Canonical Correlation Analysis Algorithm And Its Application Based On Domain Adaptation

Canonical Correlation Analysis(CCA)is a multivariate statistical analysis method that uses the correlation between two sets of random variables to reflect the overall correlation between variables.It is also a multivariate data processing method with great research value.However,the traditional CCA is an unsupervised dimensionality reduction method,and has weak processing capabilities for classified data.In order to solve these problems,this paper combines Canonical Correlation Analysis(CCA),Domain Adaptation(DA)and other methods to propose two canonical correlation analysis algorithms based on domain adaptation.Then we use these algorithms to design a positioning algorithm for Wireless Sensor Network(WSN).First of all,this paper summarizes and analyzes three algorithms of Canonical Correlation Analysis(CCA),Linear Discriminant Analysis(LDA)and Domain Adaptation(DA),and explains their advantages and disadvantages.On the basis of these three algorithms,we came up with an algorithm called Joint Distribution Canonical Correlation Analysis(JDCCA).This algorithm is based on CCA,with LDA and DA added.This algorithm not only keep the characteristics of CCA that can well represent the relationship between two variables,but also introduces the ability of LDA to process labeled data with categorical characteristics.At the same time,we use of the ability to process cross-domain data expands the ability to process different data types of DA.Experiments were performed on multiple data sets to prove that JDCCA has better performance than traditional CCA and DA algorithms.Since the discriminativeness of JDCCA is realized by adding items with inter-class divergence matrix and intra-class divergence matrix,this leads to limitations in the optimization effect,and the effect in some cases is not obvious.Therefore,we proposed a better algorithm called Joint Probability Discriminant Canonical Correlation Analysis(JPDCCA).On the one hand,this algorithm added Discriminant Canonical Correlation Analysis(DCCA)on the basis of JDCCA to enhance the discriminativeness of the objective function.On the other hand,the introduction of JPDA to enhance the distinguishability and transferability of the objective function by maximizing the joint probability distribution difference between different domains and minimizing the joint probability distribution difference of the same domain.Experiments were carried out on multiple data sets to prove that the performance of JPDCCA is better than the comparison algorithm.Positioning algorithm is an important research direction in network planning research.Accurate positioning algorithms are of great significance to network planning.This paper designs a positioning algorithm based on wireless sensor network(WSN),which uses the mapping relationship between Received Signal Strength Information(RSSI)and location data for calculation.The positioning algorithm is based on the JPDCCA algorithm,which can better use the marked information for coordinate positioning.We use actual data to verify the positioning algorithm,this paper analyzes factors affecting the performance of the positioning algorithm,compares the positioning algorithm with other positioning algorithms,which proves the performance improvement of the positioning algorithm.