Time Series Classification With Topological Data Analysis

There have been many applications of time series classification and in this paper,time series data are classified through topological data analysis.Time series data are first transformed into data point through Taken’s Time Delay Embedding and the topological structure of data are demonstrated by persistence diagram,persistence landscape and persistence image.Several variables are built to describe the data structure.The difference of topological structures between the two classes are described and persistence image is used to extract topological information.TSNE and UMAP are applied to visualize the classification and the models are also built on the combined data by concatenating the raw data and persistence image data.The data are better classified when using the combined data on t-SNE and furthermore several machine learning and deep learning methods are compared in detail when built on the raw data,topological data and the combined dataset.KNearest Neighbor,Random Forest,Convolutional Neural Network(CNN)and Recurrent Neural Network(RNN)are built on six data sets from the UCR Time Series Archive.It is shown that the models have a better performance on the raw data than on the persistence image data.The combined data cannot provide more information to improve the accuracy of classification.In deep learning methods,CNN is better than RNN but is worse than the machine learning methods.The MultiChannel Neural Network is proposed to combine the information from the raw data and the topological information.The proposed models perform well on time series classification tasks.In conclusion,a new pipeline is proposed for time series classification;the performance of several models are compared on the raw data,topological data and the combined data;a multi-channel neural network model is proposed,which improved the accuracy of classification.