Research On Linear Discriminant Analysis Based On Discriminant Criterion Optimization

Linear Discriminant Analysis(LDA)is one of the main methods of feature extraction.LDA achieves the compression of feature space's dimension and the extraction of classification features by mapping the high-dimensional pattern samples into the low-dimensional space with the best discriminating ability,so that the distance between classes is the largest and the intra-class distance is the smallest.The pattern has the best separability in this feature space.Traditional LDA algorithm has some problems such as the small sample problem,low separation accuracy and so on.To meet the demand of a wide range of practical applications,algorithm optimization research of LDA becomes attractive and far-reaching.Aiming at the problems above,the following work was done based on the previous research:1.Theoretical summary research of LDA.Firstly,the principle of LDA and deduction processare introduced and extended to multiple problems.The advantages and disadvantages of LDA are analyzed.The improved LDA algorithm,which is not easily separated from the similarity problem,is the research point of this paper.2.Optimization of LDA based on Fisher criterion.In order to avoid the separation problem,we use the Close function to adjust the weight of the distance between classes,redefine the inter-class scatter matrix,and improve the original Fisher criterion so that the classes with similar average are better separated and the phenomenon of overlap or crossover between classes will be improved,and through this way we improve the classification performance after dimension reduction.3.Simulation experiments were conducted for the comparison of different algorithms'performance.In this paper,we do the the experiment of algorithm testing and ECG identification with different algorithms.The improved LDA algorithm based on Close function can give a approach of solving the problem of the similar classes and it is helpful to improve the recognition rate.a It is demonstrated by the experiments that the algorithm has a good performance.4.Discussion on the integration method.The small sample problem in LDA is pointed out and the algorithm based on maximum scatter difference(MSLDA)discriminant analysis is analyzed and studied.The optimized LDA algorithm and MSLDA algorithm are integration.ECG identification experiments show that the integrated method combines the advantages and effective.