Transfer Learning Method For Fisher Discriminant Analysis

The fisher discriminant analysis classification problem is a supervised learning problem with insufficient learning samples.From the perspective of implementation,it can be considered as mapping data samples in high-dimensional space to a lowdimensional feature space through a nonlinear mapping function.In other words,the linear discriminant analysis classification can be considered as extracting features of data samples from low-dimensional feature spaces,and classifying the features and separating them from different categories of data samples.Linear discriminant analysis has a wide range of applications in feature extraction and classification.In this paper,we propose a new method called migration learning method called linear discriminant analysis,which can transfer the knowledge and information learned from the source domain task from the source task to the target task,and is the target task.Establish an FDA model to help classify data samples for target domain tasks.The advantage of a non-linear mapping function approach is that they can solve problems with different FDA data dimensions,different data sample distributions,and different structures in the case of nonlinear data.The function map we consider determines the projection direction and uses this projection direction to map the data set to the most separate hyperplane of the data in the feature space.We propose a method in two steps.In the first step,we take the data samples of the source and target domains as a whole,and then put the source domain data and the target task into the feature space through the mapping function.Then,we build an FDA model based on migration learning for the target task.In the second step,we optimize the proposed migration learning model to obtain the optimal projection plane and separate the data samples of the target domain.The main contributions of this paper can be summarized as follows:1.We map the source domain data samples to a feature space clock through a nonlinear mapping function,and we can get the best projection direction according to the FDA's discriminant criteria.In addition,we constructed a basic model of linear discriminant based on migration learning.2.In the mapping space,we calculate the mean and dispersion within the class and between the classes of the data samples to get the best projection direction of the source domain.Through calculation,we found the best projection direction of the source and target domains.Finally,we calculate the optimal projection direction of the target domain by introducing the Lagrangian multiplier.3.We conducted extensive experiments to study the performance of our proposed TL-FDA method.We conducted experiments on three data sets,20 Newsgroups,Reuters-21578 and Cora,using the three most classic classification methods in machine learning,such as decision trees,neural networks and support vector machines(SVM).The method was compared with nuclear principal component analysis(KPCA),nuclear linear discriminant analysis(KLDA),local linear embedding(LLE)and isometric feature mapping(ISOMAP).The results showed that TL-FDA performed better than the classical feature extraction method.