An integrated image visibility graph and topological data analysis for extracting time series features

A time series can often be characterized using machine learning techniques, which require feature vectors as input. The quality of the feature vectors reflects the accuracy of the utilized machine learning techniques. We propose a method for combining features extracted from two popular techniques, one from the persistence diagram, a summary of topological data analysis, and another from the visibility graph, a popular approach for constructing complex networks. We further present a method for extracting features from time series by transforming the series into a two-dimensional array and applying a 2-dimensional visibility graph. The 2-dimensional visibility graph improves the quality of the features for clustering. The features extracted from the techniques are utilized for clustering 1100 time series samples simulated from 11 classes. The two clustering quality evaluation metrics namely normalized mutual info score and adjusted rand score, which are scores given to clustering algorithms, are used to measure the clustering quality. Inclusion of 2-dimensional visibility graph features increases the values of these metrics for classifying the time series. Therefore, the results confirm the usefulness of including a 2-dimensional visibility graph from time series clustering and analysis.