannot correctly describe the relationship between attributes,and it is difficult to effectively process high-dimensional data.Gaussian Bayesian classification algorithm introduces covariance matrix to describe the relationship between data attributes,but the traditional covariance matrix calculation method has large error,which makes the classification accuracy of Gaussian Bayesian classification algorithm difficult to further improve.To solve the above problems,this paper presents a Gaussian Bayesian algorithm for shrinkage estimation covariance matrix.The main research contents are as follows:(1)In the Gaussian Bayesian algorithm,the accurate estimation of the three parameters of the prior probability,the mean vector and the covariance matrix directly affects the classification accuracy of the algorithm.In this paper,we use the James-Stein regularization theory to shrinking estimate of the prior probability and the mean vector respectively,and reduce the calculation error.(2)In order to solve the problem of large error in the traditional covariance matrix calculation method,this paper proposes the idea of shrinkage estimation for covariance matrix to equalize the variance and bias,and then reduce the mean square error of the covariance matrix and improve the classification accuracy of the algorithm.(3)In this paper,a natural approach iterative shrinkage estimator OAS is proposed,which uses an iterative approximation method to converge to the optimal shrinkage estimate.Unlike the shrinkage estimator that artificially imposes constraints,the iterative shrinkage estimator has a natural convergent closed-form expression with smaller mean square error.The error of the covariance matrix calculation method can be minimized,and the algorithm classification effect is further improved.The simulation experiments are carried out on UCI datasets with different dimensions and compared with the traditional Bayesian algorithm.The experimental results show that the classification accuracy of the improved algorithm is better than that of the comparison algorithm on the high-dimensional dataset.The method of shrinking the estimated covariance matrix improves the Gaussian Bayesian algorithm and improves its classification accuracy for high-dimensional data sets.