We are investigating the evolution of four big US stock market indexes' regular returns after 2000 technology crash and 2007-2009 financial crisis. Our approach is based on topological data processing (TDA). To identify measure phenomena occurring in multidimensional time series, we use persistence homology. obtain time-dependent point cloud sets using a sliding window, which connect space for....

Topological data analysis has been acknowledged as one of the most successful mathematical analytic methodologies in various fields including medicine, genetics, and image analysis. In this paper we explore potential methodology finance by applying persistence landscape dynamic time series to analyze an extreme event stock market, known Flash Crash . We will provide results our empirical invest...

In this study, we examine if engineered topological features can distinguish time series sampled from different stochastic processes with noise characteristics, in both balanced and unbalanced sampling schemes. We compare our classification results against the of same tasks built on statistical raw features. conclude that series, machine learning models perform consistently better than those st...

We have performed preliminary work on topological analysis of audio and text data for unsupervised speech processing. The assumes that phoneme frequencies contextual relationships are similar in the acoustic domains same language. Accordingly, this allowed creation a mapping between these spaces considers their geometric structure. As first step, generative methods based variational autoencoder...