Classification of Stochastic Processes with Topological Data Analysis

We used the raw, statistical and the topological features to classify time series sampled from different stochastic processes. In our simulation experiments we sampled times series from Wiener and Cauchy processes in both balanced and unbalanced sampling schemes. We then compared machine learning classification models built on topological features and statistical features we engineered on the sampled time series. The results show that the engineered topological features perform consistently better than statistical or raw features in building machine learning classification models even when a given dataset is unbalanced. Our experimental result show that the topologically engineered features alone can distinguish between different stochastic processes, even when statistical or raw features do not.