A Hybrid Metric based on Persistent Homology and its Application to Signal Classification

Topological Data Analysis (TDA) is a rising field in machine learning. TDA seeks to extract information about the shape of a data set by examining its topological and geometric properties. Persistence diagrams, one of main tools in TDA, store topological information about the data. Persistence curves, a recently developed framework, provides a canonical and flexible way to encode the information presented in persistence diagrams into vectors. Based on persistence curves, the main contributions of this work are to (1) provide new sets of features for time series, (2) prove that these features are robust to noise, (3) propose a hybrid metric that takes both geometric and topological information of the time series into account. Finally, we apply these metrics to all the datasets in the UCR Time Series Classification Archive. Empirical results show that the proposed metrics perform better than the relevant benchmark in most cases.