Research On Dimension Reduction Algorithm Based On Adaptive Weighted Multiclass Linear Discriminant Analysis

With the develop of the information technology,more and more applications will collect and use a large number of high-dimensional data to solve some problems.The higher the dimension of the data,the greater the amount of information contained,which makes it easier to use and mine data.But at the same time,the high dimensional feature space will bring inconvenience to the data processing,such as the complexity of calculation,the increase of memory,and so on,and even the information redundancy will make the experimental result unsatisfactory.To deal with the problems brought by this "curse of dimensionality",the dimension reduction algorithm becomes more and more important.The dimension reduction algorithm is a very classic machine learning methods which can reduce the high dimensional data into lower dimensional data.The data obtained by this method not only retains the main feature information in the lower dimensional space,but also eliminates the redundant information and improves the data validity.The traditional methods are linearly discriminant analysis(LDA)and principal component analysis(PCA).These classical methods have been researched continuously and researchers are committed to find their shortcomings to propose new ideas for improvement.In this paper,we focus on the defect of LDA algorithm and do some research and improvement on the problem of multiclass dimensionality reduction.The objective function of the LDA algorithm is too dependent on the distance of large distances,so that the small distances will be neglected,resulting in an overlap between the two classes in the projection space.The algorithms of this paper mainly solve this kind of problem.The main contributions of this paper are as follows:(1)In this paper,we propose an adaptive weighted multiclass linear discriminant analysis algorithm based on Cauchy inequality.Our method utilize the measurement of the pairwise distance based on the traditional linear discriminant analysis algorithm.We use the adaptive weighted method to solve the overlapping problem in multiclass of LDA method.(2)In this paper,we propose an adaptive weighted multiclass linear discriminant analysis algorithm based on the probability matrix.The method calculates the between-class scatter matrix and the within-class scatter matrix separately for each pairwise,and weights the probability parameters for each pairwise.The distances of each pairwise in the projection space are as equal as possible by adaptive weighting.Our method increase the regularization term as a cost function and through the parameter adjustment,it makes the model better than the method of adaptive weighted multiclass linear discriminant analysis algorithm based on Cauchy inequality.