Classification Of Linear Mixed Data With Stationary And Non-stationary Features

Classification refers to the process of learning,based on characteristics of several training examples,a prediction rule to map observations with unknown class labels into a given category.It has been widely utilized in many research areas,including pattern recognition,statistics,databases and blind source separation.According to the stationarity of data,multidimensional data can be mainly divided into three parts: stationary data,non-stationary data and the mixed data,where the data can be mixed in a linear way or a nonlinear way.With the deepgoing study of the blind source separation,the separation technology of mixed data has made a large improvement and the study on classification of mixed data has received increasing attention.At present,the study on classification of linear mixed data with stationary and non-stationary features still remains largely unexplored.With this context,this thesis studies the classification for linear mixed data with stationary and non-stationary features.The main contributions are listed as follows.Firstly,a classification method based on stationary subspace analysis(SSA)and relative entropy(namely,KL divergence)for the linear mixed data with stationary and non-stationary features is proposed,which is abbreviated as the SSA-KL method.The main idea is to use SSA method to reduce the dimension for both the training and test sets,and use the nearest neighbor method,based on the relative entropy in low dimensional space,to classify data.More accurate classification results are derived with an extraction of stationary features from all samples in each class.Secondly,the classification error rate is employed as an index to measure the effect of SSA-KL classification.For binary classification problems,Matlab numerical simulations are performed to explore factors affecting the classification efficiency of SSA-KL in low dimensional space.The results show that(1)For the case with identical mixed matrix and a fixed training sample size,the classification error rate would decrease when the distance between the stationary source of the positive and negative class increases,and vice versa;the stationary sources have a greater impact on SSA-KL method when compared with the non-stationary sources;distinct non-stationary sources can improve the accuracy when the stationary sources of the positive and negative class have similar distributions.(2)When the mixed matrix and the non-stationary sources for positive and negative class are the same,the proposed SSA-KL method can get reasonable classification result with fewer training samples.At the end,the comparison among SSA-KL method,dynamic time warping(DTW),principal component analysis(PCA)coupled with Euclid distance(ED)-based method,and independent component analysis(ICA)coupled with support vector machine(SVM)-based method are carried out to demonstrate the classification effectiveness of the proposed method.The results show that(1)Compared with DTW,SSA-KL outperforms DTW in attaining a higher classification accuracy with a cheaper computation cost.(2)Compared with PCA-ED and ICA-SVM,SSA-KL method achieves a good classification result in multi-class classification problem with a lowest computation cost.